Design of a Hydraulic Prosthetic Hand Adding an active thumb to the Delft Cylinder Hand

Transcription

1 Master Thesis Bio Mechanical Engineering Design of a Hydraulic Prosthetic Hand Adding an active thumb to the Delft Cylinder Hand Author: Eric Versluis Supervisors: Dick Plettenburg Gerwin Smit May 3, 2015

2 Summary Body Powered Hand Prostheses provide the user with a replacement for a missing hand. Current body powered hand prostheses are inefficient and require large input forces for the control. Improvements are needed to provide amputees with adequate body powered hand prostheses. The Delft Cylinder Hand, a promising design for an underactuated voluntary closing body powered prosthesis with hydraulic actuation, could be improved further by adding an actively movable thumb. The goal of this research is to increase the grip size of the Delft Cylinder Hand by adding an active thumb. A 1 degree of freedom mechanism is chosen to create a natural looking conical movement of the thumb. A complete design is made for an underactuated hydraulic cylinder hand with moving fingers and a moving thumb. A prototype for this design was made, tested and evaluated on the posed design requirements. The mechanism for the thumb movement adds 24 gram to the weight of the prosthesis. The total weight of the prosthetic hand (176 gram without glove and 241 gram with glove) is still 49 % lower than the lightest available voluntary closing body powered prosthesis. The prototype could grasp objects up to 99 (mm), which is a 32% increase with respect to the current grip size of 75 (mm). For objects with a size above 35 (mm) the mechanical performance is comparable to the current design of the Delft Cylinder Hand. Activation forces of 80 (N) to 90 (N) are needed to apply a pinch force of 15 (N) between the thumb and two fingers. The performance of the prototype without cosmetic glove for grasping small objects is lower than that of the Delft Cylinder Hand. Obtaining a stable pinch grip on small cylindrical objects is difficult because of the uneven movements of the finger phalanges of the prototype without cosmetic glove. Also the pinch forces are lower when grasping small objects compared to the current Delft Cylinder Hand. A pinch force of 5.5 (N) is achieved for an activation force of 100 (N) while grasping an object of 10 (mm) thick compared to a pinch force of 19 (N) with the Delft Cylinder Hand. Adding an actively movable thumb to the Delft Cylinder Hand is a promising improvement. It is possible to obtain an equilibrium between the thumb and the finger phalanges while grasping objects of various sizes with different grip types. The active thumb increases the grip size of the prosthesis. Further research is needed to develop a Delft Cylinder Hand with a movable thumb which meets the performance criteria for a larger range of object sizes. I

3 Preface The moment is there, my graduation project is finished. People close to me know the last year was a struggle for me sometimes. Dividing my time between working at E2m Technologies and the writing of my thesis proved difficult. In between dreaming of the future, going through rehabilitation after surgery and taking up new challenges at E2m Technologies I had to find the focus for this exiting project. I have learned a lot during my research in the field of prosthetics. It is satisfying to be part of a project which will bring adequate replacement for missing hands a step closer. I have come to appreciate this even more during the course of the project. Losing some of the functionality of my right leg because of nerve damage after surgery past Januari, made me (hopefully temporary) dependent on an orthotic device lifting my foot. A simple, comfortable an practically invisible device literally got me up and running again within a month even though I could not control my foot lifting muscles. Knowing first hand the joy and gratitude for having a good assistive device to compensate for a disability, the importance of the research in the field of orthotics and prosthetics became even more clear to me. I would like to express my thanks to everyone for the support during the last year. I would like to thank Dick Plettenburg and Gerwin Smit for the guidance during the project. I want to thank Jan van Frankenhuyzen for his help during the building of the prototype. Thanks to my family and my close friends for being there for me. Special thanks and a lot of love to my girlfriend. I know it was not an easy year. Signe, thank you for your love, support and patience during this whole period! II

4 CONTENTS Contents Summary Preface I II 1 Introduction Background Upper extremity deficiency Body Powered Prostheses Cosmetic gloves Delft Cylinder Hand Adding an actively movable thumb to the Delft Cylinder Hand Problem Definition Goal Method Summary Preliminary Design Challenges when adding an actively movable thumb Design Requirements Defining the desired movements of the prosthesis Hand opening of the prosthesis Weight of the prosthesis Grasping forces Thumb mechanism, the working principle Analysis of the hydraulic hand Grasp Equilibrium Small thumb movements Two Phase Cylinder Change transmission toward end of stroke Create equillibrium using passive components Adding cylinders and phalanges Flow divider Test Plan Free Movement Grasping objects Pinch Tests Pinch Test Pull Test Results Design of the hydraulic hand Finger Design Thumb Mechanism Total design of the hydraulic hand Examining the free movements of the prosthesis Force Measurements Grasping Objects III

5 CONTENTS 4 Discussion Design Free Movements Force Measurements Grasping objects Recommendations Conclusion 36 References 37 Appendices 37 A Analysis 38 A.1 Analysis - Abstract A.2 Analysis - Introduction A.3 Analysis - Problem A.4 Analysis - Method A.4.1 External Forces on the prosthetic hand A.4.2 Assumptions A The volume flow of the hydraulic fluid is divided equally between all hydraulic cylinders A The pressure is equal in all cylinders A.4.3 Glove Compensation A.4.4 Analyse Actuation forces A.4.5 Thumb A Kinematic relations A Static forces relations A.4.6 Fingers A Kinematic relations A Static forces relations A.4.7 Force transmission ratio for the fingers A.4.8 Variables to change Force transmission ratios A Fingers - Variables A Thumb - Variables A.4.9 Variables to change the movements of the hand A.4.10 Combine the models of the Thumb and the hand A.5 Analysis - Results A.5.1 Current Force transmission ratios of the fingers A.5.2 Force transmission ratio of the thumb A.5.3 Grasp forces of the hand A.5.4 Increasing the thumb force A.6 Analysis - Discussion A.7 Analysis - Conclusion B Appendix - Normative values for maximum voluntarily applied grip and pinch forces, a systematic review 54 IV

6 1 Introduction 1.1 Background Upper extremity deficiency The human hand is complex, it consists of 27 bones of which 14 are finger phalanges. Models of the hand assume 21 Degrees Of Freedom (DOF) for the fingers and thumb [1]. In total 35 muscles, located in the palm of the hand and the forearm, are involved in manipulating these DOF s. Figure 1 shows a model for the degrees of freedom of the human hand [1]. The large amount of DOF s and muscles controlling these DOF s provide humans with a large amount of fuctionality of the hand. Upper extremity deficiency can have a great impact on the life of the patient [2]. Daily activities which involve the handling of objects will become a challenge. Upper extremity deficiency can be caused by a congenital limb deficiency or can be the result of an amputation [2]. Prostheses are developed for people with an upper extremity defect. Hand prostheses are available which are meant to replace the human hand. However current prostheses do not have the same complexity as a healthy human hand. It can be argued a prosthesis does not require the same level of complexity as a healthy human hand to be an adequate replacement for it. Given certain tasks of grasping or manipulating objects, often only a few DOF s are needed to perform the task. Also redundancy is present in the movement of a healthy human hand, 35 muscles manipulate 21 DOF s. However this abundance of DOF s and muscles allow humans to do a great variety of tasks with the hands. Decreasing the number of DOF s in a prosthesis will decrease the functionality of the prosthesis. Also the movements of a prosthesis with a low amount of DOF s will look less natural. Figure 1: Model of the degrees of freedom of a Human hand, obtained from [1]. The fingers and thumb have 21 DOF combined, the location and orientation of the hand can be described by 6 DOF. 1

7 Background Figure 2: A body Powered Prosthesis consisting of the shoulder harness, a socket, a Bowden cable and the terminal device. The prosthesis is controlled by changing the length between point A and B. The figure is obtained from [2] Body Powered Prostheses A category of hand prostheses is the Body Powered Hand Prosthesis. The term body powered means the amputee operates the prosthesis providing the power with his own muscles [3, 4]. Body movements manipulate the shoulder harness and are used to open or close the terminal device. Figure 2 shows a Body Powered Prosthesis with a commonly used shoulder harness [2]. The main components of a Body Powered Prosthesis using a shoulder harness are: the shoulder harness, a socket, a Bowden cable and the terminal device. [3, 5] Body powered hand prostheses are most frequently controlled and powered using a shoulder harness. The shoulder harness consists of straps and cables which are placed on the upper torso [5]. Scapular, shoulder and upper arm movements cause the control cable length to change. Many upper torso muscles are involved in these movements and have a contribution during the use of the prosthetic device. Via the harness the muscle forces are transferred to an actuation force and the end effector, the prosthesic hand, will produce a grip force to the grasped object. Figure 3 schematically displays the transmission of the forces when controlling a body powered hand prosthesis. The main advantage of a Body Powered Prosthesis, over externally powered prostheses, is the possibility to obtain proprioceptive feedback while operating the prosthesis [4 6]. The prosthesis becomes a mechanical extension of the human body. Extended physiological proprioception is possible with body powered prostheses because the movements and forces of the prosthesis are related to body movements and forces [6]. Because the amputee uses his muscles to power the prostheses, at all times feedback of the applied input force is present [4 6]. External forces acting on the prosthesis in the direction of the controlled motion are transmitted back to the muscles which operate the device. The users develop an internal model of the prosthetic hand during the learning process. Together with the feedback of the input force this gives a good estimation of the applied force with the prosthesis. The force feedback information is readily available due to the body powered components and is in principal not available in externally powered devices [6]. The 2

8 Background Figure 3: Control scheme of a body powered hand prostheses using a shoulder harness. With the shoulder harness as a control interface the body displacements and muscle forces are related to the prosthesis hand opening and grip forces. Feedback of the hand opening and the grip force are available to the user. The images were adapted from [2] movements of the prosthesis are a direct result of the scapular, shoulder and upper arm movements. Because of this direct relation subconscious position control of the prosthesis is possible. Another advantage is the absence of an external power source and an actuator to provide the force needed when operating the prostheses. This enables a costs and weight reduction and a high reliability can be obtained due to mechanical simplicity. [3, 7] Since the power to operate the prosthesis should be provided by the amputee this directly causes the main disadvantage: operating the device requires the amputee to exert effort when operating the device. The use of the prosthesis can be tiresome, causes fatigue of the muscles and when overloaded, possibly causes injuries [5,8]. Due to the need of a harness, or another device, to transmit the muscle forces the amputee will inevitably be restricted in the range of body motion to a certain extend. Users of Body Powered Prostheses complain the shoulder harness used to control the prosthesis is uncomfortable and restrictive [9]. Body powered hand prostheses can be divided in two sub categories: voluntary opening and voluntary closing devices [2, 3]. Voluntary opening devices are forced in closed position by a passive elastic component. The elastic component also applies the pinch or grasp force. When the amputee applies an input force the prosthesis will open. Decreasing the input force causes the hand to close and apply a pinching or grasping force. [3, 4, 10 12] Voluntary opening hand prostheses will have a reversed force feedback; a decrease on the input force gives an increase in the output force and vice versa. A reversed force feedback might be considered less intuitive by the operator of the prosthesis. Voluntary closing hand prostheses work the other way around. An elastic component forces the hand in open position. Applying an input force causes the prosthesis to close and to apply a grasp or pinch force. The input and output force are positively correlated to each other in the case of a voluntary closing hand prosthesis allowing an intuitive feedback [3, 11]. A voluntary closing device is preferred for control purposes because that concept possesses more feedback paths and allows for easy operation [4, 13]. Figure 4, from Berning et al. (2014) [12], displays the working principles of both voluntary opening and voluntary closing prosthetic hands Cosmetic gloves For the cosmetic appearance of hand prostheses cosmetic gloves are used [2, 3, 14]. The cosmetic glove covers the mechanical parts of the prosthesis and improves the appearance [3]. A poor appearance of the prosthesis is one of the reasons for amputees for dissatisfaction or prosthesis abandonment [9, 11, 15]. Commonly used materials for a cosmetic glove are silicone rubber and PVC [2, 3, 15]. Cosmetic gloves have poor mechanical properties [14]. The high stiffness of the 3

9 Background Figure 4: Working principles of voluntary opening (VO) and voluntary closing (VC) prosthetic hands. VO device on the left (a): Sierra 2-load hook. The hook is forced in closed position by a passive elastic component and opens when an actuation force is applied. VC device on the right (b): APRL VC hook. The hook is forced in open position by a passive elastic component and closes when an actuation force is applied. The figure is adapted from [12] gloves reduce the grasping force which can be achieved with the prosthesis. Also the force feedback the user gets while operating the prosthetic device is reduced because of the high forces needed to deform the cosmetic glove. The highly non-linear elastic behaviour [2, 14] makes it difficult to compensate for the elastic forces the cosmetic glove applies to the prosthesis. Furthermore a high amount of hysteresis is present during the deformation of the cosmetic glove. The forces applied by the glove are non-conservative. Due to the hysteresis the user of the prosthesis has to deliver more energy to operate the prosthesis [2]. No compensation is possible to account for the hysteresis. Part of the hysteresis is the result of friction between the glove and the mechanical parts of the prosthesis Delft Cylinder Hand A promising design for a Body Powered Prosthesis is the Delft Cylinder Hand. The Delft Cylinder Hand makes use of a hydraulic system to transfer the forces within the prosthesis. The fingers are actuated using hydraulic cylinders which are placed in each finger. Hydraulic systems allow efficient transference of the energy needed to operate the prosthesis [16]. It also allows to apply the right amount of amplification of the forces by changing the piston area of the actuators. Figure 5, which was obtained from [2], shows the prosthetic hand. In the current design the thumb is fixed and the fingers move towards the thumb. Each finger has 2 cylinders bending the finger except the little finger, which has one cylinder. The fingers have 7 DOF s in total. The prosthesis has 1 DOF on the input side. This makes it an underactuated prosthetic hand [2]. This way of actuation, an underactuated hand with a hydraulic system, allows a very natural grasping of objects. When an object is grasped, all fingers will make contact with the object before the pressure will build up and the prosthesis will apply a force. For many objects this is the natural way of grasping with a healthy hand. 4

10 Problem Definition Figure 5: The Delft Cylinder Hand. The fingers are actuated by 7 hydraulic cylinders. The hand is an underactuated voluntary closing prosthesis and adapts to the shape of the grasped object. The figure is obtained from [2] Adding an actively movable thumb to the Delft Cylinder Hand In the current design the thumb is fixed. Fingers move toward the thumb to close the hand, the thumb doesn t move. However in healthy hands the thumb takes part of the movement during grasping. Also the thumb adds a great amount of functionality to the hand. The thumb is regarded to be responsible for about 40% to 50% of the hand s usefulness [17]. An actively movable thumb would possibly improve the design. Advantages of an active thumb are: ˆ The grip size of the prosthesis could be increased. The thumb can automatically open up when the pressure is released and close when it is actuated. This will widen the grip to allow the grasping of larger objects. ˆ A moving thumb will result in a more natural grasping movement. Normally the thumb takes part of the movement during grasping. So if the prosthesis can do this as well, it will look more natural. ˆ Possibly an increased number of grip types; grasping, pinching, 3 finger grip. 1.2 Problem Definition The rejection rates for body powered hands are high [8,16,18]. Body powered hands are cosmetically more pleasing but the currently available body powered hands do not meet the requirements of the users [18]. Current body powered hand prostheses are inefficient, require large input forces for the control and are still quite heavy [16]. Patients and professionals working in the field of prosthetics encourage the innovation in Body Powered systems [9]. The Delft Cylinder Hand could be a major step in the development of body powered hand prostheses. In the current design of the Delft Cylinder Hand the thumb is fixed and the fingers move towards the thumb. The fixed thumb limits the grip size of the prosthesis. The current grip size of the prosthetic hand is 75 5

11 Goal (mm). Also a grasping movement with a prosthesis where the thumb does not move looks less natural. It is desired to investigate the possibilities to add a movable thumb to the current design of the Delft Cylinder Hand. This thesis will present the research done to answer the following question: Is adding an active thumb to the Delft Cylinder Hand a feasible option to improve the functionality of the prosthesis? 1.3 Goal The goal of this research is to increase the grip size of the Delft Cylinder Hand by adding an active thumb. A design will be made for a hydraulic cylinder hand with a movable thumb. The prosthesis should have an increased grip size and a more natural grasping movement. The mechanical and functional performance of the prosthetic hand will be evaluated. The mechanical performance will be evaluated by measuring the grip. The functional performance will be evaluated by determining the range of object sizes which could be grasped with the prosthesis. The grip size and the grip force will be compared to the existing design and other available hand prostheses. 6

12 2 Method 2.1 Summary Literature will be searched to determine the desired movements of the thumb. The desired movements will be based on the movements of the thumb of healthy individuals. Design requirements will be composed which the prosthesis will have to meet. A conceptual design will be chosen to accomplish a prosthesis with an actuated thumb. Since the goal is to investigate the possibility of adding a thumb in general, a simple concept will be chosen to evaluate the effects of an active thumb on the rest of the prosthesis. A full analysis will be done on the hand with the mechanism of the the thumb. The analyses will be used to evaluate the chosen concept, check the compliance of the design with the design requirements, foresee possible difficulties and optimize the geometry of the hand for the final design. If the conceptual design meets the requirements the design will be worked out in detail. A prototype will be made to evaluate the design. The prototype will be tested for compliance with the design requirements. Functionality tests will be performed to examine the movements of the prosthesis, examine the grasping performance of the prosthesis and to examine the control of the prosthesis. 2.2 Preliminary Design This section presents the conceptual design chosen for a prosthesis with an actuated thumb. A number of challenges will be encountered when adding an active thumb to the prosthesis. These challenges will be elaborated further in Section The purpose of the design is to prove adding a moving thumb to the Delft Cylinder Hand is possible and will result in a prosthesis which can grasp objects of various sizes. Therefore the chosen design will be a simple design. In future designs the functionality of the thumb can be increased further. To keep the design simple it is chosen to give the thumb only 1 DOF. Also the control of the prosthesis will remain the same. The input force will be provided by the user of the prosthesis by means of an existing shoulder harness. The prosthesis is controlled using only 1 DOF input Challenges when adding an actively movable thumb Adding an active thumb will introduce a number of challenges. Regardless of the specific design of the mechanisms, difficulties will present themselves which are not present in the current design. The working principle of the hand is changed. In the current design four actuated fingers move towards a fixed structure, the thumb. The fingers apply a force and a reactive force is applied by the thumb. Making the thumb movable by adding one or more degrees of freedom changes the working principle of the hand. The thumb applies an active force now instead of a reactive force. The location of the contact points during grasping now depend on the movement of the thumb as well. The main challenges when adding an active thumb are: ˆ When an object is grasped an equilibrium must be reached between the forces applied by the fingers and the forces applied by the thumb. The thumb moves as well and applies a force to counteract the force of the fingers. To be able to grasp an object the applied forces must be in equilibrium. This equilibrium must be reached for a great variety of object sizes and grip types. This means the equilibrium must be reached in a great number of finger positions. ˆ It will be a challenge to acquire the right movement of the thumb with respect to the fingers. No additional degrees of freedom will be added to the control of the prosthesis. The prosthetic hand will be operated using existing shoulder harnesses. Since only 1 DOF is present as input, the free movement of the prosthesis remains the same for each grasping task. Only when the fingers touch an object, the movements change 7

13 Preliminary Design adapting to the the shape of the object. The desired movements will have to be determined. It will also be a challenge to design the prosthesis such that it makes the desired movements. 8

14 Preliminary Design Figure 6: Properties and performance of available voluntary closing hand prostheses. The mass, opening width, the required cable force for a 15 (N) pinch and the pinch force at a 100 (N) cable force will be used for comparison to the Delft Cylinder Hand. The table is obtained from [5] Design Requirements This section presents the requirements which are set for the design of the prosthetic hand. ˆ The control input for the prosthesis must remain 1 DOF. The prosthesis will be operated using existing shoulder harnesses. ˆ The thumb will be actuated and will have 1 DOF. The underactuated hand will have one more degree of freedom. ˆ The thumb should make a grasping movement which looks natural. ˆ The maximum hand opening of the prosthesis must be increased with respect to the original design. The current maximum hand opening is 75 (mm). ˆ The design of the prosthesis should be lightweight. The mechanism actuating the thumb should not add more than 30 gram to the prosthesis. Adding 30 gram to the prosthesis will increase the weight of the prosthesis with 20%. ˆ The prosthesis should maintain the current functionality. Adding an active thumb will affect the movements of the fingers. The functionality of the current design should not be decreased by adding an active thumb. ˆ The design should fit inside a cosmetic glove with a size of ˆ The prosthesis should be able to apply a grasping force of 30 N per finger. For comparison the properties and performance of some of the currently available voluntary closing prostheses are displayed in the table shown in Figure 6. The table is obtained from [5]. 9

15 Preliminary Design Figure 7: Study of hand movements by Zhang et al. Reflective markers are placed on the hand to track movements in 3D. The range of motion and the characteristic movements of the thumb are determined [17] Defining the desired movements of the prosthesis To determine the desired movements of the thumb of the prosthesis, literature of the movements of the hands of healthy individuals will be studied. Kinematic models of a human hand are made to describe the motion of the hand. The thumb can be modelled with 5 DOF s [1]. The Trapeziometacarpal joint has 2 DOF s, behaving as a saddle joint. The Trapeziometacarpal joint allows flexion and extension movements and abduction and adduction movements. The Metacarpophalangeal joint also has 2 DOF s since it allows flexion and extension movements as well as very small abduction and adduction movements. The Interphalangeal joint has 1 DOF, allowing only flexion and extension movements [1]. Zhang et al. also studied the movements of the human hand. Their research focusses on the range of motion (ROM) and the characteristic movements of the thumb [17]. Reflective markers have been placed on the fingers to keep track of the movements of the hand. Figure 7 from Zhang et al. shows the markers placed on the hand [17]. They found that the thumb has a conical motion space. The points on the thumb can be moved in a volume described by a cone. Also they found a center of rotation, i.e. the apex of the cone, and a fit for the axis of the cone. Zhang et al. obtained normative data for the location of this center of rotation. Normative values for the location of this point and the axis of the cone are useful for design purposes. The center of rotation is located close to the Trapeziometacarpal joint. The Trapeziometacarpal joint has the largest contribution to the total movement of the thumb [17]. Other studies also indicate a conical movement is a natural movement for the thumb [14, 19]. Herder et al. (1998) tested the possible thumb positions of healthy individuals with a 3D position measurement device. With this, cosmetically acceptable thumb positions for the prosthesis were determined [14]. They found the volume containing all possible thumb positions can be described by a cone. Coert et al. (2003) also used video techniques in combination with markers placed on the hand while testing healthy individuals to obtain normative data. Also this study describes a conical motion space for the thumb. As stated in the design requirements the thumb will be simplified to a structure moving with 1 DOF. Much functionality for the prosthesis can be gained introducing only 1 DOF for the thumb. Since the Trapeziometacarpal joint has the largest contribution to the total thumb movement the 10

16 Preliminary Design axis of rotation of the thumb will be placed at the location of this joint. With 1 DOF it is possible to create a conical movement with the thumb. The whole thumb describes part of a cone and the tip of the thumb describes part of a circle during the movement. For the first concept of an active thumb added to the Delft Cylinder Hand a design will be made where the thumb has only 1 DOF and describes a conical movement. Figure 8 presents a proposed movement for the tip of the thumb. The blue volume represents the range of motion of the thumb from a typical subject from the study of Zhang et al. The data is obtained from the study of Zhang et al. [17]. The blue volume in Figure 8 gives the boundaries for the movement of the thumb and will be used as limits when determining the trajectory of the thumb. The boundary volume is plotted together with the proposed movement of the thumb of the prosthesis. The whole thumb of the prosthesis describes part of a cone and the tip of the thumb makes a circular movement. The trajectory of the tip of the thumb during a grasping movement is displayed in red. The location of the center of rotation of the thumb is determined using the normative data presented by Zhang et al. [17] and is close to the Trapeziometacarpal joint. The axis of rotation for the thumb movement of the prosthesis is also determined using the data from Zhang et al.. The axis of rotation coincides with the axis fitted on the conical motion space as presented in Zhang et al. and is displayed in red in Figure 8. The movement of the thumb will be adjusted in such a way that the tip of the thumb meets the fingers in a grasping movement in the middle between the tip of the index finger and the middle finger. The movements will be simulated in CAD software and Matlab. The angle of the thumb with the rotation axis will be the maximum angle for which the thumb remains within the boundary represented by the blue volume in Figure 8 and for which the tip of the thumb meets the fingers between the tips of the index and middle finger. This way the largest hand opening will be accomplished for which the thumb has no unnatural thumb positions Hand opening of the prosthesis The hand opening of the prosthesis determines the size of the objects which can be grasped. By adding an active thumb, the grip size of the prosthesis can be increased. The hand opening of currently available prostheses is displayed in Table 6 [2]. The hand opening of the Delft Cylinder Hand in the current design is 75 (mm) which is higher than most available prostheses. Since the size of daily life objects may exceed 75 (mm) increasing the grip size is desired. When an active thumb is added, not only the hand opening determines the size of the objects which can be grasped. Another prerequisite is an equilibrium situation during grasping. The thumb and finger forces on the grasped object must be in equilibrium during grasping for the object to remain in the grip of the prosthesis Weight of the prosthesis One of the current advantages of the Delft Cylinder Hand is that it is very light compared to other prostheses [2]. The weight of the Delft Cylinder Hand is 217 grams including the cosmetic glove and 152 gram excluding the cosmetic glove. The mechanism added to actuate the thumb should be lightweight as well. The mechanism actuating the thumb should not add more than 20% of weight to the prosthesis without glove. The mechanism to actuate the thumb should not add more than 30 gram to the prosthesis Grasping forces Appendix B shows a literature review done to provide information about the maximum grip and pinch strength of healthy subjects without upper extremity defects. The systematic search has been performed to find articles containing normative values for grip and pinch strength. The purpose of the review is to serve as a basis for composing the design requirements of a prosthetic hand. In the review (Appendix B) is was concluded the maximum average grip strength is about 550 N for male subjects. The maximum avarage grip strength is about 340 N for female subjects. 11

17 Thumb mechanism, the working principle Figure 8: Range of motion of the thumb of the right hand of a subject (blue), trajectory data obtained from Zhang et al. [17]. The proposed prosthesis thumb trajectory is displayed in red and remains within the boundaries given by the blue volume. The center of rotation and the rotation axis of the proposed movement are based on normative values from Zhang et al.. Age influence on grip strength is only minimally present for subjects between 20 and 60 years old and is not relevant when an estimate for maximum grip strength is needed. Average maximum pinch forces range, depending on pinch type, from 80 N to 100 N for male subject and from 55 N to 80 N for female subjects. Ideally users would be able to apply the same forces with the prosthesis. However this is not possible with the currently available prostheses. As can be seen in Figure 6 current prostheses apply about 5-58 (N) pinch force at a cable force of 100 (N) in the shoulder harness. The Delft Cylinder Hand can apply a maximum force of 30 (N) per finger [2,16]. Measurements have been done with the Delft Cylinder Hand to determine the maximum pinch force. A force is applied between the index and middle finger and the thumb. When a pull force of 100 (N) is applied to the master cylinder, the prosthesis can apply a pinch force of 19 (N) [2]. The new design for the Delft Cylinder Hand should be able to apply the same force as the original design. 2.3 Thumb mechanism, the working principle In this section preliminary design will be presented for the thumb mechanism. The thumb will have 1 DOF as stated in the Design Requirements. The thumb will be actuated using one hydraulic 12

18 Thumb mechanism, the working principle cylinder. The desired movement of the thumb is a movement where the thumb describes a cone. A simple mechanism will be chosen to accomplish this movement. The mechanism presented here is only to illustrate the concept used for the design of the hydraulic hand. The specific design will be presented in Section Figure 9 shows the top view of the chosen mechanism for the thumb. The hydraulic cylinder, which actuates the thumb movement, is shown in blue. The thumb is shown in orange. The thumb rotates around the axis shown in black. The thumb is placed on an angle θ with respect to the axis. θ x ' y ' Figure 9: Thumb Mechanism, Working Principle, Top View. The Hydraulic cylinder, displayed in blue, actuates the thumb displayed in orange. The thumb rotates around the x axis and describes part of a cone during movement. 13

19 Thumb mechanism, the working principle Figure 10 shows a front view of the mechanism. In the figure is shown how the degree of freedom is manipulated by the hydraulic cylinder. The top figure (10a) shows the mechanism in begin position and the bottom figure (10b) shows the mechanism with the thumb rotated 50 degrees. (a) 0 degrees ϕ t ϕ t (b) 50 degrees Figure 10: Thumb Mechanism, Working Principle, Front View. The top figure (a) displays the thumb in initial (open) position. The bottom figure shows the thumb rotated over 50 degrees. The initial position is displayed transparant the bottom figure (b) to illustrate the movement. In Figure 11 is shown how the thumb moves in 3D. The tip of the thumb describes a circle and the whole thumb describes a cone. 14

20 Analysis of the hydraulic hand Figure 11: Thumb Mechanism, Working Principle. The top figure displays the thumb in initial (open) position. The bottom figure shows the thumb rotated over 50 degrees. The initial position is displayed transparant the bottom figure to illustrate the movement. The thumb, displayed in orange, makes a conical movement when actuated by the hydraulic cylinder (blue). 2.4 Analysis of the hydraulic hand This section presents a summary of the analyses done on the hydraulic hand. A complete documentation of the analyses is presented in the paper added in Appendix A. The addition of the thumb has a number of implications. The volume flow of the master cylinder, which was divided over the cylinders of the fingers, is now divided over the cylinders of the fingers and thumb. This influences both the movements of each phalanx and the force which is exerted by each hydraulic cylinder. To be able to design the prosthesis the movements of each phalanx of the fingers and the movement of the thumb should be predicted. Also the forces the prosthesis can exert should be predicted to be able to make a good design. The goal of the analyses is to provide the information to answer the following main questions: 1. How will the fingers and the thumb move when the prosthetic hand is actuated? What will be the free grasping movement? 2. Can an equilibrium be reached during the grasping of objects of various sizes? 3. What forces can be exerted by the prosthetic hand? Kinematic models where created to describe the relations between the movements of the hydraulic cylinders and the movements of the phalanges of the fingers and the thumb. Figure 12 displays the kinematic model for the fingers. Assumptions were made to be able to predict the free grasping movement of the prosthesis and the exerted forces by the fingers and the thumb. The most important assumptions made for the analyses are: 15

21 Analysis of the hydraulic hand F ext G φ 2 x H F E x y φ 1 x Cylinder2 B C A y y Cylinder1 D Figure 12: Kinematic model for the fingers. The hydraulic cylinders are displayed in blue, the finger phalanges are displayed in orange and the mechanical springs are displayed in black. The model is used to describe the relations between the movements of the hydraulic cylinders and the finger phalanges. ˆ The volume flow of the hydraulic fluid is divided equally between all hydraulic cylinders. ˆ The forces exerted by the hydraulic hand are exerted by the tips of the fingers and thumb. Since all finger positions now depend on the stroke of the master cylinder the movements could be simulated. The simulated movements could be used during the design to acquire the desired movements described in Section The concept of virtual work is used to obtain the force transmission ratios between the fingertips and the actuating hydraulic cylinders. The total virtual work applied to the finger is equal to zero. The sum of the virtual work applied by the cylinders to the finger and the virtual work applied by the object to the tip of the finger is equal to zero. δw cylinder1 + δw cylinder2 + δw object = 0 (1) If we take the forces applied by the tip of the finger to the object as positive we obtain the following relation between the forces: F cylinder δs 1 + F cylinder δs 2 = F x δx t + F y δy t + F z δz t (2) 16

22 Grasp Equilibrium Where s 1 and s 2 represent the stroke positions of the hydraulic cylinders and x t, y t and z t represent the coordinates of the tip of the finger. The relation between the forces must hold for all possible virtual displacements δs 1 and δs 2 independently. This results in the set of equations: [ ] Fcylinder1 = F cylinder2 [ δxg δs 1 δx g δs 2 δy g δs 1 δy g δs 2 δz g δs 1 δz g δs 2 ] F x F y F z = J g F g (3) The jacobian J g is calculated using the kinematic relations. The force transmission ratios between the hydraulic cylinders and the fingertip result from equation 3. The force transmission ratio of the thumb is found in a similar manner. See Appendix A for the derivations of jacobian J g and the force transmission ratio of the thumb. Using the force transmission ratios it is calculated what forces two fingers and the thumb can exert on an imaginary object when a force of 100 (N) is applied to the master cylinder. The size of the imaginary object is equal to the hand opening of the prosthesis and is a function of the stroke of the master cylinder. The forces are assumed to be in the direction of the vector V object pointing from the tip of the thumb towards the tip of the index finger. An equilibrium is reached when the thumb force is equal to the force two fingers exert on the object. These forces are calculated for all possible stroke positions of the master cylinder and are shown in Figure 13. The stroke of the master cylinder is made dimensionless in Figure 13. The configuration where the prosthesis is fully opened corresponds with a master cylinder stroke of 0. The configuration where the prosthesis is fully closed corresponds with a master cylinder stroke of 1. It can be observed the force two fingers can exert on an object during grasping is about 19 (N) for most of the stroke. Figure 13 also shows only low forces can be applied to the object by the thumb. A thumb force of below 4 (N) is obtained for most of the stroke. Furthermore it is shown in the analyses presented in Appendix A that increasing the thumb force will be at the expense of the amplitude of the movements of the thumb. The hand prosthesis can only effectively grasp objects when an equilibrium is reached during grasping. It is not possible to accomplish this with the current design. The design will be modified to meet the design requirements. Section 2.5 will present the possible solutions to accomplish an equilibrium during the grasping of objects with the prosthesis. 2.5 Grasp Equilibrium The design will have to meet the requirements set in Section In Section 2.4 it was shown the proposed design could not meet the design requirements. Before the design can be finalized first the problem of acquiring an equilibrium during grasping will have to be solved. In the Section A.4.7 of Appendix A the variables where shown which can be changed to obtain an equilibrium during grasping. The variables influence both the force transmission and the amount of thumb movement. It was shown that the thumb movements are decreased when the thumb force is increased and vice versa. The high required thumb force to obtain an equilibrium, compared to the combined force of four opposing fingers, results in small movements of the thumb. The following solutions are possible to acquire an equilibrium during grasping: ˆ Allow only small thumb movements. ˆ Add a 2 phase cylinder to the thumb. The 2 phase cylinder amplifies the actuation force when a threshold pressure is exceeded. ˆ Changing the transmission during the stroke of the thumb. ˆ Add passive components (springs) to create an equilibrium. ˆ Adding additional cylinders and phalanges to the thumb. 17

23 Grasp Equilibrium 20 2 Fingers Thumb 15 F [N] stroke [ ] Figure 13: The finger and thumb forces as a function of the master cylinder stroke. The open configuration of the prostheses corresponds with the master cylinder stroke at 0% (stroke=0), the fully closed configuration corresponds with the master cylinder stroke of 100% (stroke=1). The thumb force should be increased, and be equal to the force of 2 fingers, to be able to grasp the object. ˆ Add a flow divider. The hydraulic circuits of the thumb and the fingers are separated. The flow divider determines the volume flow to each hydraulic circuit. Each solution will be explained in the following subsections Small thumb movements When only small thumb movements are allowed it is possible to acquire an equilibrium for the whole grasping stroke for a certain grip type. The transmission ratios of the thumb and the fingers can be optimized to obtain a minimum force difference between the fingers and the thumb. A choice should be made in that case how many fingers apply a force to the object. Ideally an equilibrium exists during grasping using all of the following grip types: ˆ A tip pinch grip where the object is pinched between the index finger and the thumb. ˆ A palmar pinch grip where the object is pinched between the index finger, the middle finger and the thumb. ˆ A three fingered grip. The object is gripped between three fingers and the thumb. ˆ A four fingered grip. The object is gripped using all fingers. The thumb has to counteract the force applied by four fingers. Since each added finger increases the force the thumb needs to apply and the thumb mechanism remains the same, it is not possible to acquire a force equilibrium for all grip types. 18

24 Grasp Equilibrium Two Phase Cylinder A solution to increase the thumb movement and still be able to apply enough force during grasping could be a two phase cylinder. The two phase cylinder is shown in Figure 14. The concept is based on a 2 phase hydraulic braking system designed by Frankenhuyzen, J. and Plettenburg, D.H.. The input for the hydraulic fluid is placed on the left and is connected to the master cylinder in the shoulder harness. The output for the hydraulic fluid is placed on the right and leads to the thumb cylinder. The input and the output side are connected through a small channel, resulting in an equal pressure on the input and output side. In the cylinder a piston is placed which is held in place by a spring. The piston has a larger area on the side of the input chamber (A 1 ) than on the output chamber (A 2 ). When the pressure in the input chamber increases, a nett force will act on the piston to move it to the right. When the pressure on the input side exceeds a threshold depending on the chosen spring, the piston will close the channel connecting the input and output chambers. The input and output side are now separate systems interacting through the piston. The pressure on the output side is now amplified by a factor A 1 /A 2. Figure 14: 2 Phase Cylinder a cross section, concept based on a braking system design by Frankenhuyzen, J. and Plettenburg, D.H. A channel connecting the input and the output side ensures equal pressure on both sides. The channel is closed by the piston when the threshold pressure is reached. When the channel is closed, the pressure is amplified by a factor A 1 /A 2. With a two phase cylinder it is possible to have large thumb movements for the free movement of the thumb. When a large thumb force is needed, the pressure in the master cylinder will increase above the threshold. The channel connecting the input an output chambers will be closed off. The pressure in the thumb cylinder will now be A 1 /A 2 times the pressure in the master cylinder, allowing for higher thumb forces. A drawback of this solution might be that the threshold pressure is not reached during grasping. When the fingers are stronger than the thumb, the thumb will be pushed backwards. The object will be pushed out of the prosthetic hand. If this happens for low pressures in the master cylinder, the two phase cylinder will never reach the second phase where an amplification of the pressure will occur. Also as explained in Section it is not possible to acquire a force equilibrium for all grip types. Assuming the two phase cylinder will amplify the thumb force, it is still possible to acquire an equilibrium only for specific grip types Change transmission toward end of stroke The thumb mechanism can be designed such that it will have large thumb movements at the beginning of the stroke with only a low force transmission ratio and to have small thumb movements 19

25 Grasp Equilibrium toward the end of the stroke with a high force transmission ratio. It is then possible to have large thumb movements and still be able to apply a high thumb force at the end of the stroke. The main drawback of this solution is that the equilibrium can only be reached for a small part of the stroke. The prosthesis will only be able to grasp objects of a specific size. The large thumb movements will then only be for cosmetic reasons and will only add limited functionality to the prosthesis. Also for this solution limitations with respect to the number of grip types are present as explained in Section It is not possible to acquire a force equilibrium during grasping for all grip types Create equillibrium using passive components It is possible to add passive components which apply forces to the hand such that an equilibrium can be reached. Springs for example can be added to change the finger or thumb force. Since the prosthesis is a voluntarily closing hand, it has to open automatically. The springs can t be used to increase the thumb force since in that case the thumb would close automatically. The springs could be used to decrease the forces the fingers apply to the grasped object. The drawback would be the total grip force would be decreased to match the maximum thumb force. The added passive components increase the required input energy to close the prosthesis which is not desirable. Also this solution does not solve the limitations explained in with respect to the possible grip types Adding cylinders and phalanges If additional phalanges would be added to the thumb, the thumb movement could be increased. It is possible to obtain high thumb forces and add some movement to the thumb by additional phalanges. The added movement is limited however since the Trapeziometacarpal joint has the largest contribution to the total thumb movement according to Zhang et al. [17]. Also extra cylinders could be added without adding phalanges. The thumb force could then be increased without decreasing the movement of the thumb. This solution does not increase the number of grip types for which an equilibrium can be reached. As explained in Section the thumb can only be designed to counteract the force of a fixed number of opposing fingers Flow divider Another solution may be a flow divider. The concept of the flow divider is shown in Figure 15. A cylinder is added to the system. The master cylinder is connected to the input on the left side of the flow divider. The hydraulic fluid enters the chamber with area A 1 and applies a pressure on the piston. Two concentric cylinders are placed on the other side of the piston. The concentric cylinders create two chambers. The outer chamber is connected to the hydraulic cylinders of the fingers and has an area of A 2. The inner chamber leads to the hydraulic cylinder of the thumb and has an area of A 3. The flow divider fixes the flow fractions going to the fingers and the thumb. By fixing the flow fractions the relative movements of the fingers and the thumb are ensured. The fingers are all connected to the same chamber of the flow divider. This allows the fingers to adapt to the grasped object the same way as in the current design of the hydraulic hand. The movement of the thumb however is connected to the position of the fingers. The flow divider adds a constraint to the system. Since only 1 DOF was added to the underactuated hand by making the thumb active, the system now has the same amount of DOF s as the current design. The added constraint allows the thumb to apply a reactive force. If the fingers provide more force than the thumb, the thumb would be pressed backward. However since the volume flow is fixed, pressure will build up inside the thumb cylinder increasing the thumb force. Because the thumb can apply a reactive force, the 20

26 Grasp Equilibrium Figure 15: Flow divider, cross section. The piston connects the input chamber (left) and 2 concentric output chambers (right). The flow divider fixes the flow fractions of the hydraulic fluid going to the fingers and the thumb. By adding a constraint to the system the volume divider ensures the relative movements and allows the thumb to apply a reactive force. thumb force will be adapted to match the force applied by the opposing fingers. An equilibrium can now be reached during the grasping of an object regardless of the number of opposing fingers. Fixing the relative motion with a volume flow divider is the most promising solution. 21

27 Test Plan 2.6 Test Plan Tests will be performed to check if the prosthesis meets the requirements. The prosthesis will be evaluated on the set design requirements in Section Measurements will be done to determine the weight of the prosthesis with thumb mechanism and to determine the maximum hand opening of the prosthesis. Furthermore the prototype for the prosthesis will evaluated by functional tests. The tests should answer the questions posed in the analysis presented in Appendix A: ˆ What will be the free grasping movement of the prosthesis? ˆ Can an equilibrium be reached during the grasping of objects of various sizes? ˆ What forces can be exerted by the prosthetic hand? Free Movement The prosthesis will be designed to perform a certain movement. The relative movement of the thumb with respect to the fingers is one of the key points during the design process. The thumb will make a conical movement and meet the fingers between the index finger and the middle finger. The movement will be simulated in CAD software and in Matlab prior to the building of the prototype. The movements of the prototype will be compared to simulated movements. To compare the movements, three configurations will be compared. ˆ The configuration when the prosthesis is totally open, the stroke of the master cylinder is at 0 %. ˆ The configuration when the prosthesis is at mid stroke, the stroke of the master cylinder is at 50 %. ˆ The configuration when the prosthesis is totally closed, the stroke of the master cylinder is at 100 %. Where the stoke position of the master cylinder for which the prosthesis can not move further is taken as 100 %. This is not the end of the stroke of the master cylinder but it is the limit for the movement of the prosthesis. For the given configurations the angle of the thumb mechanism and the angles of each finger phalanx will be measured and compared to the simulations with the CAD software and Matlab Grasping objects Tests will be done to establish the range for which object sizes the prosthesis is functional. The prosthesis is considered functional when the prosthesis can close around the object without help and the prosthesis can pick up and hold the object. For this second requirement an equilibrium must be reached between the grasp forces of the fingers and the thumb. The prototype of the prosthesis will be used to pick up daily life objects of cylindrical shape with increasing diameters. For each object it will be determined if the prosthesis can pick up the object. This will give the range of object diameters for which the object can be grasped with the prosthesis Pinch Tests A mechanical evaluation of the prototype will be performed by means of pinch tests. To be able to compare the mechanical performance with other prostheses and the current design of the Delft Cylinder Hand, tests as described in the test protocol used by Smit, G and Plettenburg, D,H (2010) [5] will be used for the measurements. The tests which will be performed are the Pinch test and the Pull test. The tests will be performed using the test bench used by Smit, G and Plettenburg, D,H (2010) displayed in Figure 16. With the test bench the force on the master cylinder can be increased in a controlled way. The test bench contains two load cells to measure the pull force on the master cylinder and the pinch 22

28 Test Plan Figure 16: Test Bench for mechanical evaluation, obtained from [5]. The activation pull force on the master cylinder can be applied in a controlled way. The prosthesis pinches a load cell. The activation force and the pinch force applied by the prosthesis are measured as well as the excursion of the master cylinder. force applied by the prosthesis. Also the excursion of the master cylinder is measured by means of a linear displacement sensor. The test bench and its components are described in detail in [5] Pinch Test The pinch force of the prosthesis is evaluated for a Palmar pinch grip. A load cell is placed between the tips of the thumb and two fingers; the index finger and the middle finger. The force on the master cylinder will be increased until the pinch force of the prosthesis is equal to 15 (N ). The pinch force, the pull force on the master cylinder and the displacement of the master cylinder will be measured during this test. The pinch test will be performed with objects of different sizes. The object sizes which will be used are: 10 (mm), this is the thickness of the loadcell 35 (mm), the 10 (mm) load cell mounted on a 25 thick (mm) rectangular prism. 63 (mm), the 10 (mm) load cell mounted on a cylindrical object with a diameter of 53 (mm) 88 (mm), the 10 (mm) load cell mounted on a cylindrical object with a diameter of 78 (mm) Pull Test Again the pinch force between the thumb and two fingers is determined. The force on the master cylinder is increased from 0 to 100 (N ). The pinch force, the pull force on the master cylinder and the displacement of the master cylinder will be measured. 23

29 3 Results 3.1 Design of the hydraulic hand This section presents the design of the hydraulic hand. The preliminary design presented in Section 2.2 is worked out in detail. A volume divider is added to be able to create an equilibrium as discussed in Section 2.5. The design of the mechanisms of the fingers and the thumb will be discussed in detail. And finally the total design will be presented. The movements for the design will be simulated and tuned to match the desired movements and requirements discussed in Section Finger Design An alternative design is made for the mechanism of the finger. The goal of this design is to allow easy modifications to the geometry of the fingers. The design is displayed in Figure 17. The four parts displayed in red are made using laser cutting technology. In blue the points are displayed which determine the finger geometry. The points correspond with the points in the kinematic model displayed in Figure 12 and represent connection points of the hydraulic cylinders, connection points of the springs and the hinges of the phalanges. The four laser cut parts determine all displayed points and thus the whole geometry of the finger. The production of the four laser cut parts is relatively cheap. It is now possible to change the entire finger geometry at relatively low cost. This is an advantage in a design process where the geometry is optimized by changing certain parameters iteratively. Another advantage for this design is the possibility to change the size of the fingers at few added costs. Different sizes of the hydraulic hand could be made by changing only the laser cut parts displayed in red. Patient specific designs are easily realised to match the exact geometry of the healthy hand. For the prototype however it is chosen to use fingers which are already produced and used in the current Delft Cylinder Hand. The reasons for this choice are the saving of time and money. This way the thumb mechanism could be evaluated quickly. For future designs the alternative finger design could be used to optimize the relative movements of the thumb and the fingers Thumb Mechanism The design of the thumb mechanism is based on the working principle presented in Section 2.3. The thumb mechanism is displayed in Figure 18. The parts which compose the thumb frame are displayed in orange. These parts are fixed to the frame of the hand. The hydraulic cylinder is displayed in blue. The thumb is displayed in yellow. The points displayed in blue in Figure 18 represent the connection points of the hydraulic cylinder, the hinge of the thumb and the tip of the thumb. The points correspond with the points displayed in Figure 23 and in the formulas in Section A

30 Design of the hydraulic hand D C B A F H E G Figure 17: Finger mechanism, alternative design. The points displayed in blue represent the connection points of the hydraulic cylinders, the connection points of the springs, the hinges and the contact point of the finger tip with the object. The parts displayed in red determine the connection points, hinges and contact point and thereby determine the geometry of the finger. 25

31 Design of the hydraulic hand B A P C Figure 18: Thumb mechanism. The thumb frame is displayed in orange, the hydraulic cylinder is displayed in blue and the thumb is displayed in yellow. The points displayed in blue represent the connection points of the hydraulic cylinder, the hinge and the contact point of the tip of the thumb with the object. 26

32 Examining the free movements of the prosthesis Total design of the hydraulic hand The design of the hydraulic hand is displayed in Figure 19. The rear view, top view and side view of the hand are shown in Figure 19a, 19b and 19c respectively. The fingers have 7 DOF s in total and are actuated by 7 hydraulic cylinders. This is the same as in the current design of the Delft Cylinder Hand. All hydraulic cylinders are connected to only one input cylinder. The hydraulic fluid is allowed to flow between the hydraulic cylinders. Therefore the number of DOF s is reduced only by 1. The fingers have 6 DOF s left. The thumb has 1 DOF, actuated by 1 hydraulic cylinder. It is connected together with the fingers to the volume divider described in Section The volume divider can be seen as a constraint which reduces the number of DOF s by 1. The thumb adds 1 DOF but the volume divider subtracts 1 DOF thus the total number of DOF s remains 6. With these DOF s the hydraulic hand is allowed to adapt to the shape of the grasped object. The simulation of the movement is displayed for the hand with the alternative finger design. The prototype will be made with the fingers from an existing prototype. The geometry, all connection points of the finger mechanism, is exactly the same for the displayed hand and the existing fingers. The mechanism for the thumb movement adds 24 gram to the weight of the prosthesis. The thumb and the mechanism weigh 38 gram. The weight of the old thumb is 14 gram. The total weight of the prosthetic hand is 176 gram without cosmetic glove and 241 gram with cosmetic glove glove. The maximum hand opening of the prosthesis without cosmetic glove is 100 ±1 (mm). To simulate the movements of the hand during a free grasping movement, the volume flow is assumed to be divided equally between all hydraulic cylinders. This assumption is explained in Section A.4.2 and A in Appendix A. The hand has no degrees of freedom anymore and depends solely on the stroke of the master cylinder. The resulting free grasping movements are shown in Figure 20. The movement of the little finger is not simulated. The sub figures show the positions of the fingers and thumb for an increasing stroke. The hand is displayed for a stroke of 36%, 55%, 73% and 100% in the figures 20a, 20b, 20c and 20d respectively. The fingers and thumb are displayed transparent in the initial position (stroke = 0%) in all sub figures to visualise the movements. 3.2 Examining the free movements of the prosthesis The free grasping movements of the prosthesis without cosmetic glove were examined. The total displacement of the used master cylinder during the closing of the prosthetic hand is 23.9 ±0.1 (mm). For the configuration at 50 % of the stroke, the master cylinder was exerted 12 ±0.1 (mm). Table 1 displays the measured absolute joint angles of the phalanges in 3 configurations of the prosthesis. The columns of Table 1 represent the different configurations. The stroke positions 0, 50% and 100% are the fully opened configuration, the mid stroke configuration and the fully closed configuration respectively. The measurements are presented together with the values as simulated with the CAD software. The simulation in Matlab yielded the same results as the simulation with the CAD software. Almost all measured absolute finger joint angles differ significantly from the predicted absolute joint angles. Only the second joint angle (φ 2 ) of the middle finger is not significant different from the predicted joint angle when the prosthesis is in open configuration. The thumb does move as predicted. The absolute thumb joint angles do not differ significantly from the predicted joint angles in all 3 configurations. For better comparison Table 2 presents the relative joint angles as measured and predicted with the CAD simulations. The joint angles in the open configuration as predicted with the CAD software are taken as a reference. It is observed the measured open configuration deviates from the reference configuration. The angles of the finger phalanges, for the hand in fully opened configuration, are smaller then predicted with the CAD software. The differences are significant. The exception is the second joint angle φ 2 of the middle finger which is 1±1 o. The joint angle is not significantly different then the predicted joint angle with the CAD software. In the mid stroke configuration (Stroke=50%) it is observed some phalanges move significantly more than predicted and some phalanges move significantly less then predicted. Almost all volume displaced by the master cylinder is moved to the thumb cylinder, the cylinder actuating the first phalanx (φ 1 ) of 27

33 Examining the free movements of the prosthesis (a) Rear View (b) Top View (c) Side View Figure 19: Design of the hydraulic hand. The hand is displayed in open configuration. On the top left (a) the rear view of the design is displayed, the top right (b) figure displays the top view of the design and the bottom left (c) figure displays the side view of the hydraulic hand. 28

34 Examining the free movements of the prosthesis (a) Stroke = 36 % (b) Stroke = 55 % (c) Stroke = 73 % (d) Stroke = 100 % Figure 20: Movements of the hydraulic hand. The figures a-d display the hydraulic hand for increasing stroke of the master cylinder. The initial (open) configuration is displayed transparant to illustrate the movement. The movements are indicated with red arrows. 29

35 Examining the free movements of the prosthesis Table 1: Measured and predicted absolute joint angles of the phalanges for the prosthesis in three configurations Stroke=0 Stroke=50% Stroke=100% Measured CAD Measured CAD Measured CAD Thumb φ t [degrees] 46 ±1 o ±2 o 18-5 ±2 o -5 Index finger φ 1 [degrees] 1 ±1 o 5 27 ±2 o ±2 o 41 Index finger φ 2 [degrees] 14 ±1 o ±2 o ±2 o 58 Middle finger φ 1 [degrees] 1 ±1 o 5 1 ±2 o 24 1 ±2 o 41 Middle finger φ 2 [degrees] 23 ±1 o ±2 o ±2 o 58 Ring finger φ 1 [degrees] 1 ±1 o 5 1 ±2 o 24 1 ±2 o 41 Ring finger φ 2 [degrees] 17 ±1 o ±2 o ±2 o 58 the index finger and to the cylinder actuating the second phalanx (φ 2 ) of the middle finger. In the closed configuration it is also observed some phalanges move significantly more than predicted and some phalanges move significantly less then predicted. The first phalanges (φ 1 ) of the middle finger and the ring finger have not moved. All other finger phalanges move significantly more than predicted. The angle of the thumb is not significantly different then the predicted thumb angle. Table 2: Measured and predicted relative joint angles of the phalanges for the prosthesis in three configurations Stroke=0 Stroke=50% Stroke=100% Measured CAD Measured CAD Measured CAD Thumb φ t [degrees] -7 ±1 o 0-36 ±2 o ±2 o -58 Index finger φ 1 [degrees] -4 ±1 o 0 22 ±2 o ±2 o 36 Index finger φ 2 [degrees] -8 ±1 o 0-8 ±2 o ±2 o 36 Middle finger φ 1 [degrees] -4 ±1 o 0-4 ±2 o 19-4 ±2 o 36 Middle finger φ 2 [degrees] 1 ±1 o 0 35 ±2 o ±2 o 36 Ring finger φ 1 [degrees] -4 ±1 o 0-4 ±2 o 19-4 ±2 o 36 Ring finger φ 2 [degrees] -5 ±1 o 0-2 ±2 o ±2 o 36 30

36 Force Measurements 3.3 Force Measurements Figure 21 shows the results of the pull test while pinching a load cell with a thickness of 10 (N). The load cell was positioned in the hand by manually placing the fingers on the load cell before starting to pinch. The measured pinch force is plotted for increasing pull force on the master cylinder. The used master cylinder is larger than the master cylinder of the actual design. The pull force was scaled down with a factor to account for the larger piston area of the used master cylinder. An initial pull force of 59 (N) on the master cylinder is needed to start pinching. A fit of a straight line is made for the data with pull forces above the initial pull force and plotted in Figure 21 as well. The average force transmission ratio is the slope of the fitted line. The average force transmission ratio is 0.12 (-). The pinch force of the prosthesis for an activation pull force of 100 ((N)) is 5.5 (N). A maximum pinch force of 9.3 (N) was reached with the prosthesis. A pull force on the master cylinder of (N) is needed to apply this pinch force. When the force was increased further the grip on the load cell was not stable and the load cell slipped out of the grip of the prosthesis Pinch Force, Sensor thickness=10 mm 9 8 Pinch Force [N] Activation Force [N] Figure 21: Pull Test, Pinch force for a sensor with a thickness of 10 (mm). The initial activation force to start builing a pinch force is equal to 59 (N). The avarage force transmission ratio is 0.12(-) Figure 22 shows the results of the Pinch Test for 3 objects with different sizes. The objects have a thickness of 35 (mm), 63 (mm) and 88 (mm). The measured pinch force is plotted for increasing pull force on the master cylinder. The pull force on the master cylinder was scaled down with a factor to account for the larger piston area of the used master cylinder. The initial activation pull forces needed to start building a pinch force are 27 (N), 23 (N) and 17 (N) for the objects with sizes 35 (mm), 63 (mm) and 88 (mm) respectively. It can be observed the measured pinch force while grasping the object with a diameter of 63 (mm) starts at 0.95 (N). An initial activation pull force on the master cylinder was needed to close the hand to touch the 31

37 Force Measurements Object: D=35 mm Object: D=63 mm Object: D=88 mm 12 Pinch Force [N] Activation Force [N] Figure 22: 15 (N) Pinch Test for objects of increasing size. The initial activation forces to start builing a pinch force are equal to 27 (N), 23 (N) and 17 (N) for the objects with sizes 35 (mm), 63 (mm) and 88 (mm) respectively. The average force transmission ratios are 0.19 (-), 0.28 (-) and 0.29 (-) while grasping the objects with sizes of 35 (mm), 63 (mm) and 88 (mm) respectively. object. When the object with the sensor was positioned in the hand the activation force caused a low pinch force at the start of the measurements. It can also be observed the slope of force curve for the object with a size of 63 (mm) is lower for low activation forces and increases when the activation pull force on the master cylinder exceeds 34 (N). During the measurement it was observed the ring finger was still moving for activation forces below 34 (N). When the ring finger was at the end of its stroke, when an activation force of about 34 (N) was reached, the slope of the curve increased. Fits of straight lines were made on the data with pull forces above the initial activation pull force. For the object with size 63 (mm) the pull force of 34 (N) was used as initial force to obtain a better fitted line for higher pinch forces. The fitted lines are also plotted in Figure 22. The average force transmission ratios are the slopes of the fitted lines. The average force transmission ratios are 0.19 (-), 0.28 (-) and 0.29 (-) while grasping the objects with a size of 35 (mm), 63 (mm) and 88 (mm) respectively. A maximum pinch force of 9.5 (N) was applied to the object with a diameter of 88 (N). The material at the location of the bending of the plate at the base of the thumb started to deform. The thumb could not withstand higher forces in this configuration. Maximum pinch forces of 14.9 (N) and 14.5 (N) where applied while grasping the objects with a size of 35 (mm) and 63 (mm) respectively. Activation pull forces on the master cylinder of 79.9 (N) and 89.5 (N) are needed to obtain the pinch forces of 14.9 (N) and 14.5 (N) respectively. 32

38 Grasping Objects 3.4 Grasping Objects The prosthesis without the cosmetic glove was used to grasp objects. Table 3 shows a list of daily life objects with a cylindrical shape for which grasping was attempted with the prosthesis. The objects are sorted and presented in the table for increasing diameters. The last column shows if the object was successfully picked up with the prosthesis. A successful grasp means the prosthesis can close around the object without help and the prosthesis can pick up and hold the object. The largest object which could be grasped with the prototype without cosmetic glove is 99 (mm). An object with a diameter of 102 (mm) could not be grasped. No objects with sizes between 99(mm) and 102 (mm) were attempted to grasp. No stable grasp could be accomplished for objects smaller then 50 (mm). A pinch grip is needed to pick up the small objects. The movements of the prosthesis without the cosmetic glove do not allow for a pinch grip of cylindrical objects without help. The range of the diameter of cylindrical objects which could be grasped with the prosthesis is 50 (mm) up to at least 99 (mm). Table 3: Daily live objects with increasing size grasped with the prosthesis. Object Diameter [mm] Successful grasp Deodorant can 46 no Bottle sauce 49 no Cosmetic product can 50 yes Cleaning product spray can 53 yes Food jar 57 yes Beer bottle 59 yes Food can 65 yes Coffee thermos mugg 80 yes Peanutbutter jar 88 yes Duct tape roll 97 yes Measuring cup 99 yes Large jar 102 no Measuring cup 110 no Large bottle 112 no 33

39 4 Discussion 4.1 Design 4.2 Free Movements In section 3.2 results of the free movements of the prosthesis without glove were presented. The presented measured angles of the finger phalanges show large deviations from the predicted joint angles. The measured thumb angles were almost the same as the predicted angles. The predicted joint angles are based on the assumption of an equally divided volume flow between all hydraulic cylinders actuating the fingers. The assumption has as a result the stiffness of the glove and the added springs should not influence the movements. The measured data show this assumption does not hold. The movements of the fingers will be different when measured on the prototype with a cosmetic glove. The stiffness around each joint, caused by the cosmetic glove and the added springs to the phalanges, determine the movements of the prosthesis. The assumption of an equally divided volume flow is still useful during the design process. With this assumption it is possible to predict the thumb movements with respect to the fingers. The relative movements of the finger phalanges with respect to each other should be tuned by choosing the stiffness of the springs added to each phalanx. In the current state grasping of small objects with the ungloved prototype difficult. The uneven movement of the phalanges complicate the grasping of objects. The movements of the ungloved prosthesis look unnatural. The prosthesis is expected to have more favourable free grasping movements when the cosmetic glove is added. The springs of the phalanges are chosen such that the prosthesis makes the desired movements during the design of the Delft Cylinder Hand. Since the design of the fingers is not changed the relative movements of the phalanges are expected to remain the same. 4.3 Force Measurements In the pull test the thickness of the grasped object, the load cell, is 10 (mm). The results of the pull test presented in Figure 21 show an initial activation pull force of 59 (N) is needed on the master cylinder to start building up pinch force. This initial activation force is higher than for the original design. During measurements on the gloved Delft Cylinder Hand an activation force 20 (N) was needed to start building pinch force [2].This could be the result of the spring added to the thumb. The spring is needed to automatically open the prosthesis and counteracts the actuation force of the thumb cylinder. The absence of the cosmetic glove is also of influence. The cosmetic glove adds stiffness to the fingers. Depending on the configuration of the hand this will counteract or assist the actuation force. The measured force transmission ratio during the pull test is 0.12 (-). This is low compared to the original design of the Delft Cylinder Hand. The calculated force transmission ratio, using the data from Smit (2013) [2], is 0.24 (-). The force transmission ratio could be increased by decreasing the piston area of the master cylinder. The high initial actuation force and the low force transmission ratio result low pinch forces. A pinch force of only 5.5 (N) is achieved for an activation pull force of 100 (N) on the master cylinder. The Delft Cylinder Hand was able to apply a pinch force of 19 (N) for an activation pull force of 100 (N) [2]. The maximum pinch force which could be applied during the pull test was 9.3 (N). Increasing the activation force resulted in an unstable grip and the load cell slipped out of the grip of the prosthesis. In the pinch test also larger objects where grasped during the force measurements. Figure 22 shows the measured pinch force for increasing activation forces. It could be seen the results were better for larger objects. The larger the object the larger the force transmission ratio. It could be seen in Figure 22 the slopes of the curves increase for larger objects. The average force transmission ratios are 0.19 (-), 0.28 (-) and 0.29 (-) while grasping the objects with a size of 35 (mm), 63 (mm) and 88 (mm) respectively. The force transmission ratio of the Delft Cylinder Hand during a pull test performed by Smit (2013) [2] on a load cell with a thickness of 10 (mm) was 0.24 (-). For objects with a size of 35 (mm) the force transmission ratios are large enough to apply the required 34

40 Grasping objects pinch forces. Also the initial activation force on the master cylinder becomes lower when the object size is increased. Figure 22 shows initial activation pull forces of 17 (N), 23 (N) and 27 (N) are needed on the master cylinder to start building up pinch force on the the objects with sizes 35 (mm), 63 (mm) and 88 (mm) respectively. These initial activation forces are comparable to the initial activation force for the original design. With the Delft Cylinder Hand an activation force 20 (N) is needed to start building pinch force on an object of 10 (N) thick [2]. On objects with a size of 35 (mm) and 63 (mm) pinch forces were applied of 14.9 (N) and 14.5 (N) respectively. The test protocol was to increase the activation force until a pinch force of 15 (N) was reached. The maximum pinch forces which could be applied on the objects were not measured. During the force measurements on the objects with size 35 (mm) and 63 (mm) the grip of the prosthesis in the object was stable for the measured pinch forces. Activation forces of 80 (N) and 90 (N) are needed to apply a pinch force of 15 (N) to objects with a size of 35 (mm) and 63 (mm) respectively. This is comparable to the activation force of about 85 (N) needed to apply a 15 (N) pinch force with the Delft Cylinder Hand. The required initial actuation force for the Delft Cylinder Hand was estimated using the graph presenting the results of the pull test in Smit (2013) [2]. A maximum pinch force of 9.5 (N) was applied to the object with a diameter of 88 (mm). Increasing the activation pull force caused the material of the thumb to deform plastically. The thumb is made of a bended aluminium plate. The material at the location of the bend was already weakened during the fabrication of the part. Because of the unfavourable direction of the force on the thumb the material failed for a low pinch force. The strength of the thumb should be increased to be able to apply a pinch force of 15 (N) or higher on an object with a size of 88 (mm). 4.4 Grasping objects Table 3 showed the prosthesis without cosmetic glove can grasp cylindrical objects with diameters from 50 (mm) up to at least 99 (mm). The grasping of objects with a diameter smaller than 50 (mm) did not result in a stable grasp. To pick up smaller objects a pinch grip is needed where the object is pinched between the finger tips and the thumb. The free grasping movements of the prosthesis without the cosmetic glove do not allow for a pinch grip of cylindrical objects without help. As discussed in Section 4.2 the finger phalanges move unevenly which complicates the grasping of objects. When a cosmetic glove is added to the prosthesis the finger movements are expected to improve. This could make the grasping of smaller objects possible. The cosmetic glove will also change the friction coefficient between the object and the prosthesis. A cosmetic glove possibly limits the total hand opening. This could decrease the maximum size of the objects which can be grasped with the prosthesis. The current design of the Delft Cylinder Hand can grasp small object. The prosthesis could pick up a pen or pinch a 1 (mm) plate [2]. The hand opening of the Delft Cylinder Hand is limited to 75 (mm). Increasing the maximum object size to 99 (mm) would be an improvement. The tested prototype with the actively moving thumb performed less well with the grasping of smaller objects. 4.5 Recommendations The volume fractions which go to the hydraulic cylinders of the fingers and the thumb should be adapted. These fractions are determined by the volume divider. A larger fraction of the displaced volume should go to the fingers then in the current design. It was observed when the hand was in fully closed position, depending on the object size and the grip type, in some cases the pinch force was limited. Increasing the activation force further did not increase the pinch force of the prosthesis. In these cases the thumb was at the end of its stroke and could not move further. Since not all fingers were either touching the object or where at the end of their stroke, the pressure in the hydraulic cylinders actuating the fingers was still low. This results in low finger forces. When a larger fraction of the displaced volume moves to the fingers, this could be avoided. It is advisable to integrate the function of the volume divider with the master cylinder. The volume divider causes a large amount of friction. The friction is caused by the 2 added o-rings to 35

41 the piston of the volume divider. The large diameter of the current volume divider also contributes to the large amount of friction caused by the o-rings. Concepts are conceivable to integrate the function of the volume divider with the addition of only 1 o-ring. The thumb should have a higher strength. The material of the thumb showed plastic deformation during some of the tests. The thumb could be made of a stronger material. Also the thickness of the thumb could be increased near the base of the thumb. The functional and mechanical performance of the prototype does not meet the requirements for small objects. Further research is needed to develop a the Delft Cylinder Hand with a movable thumb which meets the performance criteria for a larger range of object sizes. 5 Conclusion This study presents a design for a prosthetic hand with articulating fingers and a moving thumb. An actively movable thumb is added to the design of the Delft Cylinder Hand. The mechanism for the thumb movement adds 24 gram to the weight of the prosthesis. The total weight of the prosthetic hand (176 gram without glove and 241 gram with glove) is still 49 % lower than the lightest available voluntary closing body powered prosthesis. Test results show adding an actively movable thumb to the Delft Cylinder Hand is a promising improvement. It is possible to obtain an equilibrium between the thumb and the finger phalanges while grasping objects. An equilibrium could be reached regardless of the number of fingers making contact with the object. By adding an active thumb the grip size of the prosthesis is increased. Without cosmetic glove the grip size of the prosthesis is 99 (mm) compared to the 75 (mm) of the current design. Further testing with a cosmetic glove should determine if the grip size will be limited by the cosmetic glove. For small objects the performance of the proposed design is less than the current design of the Delft Cylinder Hand. The prototype has difficulty grasping cylindrical objects smaller than 50(mm) when no cosmetic glove is put on the prosthesis. Also the mechanical performance is less than for the Delft Cylinder Hand when grasping small objects. A pinch force of only 5.5 (N) can be achieved for an activation pull force of 100 (N) on the master cylinder compared to a pinch force of 19 (N) with the Delft Cylinder Hand for the same activation force. For larger objects the mechanical performance is comparable to the Delft Cylinder Hand. With the measured initial activation force and force transmission ratio the required pinch force of 30 (N) per finger can be achieved. This first prototype is promising and raises the expectations the Delft Cylinder Hand could be improved by adding an active thumb. Further research is needed to develop a the Delft Cylinder Hand with a movable thumb which meets the performance criteria for a larger range of object sizes. References [1] Erol, A., Bebis, G., Nicolescu, M., Boyle, R., and Twombly, X., A review on visionbased full dof hand motion estimation. In Computer Vision and Pattern Recognition - Workshops, CVPR Workshops. IEEE Computer Society Conference on, pp [2] Smit, G., Natural grasping. design and evaluation of a voluntary closing adaptive hand prosthesis. Proefschrift. [3] Charles M. Fryer, J. W. M., Atlas of Amputations and Limb Deficiencies, 3rd Edition. American Academy or Orthopedic Surgeons, ch. 6A, pp [4] Herder, J., and Munneke, M., Improving feedback in body powered prostheses. In Proceedings of XIV European Annual Conference on Human Decision Making and Manual Control, Delft University of Technology, Delft, The Netherlands, Vol. 14, p. 16. [5] Smit, G., and Plettenburg, D. H., Efficiency of voluntary closing hand and hook prostheses. Prosthetics and orthotics international, 34(4), pp

42 [6] Plettenburg, D. H., Prosthetic control: A case for extended physiological proprioception.. Proceedings of the 2002 MyoElectric Controls/Powered Prosthetics Symposium. [7] Sullivan, T., and Teh, K., Design and fabrication of a hybrid body-powered prosthetic hand with voluntary opening and voluntary closing capabilities. ASME 2011 International Mechanical Engineering Congress and Expositions, IMECE 2011, 2, pp [8] Plettenburg, D. H., Basic requirements for upper extremity prostheses: the wilmer approach. pp [9] LeBlanc, M. A., Innovation and improvement of body-powered arm prostheses: A first step. Clin Prosthet Orthot, 9(1), pp [10] Smit, G., Bongers, R. M., Van der Sluis, C. K., and Plettenburg, D. H., Efficiency of voluntary opening hand and hook prosthetic devices, 24 years of development?. JRRD: Journal of Rehabilitation Research & Development, 49 (4), [11] De Visser, H., and Herder, J., Force-directed design of a voluntary closing hand prosthesis. Journal of Rehabilitation Research and Development, 37(3), pp [12] Berning, K., Cohick, S., Johnson, R., Miller, L., and Sensinger, J., Comparison of body-powered voluntary opening and voluntary closing prehensor for activities of daily life. Journal of Rehabilitation Research and Development, 51(2), pp [13] Radocy, B., Voluntary closing control: a successful new design approach to an old concept. Clinical Prosthetics and Orthotics, 10(2), pp [14] Herder, J., Cool, J., and Plettenburg, D., Methods for reducing energy dissipation in cosmetic gloves. JRRD: Journal of Rehabilitation Research and Development, 35 (2), [15] Biddiss, E., and Chau, T., Upper limb prosthesis use and abandonment: A survey of the last 25 years. Prosthetics and Orthotics International, 31(3), pp [16] Smit, G., and Plettenburg, D. H., Design of a hydraulic hand prosthesis, with articulating fingers. Proceedings of the 2011 MyoElectric Controls/Powered Prosthetics Symposium Fredericton. [17] Zhang, X. c. d., Braido, P. e., Lee, S.-W. d., Hefner, R. f., and Redden, M. f., A normative database of thumb circumduction in vivo: Center of rotation and range of motion. Human Factors, 47(3), pp [18] Plettenburg, D. H., Hichert, M., and Smit, G., Feedback in voluntary closing arm prostheses. Proceedings of the 2011 MyoElectric Controls/Powered Prosthetics Symposium Fredericton,. [19] Coert, J. H., van Dijke, G. A. H., Hovius, S. E. R., Snijders, C. J., and Meek, M. F., Quantifying thumb rotation during circumduction utilizing a video technique. Journal of Orthopaedic Research, 21(6), pp Appendices 37

43 A Analysis A.1 Analysis - Abstract To predict the movements and forces a hydraulic prosthetic hand can make, analyses have been done. Kinematic models where created to describe the relations between the movements of the hydraulic cylinders and the movements of the phalanges of the fingers and the thumb. Assumptions were made to be able to predict the free grasping movement of the prosthesis. The concept of virtual work is used to obtain the force transmission ratios between the fingertips and the actuating hydraulic cylinders. The analyses show the force two fingers can exert on the object during grasping is about 19 N for most of the stroke when a force of 100 N is applied to the master cylinder. The analyses show low forces can be accomplished with the thumb. For the same input force of 100 N a thumb force of below 4 N is obtained for most of the stroke. It is shown increasing the thumb force will be at the expense of the amplitude of the movements of the thumb. With the current design, with the posed requirements for the thumb movements, it is not possible to obtain a force equilibrium during grasping. Concessions have to be made with respect to the design requirements or the design will have to changed. When the grasp forces of the hand are decreased the thumb could provide enough force to obtain an equilibrium. When only small thumb movements are allowed, the thumb could match the finger forces. An alternative for the design of the hydraulic hand could entail one or more extra hydraulic cylinders to actuate the thumb. Another design change could be to separate the hydraulic circuit of the thumb cylinder from that of the fingers. A.2 Analysis - Introduction Design requirements are set when designing a prosthetic hand. The prosthesis is designed to make certain movements and to apply a certain force. During the design of the hydraulic cylinder hand with an actively movable thumb these things were unknown. There is no model to predict the movements and forces exerted by the fingers of the Delft Cylinder hand. The impact of the addition of an actuated thumb is hard to predict. The aim of this study is do analyses to supply the needed information. The analyses need to comprise a kinematic model of the hand, a study of all internal and external forces on the hand and force equilibrium equations. The goal of the analyses is to provide the information to answer the following main questions: 1. How will the fingers and the thumb move when the prosthetic hand is actuated? What will be the free grasping movement? 2. Can an equilibrium be reached during the grasping of objects of various sizes? 3. What forces can be exerted by the prosthetic hand? In the next section the problem will be elaborated and the difficulties will be explained. Assumptions will be made to simplify the problem. Methods and analyses will be proposed to obtain the required information to answer the questions above. A.3 Analysis - Problem The addition of the thumb has a number of implications. The volume flow of the master cylinder, which was divided over the cylinders of the fingers, is now divided over the cylinders of the fingers and thumb. This influences both the movements of each phalanx and the force which is exerted by each hydraulic cylinder. To be able to design the prosthesis the movements of each phalanx of the fingers and the movement of the thumb should be predicted. Also the forces the prosthesis can exert should be predicted to be able to make a good design. The prediction of the movement of the phalanges is difficult. It is a complicated dynamical problem. The design of the hydraulic hand is an underactuated mechanism. The hand has more degrees of freedom than input signals to control. This means the configuration of the hand is 38

44 Analysis - Method dependent on the external forces on the hand. [2] Non-conservative forces, the internal friction and the hysteresis of the cosmetic glove, makes the problem time dependent. A dynamic force equilibrium is present at all times. To calculate the exact configuration of the hand a dynamical problem has to be solved. A.4 Analysis - Method A kinematic model is made for the hydraulic hand. The model includes three fingers and a movable thumb. The principle of the mechanism for the fingers will be the same as used as in the current prototype. The mechanism of the thumb will be the 1 DOF mechanism as described in Section The movements of the little finger and the forces exerted by the little finger are not included in the model. The little finger has a different mechanism than the other fingers. The little finger is actuated by a single hydraulic cylinder with a small diameter and exerts relatively small forces. It is excluded from the model to simplify the force equilibrium analyses. The volume of the hydraulic fluid displaced during movements of the master cylinder of the little finger are however taken into account. The actual movements of the little finger as a result of the movements of the actuating cylinder are not determined. The hydraulic cylinder actuating the little finger applies no work. The analyses will be done for this specific design of the hydraulic hand with the proposed mechanisms. The kinematic model is parametrized to optimize the geometry of the prosthetic hand during the design process. The analysis will be divided and presented in several steps. In each step a sub question will be answered which is needed to answer the main questions. The following sub questions are formulated: A.4.1 ˆ Which external forces act on the prosthetic hand? ˆ Which passive components are present in the hand and what is the contribution of these forces to the output forces? ˆ What are the kinematic relations between the phalanges of fingers and the actuating cylinders? ˆ What are the kinematic relations between the thumb and the actuating thumb cylinder? ˆ What are the transmission ratios between the actuation forces in the hydraulic cylinders and the output forces on the finger tips. ˆ What are the transmission ratios between the actuation force in the thumb cylinder and the output forces on the tip of the thumb. ˆ Which variables can be changed to obtain equilibria during grasping? ˆ Which variables can be changed to obtain the desired movements of the hydraulic hand? External Forces on the prosthetic hand The following internal and external forces act on the prosthetic device during a free grasping movement: ˆ The external input force on the shoulder harness provided by the muscles of the user. ˆ Internal friction forces. Internal friction occurs between the hydraulic fluid and the tubes and between the hydraulic fluid and the cylinders. All the hinges of the phalanges are subject to friction. The cylinders itself are subject to internal friction. Also friction occurs between the mechanical parts and the cosmetic glove. 39

45 Analysis - Method ˆ Elastic forces. The elastic forces of the cosmetic glove act on the prosthetic hand. Also the springs which are added to the fingers apply elastic forces on the phalanges. Furthermore the hydraulic fluid is compressible and the tubes have a limited stiffness, resulting in elastic behaviour as well. Many of these forces are difficult to predict. Also other phenomena make the analysis difficult. The following things are especially difficult to predict: ˆ The stiffness of the cosmetic glove is highly nonlinear and is progressive with the deformation [2,14] Furthermore the stiffness is highly dependent on how the glove is forced to deform. The movements of the prosthesis and the shape of the mechanical parts determine the stiffness. ˆ The friction between the cosmetic glove and the mechanical parts. The shape and material of the mechanical parts which are positioned inside the glove determine this friction as well as the relative movements of the mechanical parts with respect to the glove. ˆ The hydraulic hand is underactuated. The large number of degrees of freedom makes the movements hard to predict Testing could give further information about these topics. However since these forces depend highly on the specific design, generalization of the results is difficult. Force measurements on the specific design would be more useful. A.4.2 Assumptions To be able to make an estimation of the movements for design purposes some assumptions are made. ˆ The volume flow of the hydraulic fluid is divided equally between all hydraulic cylinders. ˆ The pressure is equal in all cylinders ˆ The forces exerted by the hydraulic hand are exerted by the tips of the fingers and thumb. A The volume flow of the hydraulic fluid is divided equally between all hydraulic cylinders. If the volume flow would be equally divided between all cylinders only one degree of freedom will remain in the system. All cylinder movements and phalanx positions are directly related the movements of the master cylinder. When the volume flow is evenly divided, the movement of each piston depends only on the piston area. Hydraulic cylinders with a small piston area move faster than cylinders with a large piston area. The assumption of an equally divided volume flow may be crude and not realistic in practice. In reality no constraint exists to prevent relative movements of each actuating cylinder. The only constraint is the total volume inside the system. How the volume is divided between the cylinders is not fixed. Internal and external forces will determine the actual movement of each hydraulic cylinder. However when the movements of the current prototype are observed. The movements seem to comply with the assumption of an equally divided volume flow. Small cylinders move faster than large cylinders. Cylinder of the same size move with the same speed. Adding a thumb to the same master cylinder will influence the movements of the fingers as well. The behaviour of such a prosthetic hand with an active thumb is difficult to predict. Making a prototype and examining the movements of each phalanx could give more information. For further analyses it is assumed the volume flow will divide equally over each hydraulic cylinder including the actuating cylinder of the thumb. 40

46 Analysis - Method A The pressure is equal in all cylinders This is not actually true, (compressibility of the oil, the elasticity of the tubes and) internal friction between the oil and the tubes are of influence. But this simplification allows us to model actuation forces more easily. A.4.3 A.4.4 Glove Compensation Analyse Actuation forces The thumb and the fingers will be evaluated separately. In the evaluation of the forces a number of elements are omitted: ˆ All the internal friction in the fingers and the thumb. ˆ The stiffness of the cosmetic glove. ˆ The stiffness of the added springs to the finger and the thumb. ˆ The stiffness of the hydraulic fluid is assumed to be infinite The reason for this simplification is to analyse the influence of the actuating cylinders only on the output forces. It will be determined if an equilibrium can be reached between the thumb and several fingers when grasping an object. A.4.5 A Thumb Kinematic relations The movements of the thumb can be described as a function of the movement of the cylinder that actuates the thumb. First the axis of rotation of the thumb should be described in the global coordinate system. The same rotation matrices as in section A are used. The mechanism is shown Figure 23. The geometry is depicted in a local fixed coordinate system, the X - Y - Z coordinate system. To transform from this local coordinate system to the global coordinate system two rotations are performed. Rotation around y: X = R y (δ)x Rotation around z X = R z (α)x total: X = R y (δ)r z (α)x We can now use a local coordinate system and transform this back to the global coordinate system using: With the rotation matrices: P global = P hinge + R y (α)r z (δ) P local (4) R y (α) = R z (δ) = cos(α) 0 sin(α) sin(α) 0 cos(α) cos(δ) sin(δ) 0 sin(δ) cos(δ) (5) (6) In the local coordinate system for the thumb we can describe the tip of the thumb with: P tip = R x (φ) P (φ=0) (7) 41

47 Analysis - Method With the rotation matrix: R x (φ) = cos(φ) sin(φ) 0 sin(φ) cos(φ) And P (φ=0) is the vector pointing to the tip of the thumb when θ = 0. The tip of the thumb in the global coordinate system is now given by: (8) P global = P hinge + R z (δ) R y (α) R x (φ) P (φ=0) (9) All parameters are fixed and are design dependent except φ which is the thumb rotation. For a given design the location of the tip of the thumb in global coordinates Pt(φ) is only a function of φ. φ t C B z φ 0 A y Figure 23: Kinematic model for the thumb. The hydraulic cylinder is displayed in blue, the thumb cantilever is displayed in orange. The model is used to describe the relations between the movements of the hydraulic cylinder and the thumb. The relations between φ and s t are obtained using Figure 23. First obtain the vector s t connecting the hinges of the cylinder actuating the thumb: [ ] [ ] cos(φ) sin(φ) bx s t (φ) = B(φ) C = C (10) sin(φ) cos(φ) b y [ ] bx The vector C is given by the design parameters. The vector is contains the coordinates of B for φ = 0 and is also given by the design parameters. The length of the cylinder s t (φ) is obtained by taking the length of the vector s t (φ). A Static forces relations The relation between the forces in the actuator of the thumb and the force applied by the fingertip can be found using the kinematic relations and virtual work. The coordinates of the tip of the b y 42

48 Analysis - Method thumb is given by: Pt(φ) = x t (φ) y t (φ) z t (φ) (11) The virtual work applied by the cylinder of the thumb is equal to the virtual work applied by the tip of the thumb. This gives the relation between the forces: resulting in: δw cylinder = δw tip (12) F cylinder δs t = F x δx t + F y δy t + F z δz t (13) F cylinder = [ δxt δs t The Jacobian J t can be found by using: J t = [ δxt δs t δy t δs t δy t δs t ] δz t F x δs t F y F z ] [ δz t δs t = δxt δφ δy t δφ = J t F t (14) δz t δφ ] δφ δs t (15) Where the first term can be found by differentiating the found relation in 9 with respect to φ. The second term follows from the kinematic relations between s t and (φ) from Section A Taking the derivative of s t (φ) with respect to (φ) gives the second term in the equation. A.4.6 A Fingers Kinematic relations In Figure 24 a 2D model is shown for the fingers. Each coordinate is described in the global coordinate system (x, y), local coordinate system 1 (x, y ) or in local coordinate system 2 (x, y ). Each point in the local coordinate systems can be described in the global coordinate system using translations and rotations. x p = x c + R(φ)x p (16) [?] with: x p, the coordinates of point p in the global coordinate system. x c, the origin of the local coordinate system in global coordinates. R(φ), A rotation matrix describing the rotation of the local coordinate system with φ. [ ] cos(φ) sin(φ) R(φ) = sin(φ) cos(φ) Point E is a point with known coordinates in local coordinate system 1. [ ] E ex = e y Point E is also the origin of local coordinate system 2. Point E, as any point with known coordinates in local coordinate system 1, can be described in global coordinates with: [ ] [ ] E = R(φ 1 ) E cos(φ1 ) sin(φ = 1 ) ex (19) sin(φ 1 ) cos(φ 1 ) e y (17) (18) 43

49 Analysis - Method F ext G φ 2 x H F E x y φ 1 x Cylinder2 B A y y C Cylinder1 D Figure 24: Kinematic model for the fingers. The hydraulic cylinders are displayed in blue, the finger phalanges are displayed in orange and the mechanical springs are displayed in black. The model is used to describe the relations between the movements of the hydraulic cylinders and the finger phalanges. Point G is the fingertip and has known coordinates in local coordinate system 2. [ ] G gx = g y (20) Point G, as any point with known coordinates in local coordinate system 2, can be described in global coordinates with: G = E + R(φ 2 ) G = [ cos(φ1 ) sin(φ 1 ) sin(φ 1 ) cos(φ 1 ) ] [ ex e y ] [ cos(φ2 ) sin(φ + 2 ) sin(φ 2 ) cos(φ 2 ) ] [ gx g y ] (21) A Static forces relations Each finger has two degrees of freedom. When the finger closes around an object entirely, and both phalanges touch the object, no degrees of freedom remain. When only the tip of a finger touches the object, but it is fixed in x and y direction, also no degrees of freedom remain. However 44

50 Analysis - Method when the friction between the tip of the finger and the object is low, the tip of the finger can slip and move across the surface of the object. In that case one degree of freedom remains. If no equilibrium is reached for all moments around E, the pose of the finger will change. It is desirable to obtain an equilibrium around point E when applying a force with the finger to prevent this movement. Figure 25 shows simplified fingers with the external force on the tip of the finger and the applied moments to the first (M 1 ) and the second (M2) phalanx. The moments M 1 and M 2 are applied by the actuating hydraulic cylinders. Figure 25 illustrates what happens if the moments around point E are not in equilibrium. The initial pose of the finger is displayed without color, the new pose is displayed in color. On the left side is displayed how the pose of the finger will change when M 2 is too low. The finger will slip over the surface of the object and stretch. The right side of the picture displays how the pose of the finger will change when the moment M 2 is too high. The finger will slip over the surface of the object and bend further. F ext G G G F ext G M 2 E E M 2 E E x x M1 M1 A y A y Figure 25: Simplified fingers illustrating movements of the fingers in a non-equilibrium situation. The moments M 1 and M 2 are applied by the actuating hydraulic cylinders. On the left the situation when M 2 is too low. On the right the situation when M 2 is too high. The friction forces between the fingertip and the object, the friction forces in each hinge and the friction forces due to the cosmetic glove will contribute to the sum of the moments around each hinge. Small errors in the torques in the hinges will be compensated by the friction. The friction will prevent the finger to make the undesired movements displayed in Figure 25. It is one of the design challenges to obtain an equilibrium in all poses of the fingers. For the rest of this chapter it is assumed only friction exists between the tip of the finger and the object. Furthermore it is assumed the friction is high enough to keep the tip of the finger in place. This results in a constraint on the finger tip in x and y direction. The finger has no more degrees of freedom. The relation between the forces in the actuators of the finger and the force applied by the fingertip can be found using the kinematic relations and virtual work. The coordinates of the tip of the finger is given by: 45

51 Analysis - Method G(φ 1, φ 2 ) = x g(φ 1, φ 2 ) y g (φ 1, φ 2 ) z g (22) The fingers of the prosthetic hand touch the object. The accelerations and speeds of the prosthetic hand are assumed to be zero. The total virtual work applied to the finger is then equal to zero. The sum of the virtual work applied by the cylinders to the finger and the virtual work applied by the object to the tip of the finger is equal to zero. δw cylinder1 + δw cylinder2 + δw object = 0 (23) If we take the forces applied by the tip of the finger to the object positive we obtain the following relation between the forces: F cylinder δs 1 + F cylinder δs 2 = F x δx t + F y δy t + F z δz t (24) This must be true for all possible virtual displacements δs 1 and δs 2 independently. This results in the set of equations: [ ] [ ] δxg δy g δz g Fcylinder1 δs = 1 δs 1 δs 1 = J F g F g (25) cylinder2 δx g δs 2 The Jacobian J g can be found by using: J T g = δx g δs 1 δy g δs 1 δz g δs 1 δx g δs 2 δy g δs 2 δz g δs 2 = δy g δs 2 δx g δφ 1 δy g δφ 1 δz g δφ 1 δz g δs 2 δx g δφ 2 δy g δφ 2 δz g δφ 2 F x F y F z [ δφ1 δs 1 δφ 2 δs 2 δφ 2 δφ 1 δs 1 δs 2 Or using a short hand notation according to Einstein s convention: ( ) ( ) δx i δxi δφj = δs k δφ j δs k Where the first term can be found by differentiating the found relation in 9 with respect to φ. The second term follows from the kinematic relations between s t and (φ) from Section A Taking the derivative of s t (φ) with respect to (φ) gives the second term in the equation. A.4.7 Force transmission ratio for the fingers The user applies a force to the master cylinder. This results in an increase in the pressure in the system. The pressure is assumed to be constant in all cylinders. p = Fm A m The forces in the hydraulic cylinders of the fingers are dependent only on the force in the master cylinder and the piston areas. The relation between the forces in the cylinders actuating the finger and the force in the master cylinder is given by: [ ] [ ] [ ] Fcylinder1 A1 F c = = p = F F cylinder2 A m A1 1 A2 (28) 2 A m A 1 And the force transmission ratios between the actuation forces in the hydraulic cylinders and the output forces on the finger tips follow from 9: [ ] F g = J 1 Fcylinder1 g (s 1, s 2 ) (29) F cylinder2 Where J 1 g is the pseudoinverse of J g. ] (26) (27) 46

52 Analysis - Method Combining these formulas gives the fingertip forces: F g = F m A1 A m J 1 g (s 1, s 2 ) [ 1 A 2 A 1 ] (30) A.4.8 A Variables to change Force transmission ratios Fingers - Variables The geometry of the fingers is determined by the connection points A G. The coordinates of these points can be changed to change kinematics of the mechanism. There are however restrictions when changing the geometry. The dimensions of the fingers are adapted to normative values of the human hand. Also the mechanism should fit inside a cosmetic glove. Therefore the coordinates of the points A, E and G are fixed. The mechanism could be changed by changing the coordinates of B, C, D, F and H. Other variables which can be changed are the hydraulic piston diameters A 1 and A 2 of hydraulic cylinder 1 and 2 respectively. The coordinates of B and H determine the spring force between the phalanges. The spring force does influence the fingertip force but is not relevant for the force transmission ratios. The fingertip forces are a result of the moments applied by the hydraulic cylinders. The amplitude of these moments are a function of the cylinder forces and the effective moment arms of the cylinders on which the forces are applied to the phalanges. The cylinder forces are a direct function of their piston areas A 1 and A 2. The moment arms can be described by the functions: R 1 (φ 1 ) = AC sin(φ 1 + ψ 1 ) R 2 (φ 2 ) = EF sin(φ 2 + ψ 2 ) Where ψ 1 and ψ 2 are constants depending on the geometry. The maximum amplitudes of the moments applied by the cylinders are thus depending on A 1 and AC for cylinder 1 and on A 2 and EF for cylinder 2. The angle ψ 1 is dependent on the coordinates of D and C. The angle ψ 2 is dependent on the coordinates of B and F. The angles ψ 1 and ψ 2 determine at which moment in the cylinder stroke the moment arm, and thus the fingertip force is at a maximum. Therefore we can conclude the force transmission ratios are mainly dependent on A 1, AC, A 2 and EF. To lesser extend the coordinates B, C, D and F influence the transmission ratios. A Thumb - Variables For the thumb we can do a similar reasoning. The geometry is determined by the connection points A t, B t, C t and P t. Normative values for the dimensions of a human hand restrict the choice of the coordinates A t and P t. Also the required thumb movements restrict these coordinates. The coordinates B t and C t can be changed to optimize the thumb force transmission ratios and movements. The piston area (A t ) of the hydraulic thumb cylinder is another variable which can be changed to change the movements and forces. The cylinder force is directly dependent on the piston area A t. The thumb force is a result of the moment applied by the hydraulic cylinder. The amplitude of this moment is a function of the cylinder force and the effective moment arm of the cylinder. The effective moment arm R t can be described by the function: R t (φ t ) = A t B t sin(φ t + ψ t ) Where ψ t is a constant depending on the geometry. The maximum amplitude of the moment applied by the thumb cylinder is thus depending on A t and A t B t. The angle ψ t is dependent on the coordinates of B t and C t. The angle ψ t determine the location in the cylinder stroke where the moment arm, and thus the fingertip force is at a maximum. The force transmission ratio of the thumb is mainly dependent on A t and A t B t. The coordinates B t and C t can also be changed to influence the force transmission ratio. 47

53 Analysis - Results A.4.9 Variables to change the movements of the hand The same variables which influence the force transmission ratios influence the movements of the prosthesis. The movements of the finger phalanges ( δφ δs ) are mainly dependent on A 1, AC, A 2 and EF. The coordinates B, C, D and F also influence the movements of the finger phalanges but are less effective. The last mentioned coordinates determine mainly where in the stroke the maximum of δφ δs is located. The movements of the thumb ( δφt δs ) are mainly dependent on A t and A t B t. The coordinates B t and C t also influence the movements of the thumb. A.4.10 Combine the models of the Thumb and the hand Both mechanisms are described in terms of global coordinates. It is now possible to simulate all movements as a function of the input stroke of the master cylinder. For each position of the stroke it is possible to calculate the finger forces and the thumb force. A vector describing the object, V object, will be created pointing from the tip of the thumb toward the tip of the index finger. The thumb and finger forces are assumed to be in the direction of V object. A.5 Analysis - Results A.5.1 Current Force transmission ratios of the fingers Figure 26 presents the force transmission ratios for the current design. The transmission ratio for each force component is plotted as well as the magnitude of the force exerted by the fingertip Force Transmission Ratio Fg x /F m Fg y /F m Fg z /F m Fg /F m Transmission ratio [ ] stroke [ ] Figure 26: The force transmission ratios between the master cylinder and the finger tip for increasing stroke of the master cylinder. The master cylinder stroke ranges from 0% (stroke=0) to 100% (stroke=1). The force transmission ratios for the fingertip forces in x, y and z direction are displayed as well as the force transmission ratio of the amplitude of the fingertip force. The force transmission ratio of the amplitude of the fingertip force is about 0.1 for the whole stroke. An activation force of 100 (N) applied to the master cylinder will cause a fingertip force of about 10 (N) on the fingertip for the whole stroke. 48

54 Analysis - Results 0.04 F t /F m Transmission Ratio [ ] stroke [ ] Figure 27: The force transmission ratio between the master cylinder and the tip of the thumb for increasing stroke of the master cylinder. The master cylinder stroke ranges from 0% (stroke=0) to 100% (stroke=1). The force transmission ratio of the thumb ranges from 0.02 to 0.04 (-). An activation force of 100 (N) applied to the master cylinder will cause a thumb force of about 2-4 (N). A.5.2 Force transmission ratio of the thumb. The thumb mechanism was adjusted to make the desired movement when the master cylinder is actuated. In Figure 27 the force transmission ratio is shown for a design of the thumb mechanism which meets the design requirements with respect to the movement of the thumb. It can be seen the force transmission ratio between the master cylinder and the thumb are low. The prosthesis will be able to apply low grasp forces with this design. A.5.3 Grasp forces of the hand Figure 28 shows the forces of the hand when an object would be grasped while exerting a force of 100 N on the master cylinder. The figure shows the force two fingers would apply to the object and the force the thumb would apply to the object as a function of the stroke. The forces are assumed to be in the direction of the vector V object pointing from the tip of the thumb towards the tip of the index finger. The force exerted by two fingers is about 19 N for most of the stroke. The force ranges from 11 N at the beginning of the stroke to 19.6 N at about 70 % of the stroke and to 16.6 N at the end of the stroke. The thumb force is very low. As a result of this no equilibrium will be reached between the thumb and the fingers. Also the grasp force of the prosthesis is restricted to the force the thumb is able to exert. This will result in maximum grasp forces from 2.5 to 11.3 N. A.5.4 Increasing the thumb force Increasing the force transmission ratio of the thumb could be accomplished by changing the variables A t and A t B t. However the movements of the thumb are also determined by these variables. 49

55 Analysis - Results 20 2 Fingers Thumb 15 F [N] stroke [ ] Figure 28: The finger and thumb forces as a function of the master cylinder stroke. The open configuration of the prostheses corresponds with the master cylinder stroke at 0% (stroke=0), the fully closed configuration corresponds with the master cylinder stroke of 100% (stroke=1). The thumb force should be increased, and be equal to the force of 2 fingers, to be able to grasp the object. Figure 29 shows the effects of increasing piston area A t. The piston area is increased to 2 times and 4 times the initial piston area. The forces and movements are plotted as a ratio of the desired forces and movements. In this case the thumb is required to supply the force to counteract two fingers. The ratios for the force and the movement are given by R F = Ft 2F f and R φt = φt Φ thumb respectively. Where: F t, F f, φ t and Φ thumb represent the actual thumb force, the effective force applied by 1 finger, the actual thumb angle and the desired thumb angle respectively. It can be seen in the figure an increased piston area indeed increases the thumb force but also decreases the thumb movement. Even with 4 times the piston area the thumb can not supply enough force to oppose two fingers. Only 53 to 89 % of the required force can be supplied. The rotation of thumb starts at the desired angle and soon starts to lag behind, resulting in too small thumb movements. Figure 30 shows the effects of an increasing moment arm r. The moment arm is the length of the vector A t B t. The moment arm is increased to 2 times and 4 times the initial moment arm. Also in this figure the thumb is required to supply the force of two opposing fingers. An increased moment arm increases the thumb force and decreases the movement of the thumb. When the moment arm is increased to 4 times the initial moment arm, the thumb force is higher than the required force for the beginning of the stroke (152 %) and decreases during the stroke to only 56 % of the required force. However the movements of the thumb are decreased by this change. 50

56 Analysis - Discussion Thumb Angle and Force Ratios [ ] R phi, At R, 2At phi R phi, 4At R F, At R F, 2At R F, 4At stroke [ ] Figure 29: Thumb angle and Force ratios for increasing piston area. The thumb force and angle are displayed as a fraction of the desired value. Both the angle ratio R φ and the force ratio R F should be equal to 1. The ratios are displayed for a master cylinder stroke ranging from 0% (stroke=0) to 100% (stroke=1). The figure shows increasing the piston area to 2 and 4 times A t does increase the thumb force but lowers the thumb movement. A.6 Analysis - Discussion The thumb mechanism was adjusted to make the desired movements. 1,2 or 3 opposing fingers It was shown in section A.5.2 the force transmission ratio of the thumb mechanism is low. For this design the prosthesis will be able to apply low grasp forces. The variables which can be used to change the movements of the thumb and the thumb force are presented in section A.4.9. However difficulties present themselves when it is tried to increase the thumb force while making the desired thumb movement. The piston area A t and the moment arm, represented by the length of the vector A t B t, have the largest influence on the thumb force. However by increasing these variables to increase the thumb force the movements of the thumb are decreased. The figures 30 and 30 display the ratio of the actual force with respect to the required force and the ratio of the actual thumb angle with respect to the desired thumb angle. The figures show increasing the thumb force will be at the expense of the thumb movement. This is expected since the amount of work done by the thumb remains the same. The force applied by the tip of the thumb is a function of the moment applied by the hydraulic cylinder to the thumb. And the sum of virtual work applied to the thumb by the moment created by the external force and the virtual work applied by the cylinder force is equal to 0. This gives the equilibrium equation: Mδφ t + F cylinder δs = 0 This gives for the moment applied by the external force: M = δs δφ F cylinder The movements of the tip of the thumb are a function of the thumb angle φ t. An infinitesimal 51

57 Analysis - Discussion Thumb Angle and Force Ratios [ ] R phi, r R, 2r phi R phi, 4r R F, r R F, 2r R F, 4r stroke [ ] Figure 30: Thumb angle and Force ratios for increasing moment arm. The thumb force and angle are displayed as a fraction of the desired value. Both the angle ratio R φ and the force ratio R F should be equal to 1. The ratios are displayed for a master cylinder stroke ranging from 0% (stroke=0) to 100% (stroke=1). The figure shows increasing the moment arm to 2 and 4 times r does increase the thumb force but lowers the thumb movement. increase of the thumb angle can be expressed as a function of an infinitesimal increase of the cylinder length: φ t = δφ δs s t The thumb force is thus a function of δs δφ while the movements are a function of the inverse of this derivative: δφ δs. Therefore it is evident an increase of the thumb force is always at the expense of the thumb movements. Other variables, the coordinates of B t and C t, do change the shape of the curves for the ratios but do not have large effect on the amplitudes of the thumb force and the movements. Also these variables change both the thumb force and the thumb movement. These variables can however be used to shift the force transmission ratio curve. This can be used to design specifically to obtain the highest transmission ratios at the beginning of the stroke or towards the end. The hand prosthesis can only effectively grasp objects when an equilibrium is reached during grasping. It is not possible to accomplish this within the current design requirements. To obtain an equilibrium during the grasping of objects concessions should be made with regard to the design requirements. A possible concession is to decrease the grasp forces of the hand. In that case the thumb could provide enough force to obtain an equilibrium. The forces of the fingers should be decreased to accomplish this. A new challenge arises in that case because the variables which change the finger force also influence the movements of the fingers. A way to decrease the finger forces without increasing the movements could be to counteract the finger forces using passive components. The disadvantage of such an approach is that the efficiency of the prosthetic hand will be drastically lowered which is undesirable. Another concession is to allow only small 52

58 Analysis - Conclusion thumb movements. When the thumb movements are low the thumb can provide enough force to oppose two fingers. It is also possible to acquire an equilibrium for only a part of the stroke. The force transmission ratio of the thumb could be low for a certain part of the stroke and high for the remainder of the stroke. It is then possible to obtain the required thumb movements and still being able to grasp objects for a specific hand opening. This would however decrease the functionality of the prosthesis for a large part of the stroke. When changes are made in the design it may be possible to acquire a force equilibrium during the grasping of objects. For example one or more extra hydraulic cylinders could be added to actuate the thumb. The actuation force could be increased without changing the movements of the thumb. Another design change could be to separate the hydraulic circuits of the thumb cylinder and the cylinders of the fingers. The hydraulic cylinder of the thumb could then be actuated with a higher pressure to increase the thumb force. Future research could focus on implementing changes in the design in the model. Furthermore the assumptions made for the models could be checked. Especially the assumption of an equally divided volume flow between all hydraulic cylinders has a large impact on the presented results. When this assumption does not hold in practice the conclusions presented may not be valid. It will also be of interest to check the assumption all forces are exerted by the tips of the fingers and thumb. The use of other contact points may also have an effect on the results. A.7 Analysis - Conclusion This paper presents the analyses done to provide the information needed during the design of a hydraulic cylinder hand with an active thumb. Simplifications had to be made and assumptions have been done to be able to model the hand. A kinematic model has been provided and used to predict the forces and the movements of the fingers. The model is extended to include the actively moved thumb. The influence of the active thumb on the behaviour of the prosthesis is discussed. The free grasping movement of the prosthesis is simulated and the forces applied by the fingers and thumb are calculated. It was found that for the current design requirements the proposed design will not be able to effectively grasp objects. No force equilibrium can be reached between the forces the fingers and the thumb apply to the grasped object. Concessions have to be made with respect to the design requirements or the design will have to revised. 53

59 B Appendix - Normative values for maximum voluntarily applied grip and pinch forces, a systematic review 54

60 Normative values for maximum voluntarily applied grip and pinch forces, a systematic review Eric W.L. Versluis Graduate student BioMechanical Engineering Department of Mechanical Engineering Technical University of Delft eric.versluis@gmail.com During the design of a prosthetic hand, information is needed about the requirements the prosthesis should meet. The purpose of this systematic review is to provide information about the maximum grip and pinch strength of healthy subjects without upper extremity defects and serve as a basis for composing the design requirements of a prosthetic hand. A systematic search of databases is performed to gather literature containing normative values for grip and pinch strength constructed for upper extremity evaluation. A total of 137 articles, found during the conducted searches, were screened or read to assess eligibility based on the determined selection criteria. The results of 11 studies were included and used in a comparative analysis. Inter subject differences in age, gender, anthropometry, occupational demand and hand dominance have been shown to correlate with the maximum voluntarily applicable grip and pinch strength. Method related differences between studies as posture, instrumentation, calibration, measurement scoring type and fatigue have been shown to affect the obtained results. Although using different populations, measurement instruments, scoring methods and other method related characteristics, the included studies for comparative analysis presented consistent results. The maximum average grip strength is about 550 N for male subjects and about 340 N for female subjects. Age influence on grip strength is only minimally present for subjects between 20 and 60 years old and is not relevant when an estimate for maximum grip strength is needed. Average maximum pinch forces range, depending on pinch type, from 80 N to 100 N for male subject and from 55 N to 80 N for female subjects. 1 INTRODUCTION During the design of a prosthetic hand device, design requirements will be formulated. Research should be done on how the prosthetic hand is used, for which tasks the hand will be used and what forces will be on the hand during the use of the prosthesis. Information about the desirable maximum voluntarily applied forces with a prosthetic hand is of great interest when composing these requirements. However no clear reference values exist for this purpose. Therefore it will be of interest how much force a healthy person can exert with the hand. This information could then be implemented in the design requirements. In this review the focus will be on the maximum gripping forces a healthy person can exert with the hand. Since a lot of research has been done to construct normative values of hand strength for upper extremity evaluation, a large quantity of data exists on this subject. These normative values could give an indication of the maximum voluntarily applied forces by a normal hand. Since the prosthetic hand will replace a healthy hand in the daily tasks, the forces a prosthetic hand needs to exert in these tasks will be related to the maximum applicable forces by a healthy hand. Normative values of maximum grip and pinch forces are needed during assessing a patients hand function to compare it to a healthy population. In addition, normative data are needed to interpret evaluation data; to set realistic treatment goals; and to assess a patient s ability to return to employment. [1]. Hand grip evaluation can give an indication of a persons fitness. Also hand grip strength is a measure of the up- 1 55

61 per extremity function. Bohannon stated that hand grip dynamometry could provide a valid indication of upper extremity strength [2]. For this purpose a lot of research has been done to supply reference values for specific measurement instruments and specific populations. The study by Everett and Sills in 1952 was one of the early studies in this field. At this time a person s grip strength was already used as a measure of physical fitness [3]. The norms used at the time were stratified by age, weight and classification index categories. The Jamar dynamometer was introduced as a measurement instrument to assess grip strength by Bechtol in 1954 [4]. The hydraulic Jamar dynamometer later became the most used instrument for grip strength evaluation for medical purposes. The American Society of Hand Therapists (ASHT) proposed a standardized protocol regarding posture and upper extremity positioning, during hand strength measurement [5]. The ASHT recommended the tested individual should be comfortably seated and positioned with the shoulder adducted, the elbow flexed at 90 o, and the forearm and wrist in neutral position [5]. Mathiowetz et al. (1985) adopted the standardized protocol from the ASHT and also recommended a standardized method concerning instrumentation, instructions to subjects, the measurement scoring type and calibration [1]. Most studies since 1985 establishing norms for grip strength evaluation use the standardized method as recommended by ASHT and Mathiowetz et al. Mathiowetz et al. recommended the Jamar dynamometer for measuring grip strength [1]. They claimed the instrument had the highest test-retest reliability at the time. Therefore the majority of the studies adopted the Jamar dynamometer as their measurement instrument. The aim of this systematic literature review is to determine the desirable maximum voluntarily applicable force with the prosthetic hand. For this a comparison will be made with the functional abilities of healthy individuals. Data from selected studies will be presented next to each other for comparison. This review will function as a basis for composing design requirements of a prosthetic hand device. 2 METHODS The following databases were used during the literature search: Scopus and Pubmed. These databases where searched between the 1 st of January and the 11 th of March Also a number of articles were brought to attention by colleagues. These articles were added to the search results database. A literature search was conducted using the Scopus library searching for articles with the word grip or pinch in the article title and with the words normative data or normative values in the title, abstract or key words. This results in the search query (search #1): TITLE(grip OR pinch) AND TITLE-ABS-KEY( normative data OR normative values )) A literature search was conducted using the Pubmed library searching for articles with the word grip or pinch in the article title and with the words normative data or normative values in the title, abstract or key words. Since we are interested in the data of healthy individuals only, the articles that contain one of the words disorder, syndrome or deficiency are excluded from the search. This results in the query for Pubmed (search #2): (grip[title] OR pinch[title]) AND ( normative data [Title/Abstract]) NOT ((disorder[title] OR syndrome[title]) OR deficiency[title]) During the reading of the full-text articles it was noticed relevant articles found in the reference lists were not included in the database of searched articles. An additional search was done in both Scopus and Pubmed to obtain a more complete database. The terms grip strength and hand strength were used in the database search in combination with one of the terms normative data, normal values, normative values or reference values. A literature search was conducted using the Scopus library searching for articles with the search query (search #3): TITLE( grip* strength OR hand strength ) AND TITLE-ABS-KEY( norm* data OR norm* values OR reference values ) A literature search was conducted using the Pubmed library searching for articles with the words grip strength or hand strength in the article title and with one of the combination of words: normative data, reference values, normal data or normal values in the title or abstract. This results in the query for Pubmed (search #4): ( grip strength [Title] OR hand strength [Title]) AND ( normative data [Title/Abstract] OR reference values [Title/Abstract] OR normal data [Title/Abstract] OR normal values [Title/Abstract]) Because the used method differed greatly per study, comparison between studies may not be justified. Therefore selection criteria will be introduced to decrease the discrepancies between studies as a result 2 56

62 (a) Key pinch [6] (b) Palmar pinch [6] (c) Tip pinch [6] (d) Grip strength [7] Fig. 1: Three different types of pinch strength and grip strength, finger positioning of the used method. Although the used instrumentation and the method to score grip strength have been shown to influence the results it was chosen to include studies with a different method regarding these variables. On the subject of instrumentation it is important the measured values are representative to the underlying quantity; the grip or pinch strength of a subject. There is no preference for a specific instrument. The precision, accuracy and the test-retest reliability of an instrument however are of importance. All identified articles were quickly screened by reading the abstracts and tested on compliance with the selection criteria. Apparent relevant articles were read in total and again tested on compliance with the selection criteria. Reference lists of these articles were also screened to find potentially relevant articles which are not included in the database of search results. The identified articles were selected for the comparative analysis using the following selection criteria: 1. The article should be written in the English language. 2. The article should contain measurement data about grip forces, tip pinch forces, key pinch forces or palmar pinch forces. In Figure 1 the finger positioning for measuring the grip strength and the different pinch types are displayed. 3. The data should be acquired using a clear described, preferably standardized protocol. The protocol should include a description of upper extremity positioning and finger positioning during the measurement. To be able to compare the selected 3 57