Design of a pneumatic hand prosthesis

Design of a pneumatic hand prosthesis An old approach revived K.H. ter Stege Report no: BMTE05.46 TU/e Internship Report 7 th December 2005 Supervisors: dr. ir. D.H. Plettenburg (TU Delft) Prof. dr. B.A.J.M. de Mol (TU/e) Eindhoven University of Technology Department of Biomedical Engineering Division Materials Technology Delft University of Technology Department of Mechanical Engineering Division BioMechanical Engineering

Contents Introduction v 1 General information 1 1.1 Grasping types.................................... 1 1.2 Little finger as support................................ 2 1.3 Force needed during grasp.............................. 3 1.4 Two moving phalanxes instead of three....................... 3 1.5 Power supply..................................... 4 1.6 Glove......................................... 4 1.7 Conclusions..................................... 5 2 Determining the parameters of the non-prosthetic hand 7 2.1 Literature data.................................... 8 2.1.1 Length of the fingers............................. 8 2.1.2 Thickness of the fingers........................... 9 2.1.3 Length of the palm of the hand........................ 10 2.1.4 Thickness of the hand............................ 10 2.2 Experimentally specified parameters......................... 10 2.2.1 Length of the phalanxes........................... 11 2.2.2 Angle between the points of application of the fingers............ 11 2.2.3 Angle between the fingers and the thump.................. 14 2.2.4 Length of the palm of the thumb....................... 14 2.2.5 Angle within the fingers and the thumb in the resting state.......... 14 2.2.6 Final angle of the little finger......................... 15 2.2.7 Angles in the fingers in a semi-closed and a closed position......... 17 2.3 Discussion...................................... 18 2.4 Overview of all the parameters............................ 18 3 Force delivered by the prosthesis 21 3.1 Open prosthesis................................... 21 3.2 Closed prosthesis.................................. 21 3.3 Formulas to calculate the force within the prosthesis................ 27 3.3.1 Force at the piston.............................. 27

iv 3.3.2 Force at Gear D................................ 30 3.3.3 Force at the tip of the finger......................... 30 3.3.4 Assumptions................................. 31 3.4 Calculation of all forces................................ 32 3.4.1 Even the forces................................ 32 3.4.2 Force in grasping huge objects........................ 33 3.5 Conclusion...................................... 33 4 Working drawings 35 4.1 Building blocks of the design............................. 35 4.1.1 The piston................................... 35 4.1.2 Gears..................................... 35 4.1.3 Supporting frame............................... 37 4.2 Unigraphics design.................................. 37 4.2.1 The Piston.................................. 37 4.2.2 Gears..................................... 37 4.2.3 Supporting frame............................... 37 5 Conclusion 41 6 Recommendations 43 I Experiment data 45 I.1 Length of the phalanxes............................... 45 I.2 Angle between the points of application....................... 47 I.3 Angles within the fingers and the thumb in the resting state............. 50 I.4 Final angle of the little finger............................. 50 I.5 Angles in the fingers in a semi-closed and a closed position............ 51 II The m-file to calculate the forces 53 Bibliography 60

Introduction When researchers on pneumatically prosthesis tried to create an overview of all the pneumatically prosthesis ever designed [7], they encountered a design in a review created in the early 1900 s. Very less is known about this design; who made the drawings, if the design was ever created in real and of course if the design was ever used. All known is that Schlesinger took it up in his book in 1919 [1]. All that he showed was the design that can be seen in Figure 1. Figure 1: Anonymous design of a pneumatic prosthesis This design is pretty interesting because the four fingers are moved separately, but the four pistons operate on one gas supply. This leads to a natural looking hand prosthesis. When the myoelectric prosthesis came up in the late 1960 s [11], [12] they proved to be functional and pretty good manageable. In a short time these prosthesis were so much improved this lead to a kind of a catastrophe for the pneumatic powered prosthesis. This because most of the research was

vi now focused on the improvement of the myo-electric prosthesis. This chapter first explains why the anonymous design needs investigation and after that explains how all this is dealt with. If one looks at figure 1 a little longer, some things will catch the eye: The whole hand is actuated by only one gas-supply The hand has only two bending points instead of three bending points, the third phalanx seems fixed The thumb is situated under a 90 angle with respect to the other fingers The pistons are moved back to their initial state with a spring The force delivered by the piston is carried over on a wheel, that is joined to another wheel (that simulates the second knuckle) This design can be seen as a interesting design on the whole. A lot of interesting and innovating solutions are sketched. The main problem is that no technical information of the prosthesis is available except for the sketch. In order to try to create this prosthesis and give it a new life the assignment of this internship is: Create 3D-CAD drawings of the anonymous prosthesis (figure 1) The following additions should be taken into account: - Make sure the prosthesis looks as natural as possible - Little adaptations to the design can be made - Make sure the prosthesis has the right force-delivery To come to these 3D-CAD drawings several specifications and calculations have to made. One has to know what types and amounts of forces influence a simple grasp, but first of all what kind of grasp will be used in the prosthesis. This kind of specifications can be found in Chapter 1. Furthermore it is necessary to know what the most natural bending angles of the fingers are (see Chapter 2). This information together can lead to a specific calculation of the force as is done in Chapter 3. The last Chapter shows a summary of the most important 3D-CAD drawings made for this prosthesis.

Chapter 1 General information In the introduction it is mentioned that some specifications about the kind of grasps and other points need to be given before any real calculations can be done. In this chapter several of these specifications are pointed out. 1.1 Grasping types When designing a prosthesis one of the first decisions you have to make is the kind of grasp you want the prosthesis to perform. In the design chosen the prosthesis is probably able to perform one or maybe two of the human hand functions. Only a few types of hand prehension patterns are used for prosthesis as can be seen in Figure 1.1 [2]. Here a separation can be seen in a 2-points (precision) grasp and the 3-point (precision) grasp. Both these grasps are best if the prosthesis is mainly designed to pick up little stuff. The main difference between those grasps is the fact that the picking up will occur with 2 or 3 fingers. Both these types have there own advantages. The 2-point precision grasp (Figure 1.1c) is a very precise grasp that allows the patient to grasp a flat paper without folding is. The disadvantage of this grasp is the fact that picking up a pencil can become difficult, because of the round forms of this object. Both the 3-point grasps, Figure 1.1a and 1.1b are palmar grasps. The 3-point precision grasp (Figure 1.1a) has the advantage that round objects like the earlier mentioned pencils don t slip away from the fingers, because the object can be tightened. When an object is picked up and held tight most people use a palmar grasp (Figure 1.1b). This grasp can be seen as a precision grasp that is not totally closed. In this design the 3-point precision grasping is used, because of the advantage of the tightening. In case a larger object is picked up, the three fingers will close around this object and the user will be able to pick up the larger object. Most of calculations are done on both the index finger and the middle finger in composition to the thumb, to make sure the prosthesis becomes as natural as possible.

2 1.2 Little finger as support Figure 1.1: Several hand prehension patterns [2] One advantage of this prosthesis with respect to the current ones not mentioned yet, is the fact that the force this prosthesis needs for the same firm grasp will be lower than the force used nowadays. The little finger has it s own piston and is allowed to move separately from the other fingers (on the same supply). This movement can be used as an advantage. The little finger can now be used as a bearing surface for the object that s picked up. In normal life many people use their little finger as a support-tool in picking up stuff as can be seen in Figure 2.6. Because the power supply of the little finger will keep producing force during a grasp it is necessary to build in a final position, for the little finger, at which it gets locked. Figure 1.2: Little finger as a support, bottom view

1.3 Force needed during grasp 3 This point should be located as central as possible, so that the picked up object is as stable as possible. In that case the force the prosthesis delivers can be lowered by far, because this force is now only needed to keep the object in balance and it s no longer the force to keep the object lifted. One of the advantages of this system (when optimized) is the fact that the prosthetic user should now able to pick up a plastic coffee mug. 1.3 Force needed during grasp The force applied on the object by a prosthesis nowadays is not known exactly. In literature the force your fingers deliver when they re grasping a mug or a stencil isn t found easily too. These values would be useful in prosthesis design and even more in this case where less force can be applied on the object. One remark that needs to be made is the fact that even when these forces are known precisely, they will only be useful if the force is compared to the force a prosthesis delivers. The amount of friction from your fingers to the mug is different from the amount of friction of the prosthesis to the mug. For this reasons it makes more sense to approach the force in comparison to the forces present prostheses deliver. For several prostheses the force they develop is known in a range. From a hook prosthesis for children is known to deliver a force around 6 N [8], a myo-electric prosthesis for adults delivers around the 160 N [13]. In comparison to a hook prosthesis for adults which delivers a force between 40 and 55 N (3 to 4 times less than a myo-electric prosthesis [16]). This clears up that a wide range is possible, but the least necessary force isn t known yet. The previous described advantage of this design makes it possible to let it function well when producing less force. Therefore the force needed is now considered to be between the 40 and 55 N. In Chapter 3 a calculation/ estimation of the force at the end of the fingers is made, because one wants to be sure if the design delivers enough force and of course how the force develops during action. 1.4 Two moving phalanxes instead of three Figure 1 shows five fingers with only two phalanxes instead of three. Experiences learn that prothetic carriers are unpleased with such a very unnatural look. Figure 1 looks very natural on the whole, but if one looks a little more careful, it can be seen that this kind of smoothness isn t easy to provide on a real design. Eventually this will lead to an unnatural look and there is decided to create 5 fingers with 3 phalanxes of which only 2 are moveable. The difference can be seen in figure 1.3. In that way the mechanism of the old design can be used and the new design will look more natural to the users. In this case there is chosen to fix up the phalanx near the finger top. The angle at which this phalanx is set will be given in the conclusions of the performed experiment and can be read in Table 2.4.

4 1.5 Power supply Figure 1.3: Difference between 2 and 3 phalanxes A pneumatically powered prosthesis needs a pressure supply. At the WILMER-group in Delft the most common used power supply is a cilinder filled with 7 grams of carbon dioxide gas at a pressure of 5.6 MPa [5]. At the WILMER-group a special miniature gas pressure valve is developed which is able to decrease the pressure to 1.2 MPa, which is shown to be the optimal pressure for a pneumatic prosthesis [6] (Figure 1.4). In the current design one gas cylinder is used on which a pressure valve should be placed. This pressure valve has to reduce the 5.6 MPa to 1.2 MPa and with that pressure supply the whole prosthesis. The output can be one supply or be divided in two; there s one output needed for the four fingers and one output for the thumb, but because only one pressure is used this separation can be done behind the valve. When the piston is contracted due to the CO 2 -pressure the prosthesis gets contracted, and when the CO 2 -pressure drops, the prosthesis will stay contracted until a force forces the piston to go to it s initial state. In the design evaluated in this report the re-contraction is performed by a spring integrated in the piston. As soon as the force delivered by the pressure cylinder drops the spring force is used to bring the piston in it s initial state. To make sure that no movement of the piston is lost the spring will be a little bit preloaded. In that case every movement of the piston is passed on to the rest of the prosthesis. 1.6 Glove Patients that wear a prosthesis usually want the most natural prosthesis they can get. In this process they even prefer a natural looking prosthesis over an better functional prosthesis. For this purpose several gloves are available, which can be put over the metal prosthesis to give the prosthesis a more natural look. Because these gloves are only made in a few normalized sizes, it is a goal to produce a prosthesis on which one of the gloves fits. However with little adaptations there is always a glove found that fits nice. The company Otto Bock sells several of these gloves

1.7 Conclusions 5 Figure 1.4: Figure showing 1.2 MPa as optimal power supply [6] for male and female adults and children [14]. The producer of the sketch found in the early 1900 s didn t assumed the user to take a glove over this prosthesis. Probably the idea behind the sketch was a plate metal layer as a cover for the prosthesis or no covering at all. During that days it was not normal at all to hide the prosthesis or give a most natural look as possible. The only goal was to provide as much function for the handicapped person. Because a glove provides more friction than no glove and because it influences the functionality of the design the old ideas will be used and no glove will be taken up in the design. 1.7 Conclusions At the end of the chapter the most remarkable conclusions/ decision will be pointed out. During the rest of the report these conclusions are used. The grasp performed by the prosthesis will be a 3-point precision grasp The force the prosthesis is going to deliver should be set between 40 and 55 N The fingers of the prosthesis consist of three phalanxes, with a fixed top phalanx The power is supplied by a CO 2 -cylinder that contains a pressure of 5.6 MPa, which is reduced to 1.2 MPA (the optimal pressure for a prosthesis) No glove will be added to the design, because it causes unexpected side effects and it was not the original idea of the design

6

Chapter 2 Determining the parameters of the non-prosthetic hand Now it is known which kind of grasp will be performed by the design, the parameters of the prosthesis can be determined. Not all the sizes of the hand can be easily found in literature, so some of them should be determined experimentally. In literature the following parameters are found: 1 length of the fingers 2 thickness of the fingers 3 length of the palm of the hand 4 thickness of the hand Figure 2.1: Overview of the several parameters [3]

8 Now experimentally need to be analyzed: length of the several phalanxes angle within the points of application angle between the thumb and the other fingers length of the palm of the thumb natural bending of the fingers and the thumb final angle of the little finger angles in the fingers in a half and fully squeezed position For these parameters a picture will be shown at the part where they are determined, because no simple picture for all these parameters can be presented. This chapter will give a value for each of the mentioned parameters. The experimental set up will be explained in Section 2.2 about the experiment. 2.1 Literature data Some sizes of the human hand are known from literature. This literature is normally meant for ergonomic requirements in product development [3]. Therefore the data is arranged in a special way. The sizes of the human hand are represented in the case they include 5% of the population, 50% of the population or 95% of the population. In other words the data are represented as a Gaussian distribution one knows from statistics. In Figure 2.2 this distribution is shown once more. There s decided to work with the 95% data, because in that way the most extreme cases are filtered out, but still the major part of the population is taken into account. In that case the made prosthesis is looking very natural on most of the users, because extremes have a large influence on the final values for the prosthesis. 2.1.1 Length of the fingers The length of the fingers (see Figure 2.1, number 1) is given in the ergonomic handbook [3] as follows:

2.1 Literature data 9 Figure 2.2: Gaussian distribution [4] Table 2.1: Length of the phalanxes thumb index finger middle finger ring finger little finger total length 76 mm 83 mm 92 mm 86 mm 70 mm These total lengths seem very useful, but within the investigated design one was especially interested in the lengths of the several phalanxes. In this design it is important where the bending points of the fingers are located. The length of the phalanxes is measured in subsection 2.2.1 2.1.2 Thickness of the fingers This parameter is given for both the proximal and the distal part of the fingers (see number 2 in Figure 2.1, because the thickness isn t constant over the finger. Although the assumption is made that the finger can be seen as a round object, which has a diameter of the given values in Table 2.2.[4]

10 Table 2.2: Thickness of the fingers proximal distal thumb 25 mm 25 mm index finger 23 mm 20 mm middle finger 23 mm 20 mm ring finger 21 mm 19 mm little finger 18 mm 17 mm 2.1.3 Length of the palm of the hand For this parameter the length from the start of the middle finger to the wrist is given. See in figure 2.1 number 3. The length for the normal man is 117 mm. 2.1.4 Thickness of the hand For this parameter only one value is given 32 mm. This seems a bit inconsistent, but the size given is actually the thickness of the hand near the knuckles. (see figure 2.1) As an assumption this parameter is taken as the mean for the overall thickness of the whole hand. This will be the assumption at the start, but in case during the development of the prosthesis it shows that a gradient or another thickness is necessary that s always possible and can be made to develop the most natural look. 2.2 Experimentally specified parameters The experimental setup seems very easy: Photograph 20 male and 20 female right hands and then determine the parameters needed. In real life it is indeed that easy when you are disposed of as many time as you want. The main reasons why it was that time-consuming: the several parameters need different pictures which lead to an enormous amount of pictures many pictures in which the testers don t keep their hands exactly the same, so drawing conclusions becomes very hard. The goal of this internship was to create working drawings of the pneumatic prosthesis and not to do an enormous experiment on hand sizes. Therefore a more accurate estimation is given with the few pictures that were analyzed and no experimental value is calculated. The pictures that were analyzed were from both male and female testers. In all cases they were analyzed together, which could be done because the parameters that were investigated were angles or

2.2 Experimentally specified parameters 11 Figure 2.3: Length of the phalanxes. In this figure some sizes are ascribed to the several phalanxes. These sizes aren t sizes in cm or anything, they are just ascribed to the measuring rod by the program used. These numbers are therefore only used to determine the lengths of the phalanxes in terms of percentage percentiles. In the next subsections the analyzing results are given. More information can be found in Appendix I. 2.2.1 Length of the phalanxes In this experiment pictures of the dorsal top of the flat hand were analyzed (like the picture seen in Figure 2.3). The length of the several phalanxes was determined by hand and with this data the lengths of the phalanxes were determined in terms of percentage of the total measured length. With these percentages it was possible to calculate the length of the phalanxes with the finger lengths given in Table 2.1 and the results are summarized in Table 2.3. From this table it is clear that the standard deviations in this case are very promising, but still only 6 pictures from different people were analyzed. Still it might be said that the estimations in this case are not that bad. 2.2.2 Angle between the points of application of the fingers If you look at your own hand, you can see the knuckles ain t located in a straight line. To determine the angle in this line again the pictures of the dorsale flat hand were taken. In order to make the estimation more reliable also pictures of the palmar flat hand were determined. This parameter is a little vague to determine, because it was very hard to determine the same points on the knuckle on every hand. Even the results from one persons hand were different in both the dorsal and

12 Table 2.3: Length of the phalanxes thumb index middle finger finger percentage lower part 54.60% ± 1.57% 50.20% ± 3.21% 49.12% ± 3.13% percentage middle part - 28.19% ± 2.45% 29.80% ± 1.34% percentage top part 45.40% ± 1.57% 21.61% ± 2.07% 21.08% ± 2.30% total length (male) 76 mm 83 mm 92 mm length lower part 41.5 mm 41.7 mm 45.2 mm length middle part 0 mm 23.4 mm 27.4 mm length top part 34.5 mm 17.9 mm 19.4 mm ring little finger finger percentage lower part 46.60% ± 2.94% 46.51% ± 2.84% percentage middle part 29.94% ± 1.71% 26.40% ± 3.30% percentage top part 23.47% ± 2.79% 27.09% ± 1.60% total length (male) 86 mm 70 mm length lower part 40.1 mm 32.6 mm length middle part 25.7 mm 18.4 mm length top part 20.2 mm 19.0 mm

2.2 Experimentally specified parameters 13 Figure 2.4: Point of application

14 palmar pictures as one can see in Figure 2.4. Because this parameter isn t the most important one there s decided to draw the conclusion that the little finger is positioned a little lower than the other three fingers (at a 25 angle). (In this case this conclusion was represented in 5 of the 6 processed pictures, see appendix I. The other fingers are positioned on the same (straight) line. 2.2.3 Angle between the fingers and the thump To give the prosthesis an as natural appearance as possible this angle needs to be determined as well. Here the pictures caused som trouble. The testers were told to keep their hand relaxed. This lead to the problem that some people had an open position and some people had a more closed position of the hand. This open/ closed position manifests itself mainly by a smaller/ bigger angle between the thump and the fingers. In order to produce a functional prosthesis that is able to make an squeezing movement the open position had a preference. The measured open angles are respectively: 53, 58, 40, 39, 57 and 31. This leads to a mean of 46 with a standard deviation of 11.1. Figure 2.5: Angle between the thump and the fingers 2.2.4 Length of the palm of the thumb Now that the length of the palm of the total hand and the angle between the fingers and the thumb are known the length of the palm of the thumb can be calculated. This can be done with help of the Pythagoras equation (see Figure 2.5. This can be done under the assumption that the triangle formed has an perpendicular angle. With the length of the palm at 11.7 cm and the angle between the fingers and the thumb at 46 the length of the palm of the thumb becomes 9.2 cm. 2.2.5 Angle within the fingers and the thumb in the resting state For the natural appearance the angle within the fingers play an even more important role. If the prosthesis in rest looks like a straight plank, this looks very unnatural. On the other hand when the prosthesis in rest looks like a fist this is very unnatural either. For this parameter two different

2.2 Experimentally specified parameters 15 Figure 2.6: Fingers and thumb in resting state Table 2.4: Angles within the fingers mean standard deviation lower part 25 ± 10.14 middle part 24 ± 4.82 top part 12 ± 5.24 Table 2.5: Angles within the thumb mean standard deviation lower part 23 ± 7.14 top part 20 ± 4.76 calculations are made. One for the fingers (all the fingers get the same bending) and one for the thumb. Again the problem with people s own preference arises. Therefore it is suggested that when this prosthesis is made for a specific person his own preferences are used to determine the design parameters of the prosthesis. Because a value for the parameter is necessary in order to make a design all the pictures are taken into account. The extensive table with information can be found in Appendix I. The mean of this data is used as the parameter, even though the standard deviations are very high in this way. These angles are used as starting angles for all the fingers, so that in the resting fase all the fingers look pretty much similar. If there is assumed that all the fingers make the same angles this will result in a even more natural look. If your own hand is in rest not all the fingers fit exactly over each other. If the fingers have different lengths but the same angles, the fingers will look all a little bit different, which causes the more natural look. For the thumb other starting angles are used. These angles are given in Table 2.5. 2.2.6 Final angle of the little finger This parameter is very useful in the design of this prosthesis. When a normal non-prosthetic person picks up a mug most of the time this person uses his little finger to support the mug from falling. This means that the force this person has to deliver to the mug is lowered. This system seems very useful for this prosthesis, because the squeezing force can be lowered and the person with the prosthesis can pick up flexibel plastic mugs without spoiling his drink. In this idea the

16 Figure 2.7: Final angle little finger pneumatics are very useful, because they make sure that the little finger will move on when all the other fingers come onto resistance. It s necessary to determine the final position of the little finger and limit the finger to this position, because when it keeps turning the advantage is gone. One can see in Figure 2.7 that in this case the little finger is bent under the mug. Some people prefer to keep their little finger straight. This preference was present in 40% of the cases, but this preference is much more difficult to implement in the prosthesis. The fingers are pre-bended as calculated in the previous subsection. Therefore it is only possible to let the little finger only hinge around the first knuckle, but not to straighten the finger in it s turn. The data are evaluated for the other 60% leading to the following: Table 2.6: Final angle little finger mean standard deviation lower part 47 ± 18.02 middel part 27 ± 10.80 top part 23 ± 15.18 In this case the standard deviations are enormous (see for the complete data Appendix I) that it must be pointed out again that the given values for the parameters are only estimations. On the whole these parameters will get smaller standard deviations if the sample size is increased. Given is the fact that with these values for the parameters it is possible to create a valuable design and in case of the final angle of the little finger, it is even possible to change the angle to another if the prosthesis is finished. Most important in this case is the fact that when the little finger is bent under the mug, the mug must find some kind of stability. Therefore it is nice when the second knuckle of the little finger is bent as much as possible, because in that scenario the chance that the mug will find stability is optimized.

2.2 Experimentally specified parameters 17 2.2.7 Angles in the fingers in a semi-closed and a closed position These parameters might be the most important ones in the design of the prosthesis. It is truly necessary that the fingers close very well, because otherwise it won t be possible to perform a precision grasp or even to pick up a piece of paper. On the other hand it is necessary that the opening between the fingers is enough to pick up the greater objects and that the closing goes in the right proportions. Therefore the design tries to follow the angles in it s closing to the closed position which certainly must fit. Figure 2.8: Angles within the precision grasp or the power grasp As can be seen in the pictures of Figure 2.8 much more angles need to be measured form this photographs. The deviation becomes more along with the impossibility to mark the exact same spots on the testers hands. Therefore the deviations in Table 2.7 are huge, but the angles give an impression on how the prosthesis should close. The data used to calculate these values again can be found in Appendix I. Table 2.7: Angles within the precision grasp or the power grasp mean standard deviation 1 52 ± 9.60 2 58 ± 9.29 3 58 ± 15.06 4 68 ± 15.29 5 28 ± 13.65 6 75 ± 13.53 7 27 ± 9.50 mean standard deviation 1 32 ± 3.11 2 48 ± 8.11 3 42 ± 12.83 4 60 ± 18.31 5 54 ± 9.92 6 20 ± 11.88

18 2.3 Discussion As said many times before, the parameters are determined only on a few measurements. Only in one case this lead to low standard deviations (with the length of the phalanxes) and in all the other cases the standard deviations are not good at all. If an experimental study on the sizes of the hand was performed these data would be very bad, but in this case they provide better estimations as they were purposed to do. Another point to bring up is the fact that within the measurements a big variation is set up due to the fact that the parameters are determined with the human eye. This leads to variations in two points. First the lines on which for example the angles depend on specified points of the hand. To locate these points in all testers exactly the same causes an error and second the angle between two lines is determined by hand which probably causes another error. 2.4 Overview of all the parameters In the introduction of the chapter all the parameters needed from literature and the experiment were listed. To keep everything well organized a brief overview of all these parameters is presented. Parameters necessary for the prosthesis design: (1) length of the fingers thumb index finger middle finger ring finger little finger total length 76 mm 83 mm 92 mm 86 mm 70 mm (2) thickness of the hand This parameter is set on 32 mm for the whole hand. (3) thickness of the fingers Here the following table can be shown: proximal distal thumb 25 mm 25 mm index finger 23 mm 20 mm middle finger 23 mm 20 mm ring finger 21 mm 19 mm little finger 18 mm 17 mm

2.4 Overview of all the parameters 19 (4) length of the phalanxes For this parameter the simplified table can be made thumb index middle ring little finger finger finger finger length lower part 41.5 mm 41.7 mm 45.2 mm 40.1 mm 32.6 mm length middle part - 23.4 mm 27.4 mm 25.7 mm 18.4 mm length top part 34.5 mm 17.9 mm 19.4 mm 20.2 mm 19.0 mm Figure 2.9: Overview of the several parameters (5) angle within the points of application Here the conclusion was that the index finger, the middle finger and the ring finger are located on the same line and that the little finger is located a little lower within an angle of 25. (6) angle between the thumb and the other fingers This parameter was set on an angle of 63.

20 (7) natural bending of the fingers A little table will show the values for the angles between the lower, middle and top part. lower part middle part top part angle 25 24 12 (8) final angle of the little finger Again a little table will show the answers: lower part middle part top part angle 46 30 29 (9) angles in the fingers in a power grasp and a precision grasp In two columns these angles are represented as: power precision 1 32 52 2 48 58 3 42 58 4 60 68 5 54 28 6 20 75 7-27

Chapter 3 Force delivered by the prosthesis 3.1 Open prosthesis As described in Section 1.3 the force the prosthesis delivers should be calculated to make sure enough force is delivered at the tips of the fingers. The angles the prothetic fingers should make in the resting state and the necessary parameters of the hand are described in Section 2.2.5. Together with the picture from 1919 two figures of the prostheses can be generated: one for the index-finger and the thumb and one for the middle finger and the thumb. These figures can be seen in Figures 3.1 and 3.2. In these pictures the parts of the prosthesis are shown in black, the dimensions are shown in blue and the forces are shown in red. In these figures the wheels are shown the largest near the palm and smaller further on the fingers. The sizes of these wheels will be determined later and depend on the conveyance (the sizes shown are the actual sizes). In this picture all the sizes and relations collected in Chapter 2 are used. If one starts to calculate the force that is delivered at the tip of the fingers, it will soon be figured out that the method represented in the old model will not force the second knuckle to move. This is due to the fact that when the first wheel (the one closest to the piston) moves down, the spindle of the second wheel moves (the one representing the 2 nd knuckle) down too. The distance between these wheels won t change and the second wheel shall not turn as a consequence of the force in the rope. To solve this problem two new wheels in the appearance of gears are introduced as can be seen in the left of Figure 3.3. The force of the piston is applied on the first wheel, gear A and passed on to gear C via gear B. In this case gear C contains the rope. To be space-saving gear C will be placed at the same side of gear B as gear A, as can be seen in right part of Figure 3.3. To make sure the solution works, gear A and gear C cannot have the same radius. Otherwise the situation would be the same again. Gears A till D are presented in Figure 3.1 as well, so that the solution is made clear in the total overview too. 3.2 Closed prosthesis To close the hand it would be most logical to close the hand according to the angles determined in Section 2.2.7. If this is adopted on Figures 3.1 and 3.2 the fingertips won t reach one another.

22 Figure 3.1: Total system of the index finger and the thumb

3.2 Closed prosthesis 23 Figure 3.2: Total system of the middle finger and the thumb

24 Figure 3.3: Solution to the turning problem Table 3.1: Angles of the index finger of the prosthesis before after rotation radius R A,α 25 37 12 12 mm R B,β - - 48 3 mm R C,γ - - 24 6 mm R D,δ 24 72 48 3 mm R E,ε 12 12 0 - For this reason a point is chosen (a squeeze point) to which the fingers come together. Now the total system is ready and shown in Figures 3.4 and 3.5. Again two pictures are shown; One for the index finger and the thumb and one for the middle finger and the thumb. It is necessary to make the point of squeeze the same points. Otherwise it won t be possible to create the design for real. To establish this, there is chosen to copy the position of the thumb (when it s closed with the index finger) to the system with the middle finger. From these pictures an overview can be generated of the angles the several phalanxes proceed during closing. In the Tables 3.1, 3.2 and 3.3 the angles at rest, the angles in closing position and the rotation of the gears is given for the three separate fingers. With this information it is at once possible to calculate the diameters of all the gears, and those will be presented in the tables to. The diameter of gear A is chosen with use of the limitations of the human hand. As described in Section 2.1.4 the thickness of the male hand is given at 32 mm. This means the gears can maximal have a radius of 16 mm. Still not all the space can be filled with the gears, because also the glove and the surrounding of the prosthesis need to fit within the 32 mm. There is chosen to take 3 mm at both sides to fit in with the glove and the surrounding. This means the radius is reduced to 10 mm, but because the knuckles of the fingers are a little thicker too, there is chosen to take the radius of gear A at 12 mm at the index finger and the thumb and for the middle finger at 14 mm. For the system shown in figures 3.4 and 3.5 it is possible to give a well built estimation of the

3.2 Closed prosthesis 25 Figure 3.4: Total system of the index finger and the thumb

26 Figure 3.5: Total system of the middle finger and the thumb

3.3 Formulas to calculate the force within the prosthesis 27 Table 3.2: Angles of the middle finger of the prosthesis before after rotation radius R A,α 25 30 5 14 mm R B,β - - 23.33 3 mm R C,γ - - 11.67 6 mm R D,δ 24 85 61 1.15 mm R E,ε 12 12 0 - Table 3.3: Angles of the thumb of the prosthesis before after rotation radius R A,α 23 29 6 12 mm R B,β - - 24 3 mm R C,γ - - 4 9 mm R D,δ 20 32 12 6 mm force at the end of the finger. The parts are named the same as they are named in Chapter 2. In order to calculate the force, first the way the force is prolonged to the tip of the fingers should be made clear. 3.3 Formulas to calculate the force within the prosthesis In this section the formulas to calculate the force at the end of the fingers are given. When the force is calculated one starts at the piston and ends at the tip of the finger. All the forces are represented in both the open and closed figure presented above. The calculation is done in little fragments, so that it is orderly till the end. At the end of each fragment the just specified force is calculated for the index finger. The forces for the middle finger and the thumb can be found in Appendix II, where also an m-file is presented to calculate the forces. 3.3.1 Force at the piston The force starts at the point were the pressure in the CO 2 -cylinder is reduced to 1.2 MPa. This force is the driving force of the piston. At the end of the cylinder the force is given by formula 3.6. F = p A[N] (3.1)

28 Because a piston is used in which a springs makes sure the piston return to it s initial state after the power supply is lost, the force it takes to push the spring should be calculated to. This force is off course subtracted from the initial force calculated. To make sure that no shaky movements develop during grasping it is necessary to take up a precompression within the spring. For this design this compression is set on: u pre = 0.5 movement (3.2) In order to make the piston work as properly as possible, it is necessary to make sure the movement of the piston is as much as possible. When the arm of the piston grips gear A under a 90 angle, the moment around the center of gear A will we be reduced to zero and in the theoretical case this happens, the force won t proceed over on gear A. Still it is best if the angle of grip comes most close to the 90 angle, because the movement will be largest in that way. This is useful in this case, because only little turns are made (by gear A) so this won t cause a large movement and in this way the largest movement is reached. To realize an even more great movement the arm of the piston clutches at 83.333% of R A. The movement can be calculated with help of formula 3.8 and with help of figure 3.6. S = sin(12 ) R A = sin(12 ) 12 10 3 = 2.49 10 3 (3.3) Figure 3.6: Total movement of gear A Now the movement is known, it is possible to give the formula s to calculate the force of the piston (F piston in Figure 3.1). Within these formula s some variables appear that are not defined yet. These will be explained a little further where the index finger is used as an example. F P = C u pre (3.4) F V = C movement + F P (3.5) F piston = p A F V (3.6)

3.3 Formulas to calculate the force within the prosthesis 29 The force at the side of gear A can now be calculated form the force at the end of the arm of the piston by taking a moment-equilibrium around the center of gear A. This is a little more clarified in Figure 3.7 F A = F piston d p d A (3.7) with d A = R A d P = cos(15) 5/6 R A Figure 3.7: Moment-equilibrium to calculate F A For the index finger the force of the piston can be calculated as follows: The maximal rotation of Gear A can be found in Table 3.1 as 12. With this rotation the maximal movement of gear A can be calculated. This is shown in Figure 3.6. With Formula 3.8 the movement is calculated. movement = S = sin(12 ) R A = sin(12 ) 12 10 3 = 2.49 10 3 (3.8) Now the movement of the piston is known, the pre compression of the force at the piston can be calculated with the following equations: u pre = 0.5 S = 0.5 2.49 10 3 = 1.25 10 3 (3.9) F P = C u pre = 10000 1.25 10 03 = 12.45 (3.10) F V = C S + F P = 10000 2.49 10 3 + 12.45 = 37.35 (3.11) F piston = p A F V = 1.2 10 6 (pi 12 10 3 ) 2 37.35 = 505.52N (3.12) With this force known the force on gear A can be calculated. This will happen with the moment of equilibrium as described in Equation 3.7. This will lead to the following:

30 Figure 3.8: Fast method to calculate F ( Squeeze) F A = F piston d p d A = 505.52 9.6 10 3 12 10 3 = 406.91N (3.13) with d A = R A = 12 10 3 d P = cos(15) 5/6 R A = 9.6 10 3 3.3.2 Force at Gear D The solution sketched in Figure 3.3 makes it necessary to calculate first the force at the third gear before the force in the rope (F rope ) can be calculated. Gear B, as can be seen in Tables 3.1, 3.2 and 3.3, has a much smaller diameter than gear A. The third gear, gear C, is placed next to gear A, but without contacting it. The force working on gear A will be proceeded on to gear B and finally on gear C. The friction that causes the initial force on gear A to reduce to the force which can be found on gear C is not known precisely. Therefore at the of the calculation there will be taken of one amount foor all the friction at once. Assumed for now is that the force on gear C is exactly the same as the force calculated on gear A The force in the rope is the same as the force in gear C and therefore the force in gear D will be same to. This is all only because the friction is not taken into account at this point. For the index finger this will result in the same force as F A and F D, so F D = 406.91N 3.3.3 Force at the tip of the finger Now the force on the fourth gear is known, the only obstacle to pass are come angles within the fingers of the prosthesis. The force at the end of the finger can now be calculated with use of sine and cosine rules. This can be done in two fases, but it is much more easy if it is done in one calculation. Both systems have the same answer, but the calculation is only made with the fast method (shown in Figure 3.8.

3.3 Formulas to calculate the force within the prosthesis 31 This is done under the assumption that the force F D 2 is parallel to the connection between the gears A to C and gear D. The moment of equilibrium is taken over center of gear D, which leads to the following formula: F squeeze = F E = F D d 1 d 2 (3.14) with d 1 = R D d 2 = sin(12) L p halanx For the index finger this results in the substitution of the variables within formula 3.14. F squeeze = F E = F D d 1 d 2 = 406.91 3 10 3 4.87 10 3 = 250.91N (3.15) with d 1 = R D = 3 10 3 d 2 = sin(ε) L p halanx = sin(12) 23.4 10 3 =4.87 10 3 Now the force at the end of the index finger is set at 250.91 N 3.3.4 Assumptions During the whole process of determining the force at the end of the fingertip some assumption are done, which need to be written down more specific. Friction Parallelism Movement Standards for the piston Friction:The force that is now calculated ain t the real force that is practised by the prosthesis.the friction isn t taken into account as mentioned earlier and there are many more factors that must be taken into account. Because this an estimation the calculation described in this section should be enough. During this research it was no spearhead to reduce the force to the less force necessary in grasping stuff. This is a research on it s own and can be performed after this one is finished. The only thing known about the force is described in Section 1.3. There it is said that the prosthetic force for a male prosthesis should at least be more than 55 N. If one tries to estimate the amount of force that gets lost due to the friction, this will be no more than 20 N, so this value is subtracted from the end value calculated for the force in index finger, the middle finger and the thumb.

32 Parallelism: During the calculation in some cases a parallelism is assumed. In fact this is done when the force at the end of the finger is calculated (Section 3.3.3), there is assumed that the axis drawn through gear C and gear D is parallel to rope. This is in fact not the deal, but with small gears it can be assumed. Movement: There is assumed that during the movement of the piston gear A turns as an effect of the force the piston practises on this gear. The movement of the piston should cause this turning and therefore it will turn along with the gear. On huge objects this would result in a twisting force on the piston that would eventually make the piston break down. Normally very complicated solutions should be made up, but in this case the assumption is made that the turning and the gear are that kind of small, that nog twisting forces will appear. Standards for the piston: To make sure the force of the piston is proceeded on to gear A the angle between the piston and gear A can never become 90. To accomplish this there is made sure that this angle will never proceed over 85 (so this will be the final angle after grasping). To make sure that the force proceeded on to gear A, the arm of the force in the piston to the center of gear A should be as huge as possible. For that reason the piston grips at gear A at 5/6 of the total radius. 3.4 Calculation of all forces In appendix II a m-file can be found with which the calculations mentioned above are performed. This is again done for the index finger, the middle finger and the thumb. When all the pistons have a diameter of 24 mm, the forces are calculated at 251 N, 85 N and 497 N for respectively the index finger, the middle finger and the thumb. After the reduction of the friction this will end up at respectively 231 N, 65 N and 477 N. First thing to catch the eye is the fact that the middle finger contributes less to the grasping force. This can be seen as an advantage, because in this way the middle finger function mainly as a support. When grasping with a non-prosthetic hand the index finger and the thumb provide in most of the force. The middle finger is in that case used to support and to prevent the picked up stuff from slipping away. 3.4.1 Even the forces In this design there is been chosen for a 3 point precision grasp (see Section 1.1). Therefore the force of the index finger and the middle finger together should be same as the force at the end of the thump, to prevent the prosthesis from malfunctioning. To obtain this, the area of the piston can be modified. This is nearly the only parameter which is not dependent on all the other parameters and it s a easy to change parameter in the design. Because the force of the index finger and the middle finger together is smaller than the force of the thumb, the diameter of the piston in the thumb is reduced to 19 mm. The force is now reduced to 296 N too for the thumb. The force seems a little high when compared to the minimal required 55 N and it is. The ultimate goal of this design is to create a much lower force, because the object is able to get lifted by the

3.5 Conclusion 33 little finger. In Section 1.3 the force needed is set on this 55 N. For now there will be worked with the newly calculated forces of 296 N. 3.4.2 Force in grasping huge objects Now it would be really nice if the force is some bigger in case a huge objects is grasped with the prosthesis. This is with the assumption that larger things have more weight and need more force to be picked up. This bigger force can be reached if the attachment of the piston to the first gear is placed under another angle. In the design now sketched the force increases as the fingers become more close to each other. This is not in line with the advantage sketched above. This can be solved pretty easy. In that case the piston should function the other way around and the place where the pistons seizes should be changed to the angle at which the angle plus the total turning of gear A. 3.5 Conclusion It can be said that it is possible to close the index finger and the middle finger of the prosthesis to the same squeeze point, with a hopeful amount of force. The prosthesis is now ready for design in a 3D-CAD design program.

34

Chapter 4 Working drawings Now all the parameters necessary for the design are known, the planning for the final design can be made. This chapter starts with how the design should be drawn in Unigraphics, after which a little expand wil be made to the several gears. Then some information about the drawings is given and finally several properties of the final prosthesis design are made. 4.1 Building blocks of the design If one starts to design the prosthesis in a 3D-CAD program like Unigraphics first all the small parts need to be made after which those parts can be recombined to a new total figure. This prosthesis will be made from several important parts: The piston, the gears and the supporting frame. All these parts need to be created first within Unigraphics before the total working drawings can be generated. 4.1.1 The piston The piston is made of several components itself, which can all be created themselves in Unigraphics. With the use of the assembly tool it is possible to create a piston that is seen as one part and which can be used in a new assembly as a total part. For the prosthesis all the sizes are known and it can be made at once. A very important part of a piston is the O-ring. For these O-rings a special groove is made, so that it can be fitted in. O-rings are easily ordered online [9] and [10], but one should take into account that an O-ring can t fit to tight, but on the other hand it must not leak [6]. 4.1.2 Gears Because only so little gears are needed within this design and because it is very hard to create precise gears it is much easier to buy these gears in a shop. On the internet several websites are specialized in small gears [15],[17] and [18]. When the gears are ordered there, it is no longer possible to create the exact gears that are necessary, but with little modifications it is still possible.

36 Table 4.1: Gears needed for the thumb radius diameter model calculated found number gear A 12 mm 24 mm SS1-24 [15] gear B 3 mm 6 mm DS0.5-12 [15] gear C 9 mm 18 mm S10S05M036P0808G [17] gear D 6 mm 12 mm SSY1-12 [15] Table 4.2: Gears needed for the index finger diameter diameter model calculated found number gear A 12 mm 24 mm SS1-24 [15] gear B 3 mm 6 mm DS0.5-12 [15] gear C 6 mm 12 mm SSY1-12 [15] gear D 3 mm 6 mm DS0.5-12 [15] For example, there are gears available with a radius of 6.34 mm [17] that are little more thick than the huger gears. So it is still possible to work with the solution sketched in Section 3.2. For all the gears necessary this will lead for example to the purchase of the gears as pointed out in Tables 4.1,4.2 and 4.3. As can be seen in table 4.3 gear D for the middle finger is the only one that can t be ordered directly. This one should be made hand-made or the design should be adapted. Furthermore it is nice if most (or all) the gears are ordered at one company. Not only because the delivering occurs at one time, but also because these gears are more adjusted to one another. Table 4.3: Gears needed for the middle finger diameter diameter model calculated found number gear A 12 mm 24 mm SS1-24 [15] gear B 3 mm 6 mm DS0.5-12 [15] gear C 6 mm 12 mm SSY1-12 [15] gear D 1.15 mm??

4.2 Unigraphics design 37 4.1.3 Supporting frame For the supporting frame it is necessary to bear in mind that the gears need the right support. This means that the axis of all the gears need to be tightened to the same stationary world. If that s not the case the solution sketched in Section 3.2 will not work. This problem can be overcome by the introduction of hinges. Another important thing that needs to be implemented in the supporting frame is the final angle of the little finger. The supporting frame should be designed in such a way that the little finger is allowed to turn any further than the angles specified in Section 2.2.6 With these it will be possible to created a stationary world that is still moveable. 4.2 Unigraphics design Now all the building blocks are known the separate designs of the building blocks can be finished. The working drawings are made with use of the program Unigraphics. This is a 3D-CAD design program that allows you to work with solid modeling instead of the normal line drawings. 4.2.1 The Piston Because all the sizes of the piston are known it is possible to create the working drawings for the piston. There needed to be created 5 different pistons. One for each of the fingers with it s own specificities. Here the piston of the index finger will be shown. In Figures 4.1 and 4.2 the piston is shown in the working screen of Unigraphics. Now the piston exists in Unigraphics it is possible to let Unigraphics create the correct working drawings, that can be seen in Figure 4.2.1. The working drawings Unigraphics creates itself don t contain any sizes. These can be added by some extra commands. 4.2.2 Gears For each of the necessary gears a corresponding gear is found on the websites. This will lead in the design to just simple easy circles, with the reference to the specified gear. This looks like the figure shown in Figure 4.2.2. This is done for all the gears shown in Tables 4.1, 4.2 and 4.3. 4.2.3 Supporting frame The final working drawings of the supporting frame could not be finished due to a lack of time. The supporting frame is very difficult to design, because it s a one piece unit with a very unnatural shape. The ideas are all finished and represented above, so it should be easy to complete the design if one knows how to work with Unigraphics.

38 Figure 4.1: The piston shown in the working screen of Unigraphics (wire frame)

4.2 Unigraphics design 39 Figure 4.2: The piston shown in the working screen of Unigraphics (rigid body) Figure 4.3: The working drawing of index fingers piston

40 Figure 4.4: The Unigraphics screen with the gear and it s properties

Chapter 5 Conclusion During the research to the design found in the early 1900 s some remarkable things have come across. Therefore here in de conclusion all the things that are now different from the design sketched in the introduction will be presented. The thumb attaches the index finger under an angle of 90 Now there is chosen to work with an 3-point precision grasp, because this looks more natural The little finger turns as long as it can Now there is chosen to give the little finger a final angle to make sure that the grasping force can be lowered There are only two phalanxes in the design To make the prosthesis look more natural there is decided to keep work with two moving phalanxes and one fixed phalanx With these adaptations it was possible to calculate the force applied at the squeeze point and it was possible to calculate all the sizes needed to start creating the working drawings. It is very disappointing that the design could not be finished in time and it is probably very neat possible. Furthermore the design is not as bad at all. Some adaptations should be made (as described above), but still the design is very promising and useful. The designer was way upon his time when he wrote it down on paper.

42

Chapter 6 Recommendations Some things need to be investigated more deeply in this research area if one would like to continue with this research. Now there is known that the force can be reduced due to the end position of the little finger, there should be investigated how much force there is needed. There should be investigated what force of a prosthesis comes across with what kind of force of the natural hand and how much force there is needed. In that case another advantage of this prosthesis can be exploit. There should also be investigated if it is possible to find an optimal point for the squeeze point. If the squeeze point is a little moved, the turning of the several gears changes drastically and the force distribution over the several fingers becomes totally different. The prosthesis should be made and tested for real. Probably some adaptations can be made for the operating speed, the material and it s corresponding weight and so on. This means that if it is possible to create and develop the prosthesis many more adaptations and improvements can be made. The power supply of the CO 2 cylinder should be tested. It is know that for several other children prosthesis the mentioned cylinder contains enough power for 2 days or sometimes more. It is thinkable that with this prosthesis more power is needed than for a simple children prosthesis, but it should be optimized and the patient should not be carrying way to much power supply whole day long A better estimation of the friction during the process should be made. Probably it is not possible to calculate this coefficient, but is should be possible to determine this parameter from several experiments. The carrying comfort of the prosthesis is not checked yet and should be investigated to. It is known that different people have different wishes for a right prosthesis, but one advantage of this prosthesis is the fact that many changes can be applied, so every patient can get it s own best design.

44 The prosthesis is now designed with no use of a glove. The fact that no glove is used will be a disadvantage in the eyes of the users. A new study should be performed on the fact of a normal glove can applied without losing functionalities Even another study can be performed to new materials for the covering of the prosthesis the use of the

Appendix I Experiment data In this appendix more data of the experiment done to determine some parameters for the prosthesis are presented. This is done in the same order as they are represented in the report. I.1 Length of the phalanxes First the data on the length of the phalanxes is presented. Five tables are given, for each finger one. The most important conclusions from these tables are represented in Table 2.3 Table I.1: Length of the phalanxes, thumb Thump man 1 man 2 man 3 man 4 woman 1 woman 2 mean standard deviation lower part 0.21 0.21 0.19 0.24 0.24 0.22 0.22 0.02 top part 0.16 0.17 0.17 0.21 0.19 0.19 0.18 0.02 total length 0.37 0.38 0.36 0.45 0.43 0.41 0.40 0.04 percentile man 1 man 2 man 3 man 4 woman 1 woman 2 mean standard deviation lower part 56.76 55.26 52.78 53.33 55.81 53.66 54.60 1.57 top part 43.24 44.74 47.22 46.67 44.19 46.34 45.40 1.57

46 Table I.2: Length of the phalanxes, index finger Index finger man 1 man 2 man 3 man 4 woman 1 woman 2 mean standard deviation lower part 0.28 0.26 0.25 0.32 0.34 0.28 0.29 0.03 middle part 0.13 0.17 0.15 0.17 0.17 0.18 0.16 0.02 top part 0.09 0.11 0.12 0.15 0.15 0.13 0.13 0.02 total length 0.50 0.54 0.52 0.64 0.66 0.59 0.58 0.07 percentile man 1 man 2 man 3 man 4 woman 1 woman 2 mean standard deviation lower part 56.00 48.15 48.08 50.00 51.52 47.46 50.20 3.21 middle part 26.00 31.48 28.85 26.56 25.76 30.51 28.19 2.45 top part 18.00 20.37 23.08 23.44 22.73 22.03 21.61 2.07 Table I.3: Length of the phalanxes. middle finger Middle finger man 1 man 2 man 3 man 4 woman 1 woman 2 mean standard deviation lower part 0.32 0.33 0.27 0.31 0.39 0.31 0.32 0.04 middle part 0.17 0.21 0.17 0.21 0.21 0.20 0.20 0.02 top part 0.10 0.14 0.13 0.16 0.16 0.14 0.14 0.02 total length 0.59 0.68 0.57 0.68 0.76 0.65 0.66 0.07 percentile man 1 man 2 man 3 man 4 woman 1 woman 2 mean standard deviation lower part 54.24 48.53 47.37 45.59 51.32 47.69 49.12 3.13 middle part 28.81 30.88 29.82 30.88 27.63 30.77 29.80 1.34 top part 16.95 20.59 22.81 23.53 21.05 21.54 21.08 2.30

I.2 Angle between the points of application 47 Table I.4: Length of the phalanxes. ring finger Ring finger man 1 man 2 man 3 man 4 woman 1 woman 2 mean standard deviation lower part 0.28 0.29 0.23 0.27 0.37 0.28 0.29 0.05 middle part 0.17 0.20 0.15 0.19 0.20 0.19 0.18 0.02 top part 0.12 0.13 0.14 0.17 0.16 0.14 0.14 0.02 total length 0.57 0.62 0.52 0.63 0.73 0.61 0.61 0.07 percentile man 1 man 2 man 3 man 4 woman 1 woman 2 mean standard deviation lower part 49.12 46.77 44.23 42.86 50.68 45.90 46.60 2.94 middle part 29.82 32.26 28.85 30.16 27.40 31.15 29.94 1.71 top part 21.05 20.97 26.92 26.98 21.92 22.95 23.47 2.79 Table I.5: Length of the phalanxes. little finger Little finger man 1 man 2 man 3 man 4 woman 1 woman 2 mean standard deviation lower part 0.23 0.24 0.18 0.26 0.28 0.21 0.23 0.04 middle part 0.12 0.17 0.12 0.14 0.12 0.12 0.13 0.02 top part 0.13 0.13 0.12 0.15 0.15 0.13 0.14 0.01 total length 0.48 0.54 0.42 0.55 0.55 0.46 0.50 0.05 percentile man 1 man 2 man 3 man 4 woman 1 woman 2 mean standard deviation lower part 47.92 44.44 42.86 47.27 50.91 45.65 46.51 2.84 middle part 25.00 31.48 28.57 25.45 21.82 26.09 26.40 3.30 top part 27.08 24.07 28.57 27.27 27.27 28.26 27.09 1.60 I.2 Angle between the points of application In Chapter 2 it is mentioned that 5 of 6 persons show a little finger which is positioned lower than the other three fingers. All the figures are shown here.

48 Figure I.1: Point of application, testee 1 Figure I.2: Point of application, testee 2 Figure I.3: Point of application, testee 3

I.2 Angle between the points of application 49 Figure I.4: Point of application, testee 4 Figure I.5: Point of application, testee 5 Figure I.6: Point of application, testee 6 From these pictures it can be seen that only testee 1 differs from the conclusion drawn, but even this testee has the beding in the line, only at the index finger instead of the little finger.