Design of a double quadruped for the Tech United soccer robot M.J. Naber (0571509) DCT report number: 2009.134 Master Open Space project Eindhoven, 21 December 2009 Supervisor dr.ir. P.C.J.N. Rosielle
Table of contents Abstract p 2 1 Introduction p. 3 2 Constructive steps p.4-2.1 Step size p. 4-2.2 Timing and required speeds p. 5-2.3 Height of the robot p.6 3 Design of one leg p.7-3.1 An extending pendulum p.7-3.2 Pendulum p.7-3.3 Extending mechanism pendulum p.8-3.4 Assembly drawing p.11 4 Setup of multiple legs in the robot p.14-4.1 Coupled pair of legs p.14-4.4 Multiple couples p.15 5 Conclusion and remarks p.18 6 References p.19 1
Abstract This report outlines the design of legs for the robot of the Tech United soccer team. The team is currently playing in the mid size league in the Robocup with a robot which has wheels. In future it will be necessary to have legs instead. These legs have to fulfill the same functionality as the wheels have nowadays. The designed legs can make a step of 220 mm by coupling the motion of a pendulum with elongation. The elongation is done with a planetary gear inside a conic pendulum. Via coupling multiple legs the whole robot can be supported and can steer with the use of only 6 motors. The arrangement of the legs and drawings of a single leg are shown in this report. 2
1. Introduction The Tech united team is a team of engineers who participate in a global competition of soccer robots. In this competition the goal is set to win in 2050 a game of soccer of the winner of the world cup of human soccer. The robots have to be fully autonomous and comply with the FIFA rules. One of the FIFA rules [1] is that a soccer game has to be played on grass or on an artificial surface which complies with certain requirements. In the middle size league, where the tech united team is participating, they are currently playing on an artificial surface which doesn t match with the requirements. The field is made almost perfectly flat and doesn t contain any roughness. Therefore the current robots can use wheels to move around. In the future the field of the middle size league will change to the FIFA requirements and will make it hard to move with wheels. Therefore a different driving force has to be developed, which can cope with the roughness of a natural or artificial surface. The design of the mechanism which will make this possible is the goal of this open space master project and the design is explained in this report. In more detail the goal is described with the use of some requirements. The robot must be able to reach a forward velocity of 3 to 4 m/s and the design is vaguely constrained by the requirement that legs have to be used. In nature it can be seen that there is a whole variety of legs and therefore the term leg can be interpreted freely. The only constraint can be seen in the fact that a single leg has moments with and moments without ground contact. In this report a design is presented which will be able to reach the requirements. First the steps in the assumptions for the design will be explained, after that the mechanism is presented with technical drawings. After the design of one leg, the arrangement for multiple legs in the robot will be shown. 3
2. Constructive steps This chapter explains the assumptions which lead to the final design. Among other things this is done with the rules of Robocup [2] and comparisons with nature. 2.1 Step size The size of the robot is limited by a base frame of 500 500mm ( w d) in which the legs have to remain the whole time (see figure 2.1). To create a stable robot which does not fall at stand still, at least 3 legs have to support the robot. For stability and symmetry a 4 point leg supported robot is chosen in which a supporting leg doesn t cross the symmetry axes. A sudden standstill, change in direction or another not expected change in movement will therefore not be able to create an instable configuration. A safety distance of 30mm from the symmetry axes is also taken into account. Taken these demands in account limits the supporting area per leg. This is now limited to 4 squares of 220mm by 220mm. They are positioned in the corners of the 500x500mm frame and are shown with gray squares in figure 2.1. Figure 2.1: Top view of the available area for positioning legs The main driving direction is taken parallel to the side of the base frame as is shown with an arrow in figure 2.1. The movement of a leg is taken linear, relative to the driving direction which limits the stoke which can be made with one step to 220mm. 4
2.2 Timing and required speeds For the movement of the robot the run-profile of a hare can be considered. In steps this profile is shown in figure 2.2. It can be seen that there are moments where none of the legs touch the ground. When one leg is considered it is visible that there are two different phases. One is the take off phase in which the leg provides support of the body and provides power to push the hare forward. The other phase is the return phase in which the leg is moved back to starting position of the take off phase. To make the period in which there is no ground contact shorter, it is chosen to make couples of legs in the robot. One leg in the hare is replaced by two legs in the robot. In this couple the legs are in opposite phase. Therefore one leg is in the take off phase when the other is in the return phase. This coupling can ensure that it is possible that there is always a leg supporting the robot. If required this can be changed by changing the timing in the motions. Effectively the couple will create more contact time with the ground and therefore create more stability and steering precision. Figure 2.2: Running hare [3] It is possible to make a step size of 440mm with a couple, when one leg can make a step of 220mm. To achieve a velocity of 4 m/s will therefore require 9 steps per second (0.11 s per step). This is taken as a design parameter in the next chapter. 5
2.3 Height of the robot During movement of the robot it is not required that the robot remains at a constant height. As can be seen in figure 2.2 the center of gravity of the hare changes per picture in height. There are however some negative side effects which come with variation of height. The camera on top of the robot, which controls the position of the robot on the field, will need more processing capabilities when images aren t taken at a constant height and at a constant angle relative to the ground. The more variation between pictures the harder it will be to calculate accurate coordinates. Next to this will variations in height cause additional energy losses. The energy which is stored in the robot because of an increase in height will not be fully used for the forward movement. Therefore variations in height of the robot will be kept low, but they are allowed. During the returnphase the height of the robot is determined by the coupled leg and there is only one demand for the leg which is in the returnphase. This leg is not allowed to touch the ground at any moment. It has to retract to create a clearance to the ground. The profile of the tip of a leg is schematically shown in figure 2.3. In this figure the different phases can be seen. The take off phase is shown with a dashed line. During this phase there is a direct coupling to the height of the robot. Variations in the tipheight will therefore cause variations in height of the robot. In the returnphase the ground clearance can be seen. Figure 2.3: Height of the tip of the leg 6
3 Design of one leg The assumptions of the previous chapter lead to a design which is presented in this chapter. To simulate the motions SAM 5.0 is used. SAM is a 2 dimensional simulation package for simulating mechanisms. In the figures made with SAM, the elements have a circle around their assigned number. Nodes do not have this circle. The path which a node follows can be displayed and is shown with a purple line. 3.1 An extending pendulum The requirement for the mechanism is that it follows as close as possible the profile of figure 2.3. This profile can be made with a 4-link-mechanism [4]. But the downside of this type of mechanism is that relatively large parts are required for a step of 220mm. This can be seen in the report of T.A.J.M van Ven Concept design of a walking robot for Tech United [5]. To create a mechanism which is not much larger than the step size, the movement of the tip of the leg is decoupled into a pendulum motion and an extending motion. 3.2 Pendulum The pendulum (element 1 and 4) shown in figure 3.1 can swing from -45 to +45 relative to a vertical orientation. The distance from the point of rotation to the tip is 110mm. The point of rotation is the link to the body of the robot and is therefore shown as a fixed point. To drive the pendulum a crankshaft is used. At point 4 the crankshaft is driven by a motor. Via a conrod (element 3) the crank is coupled to the pendulum. Figure 3.1 Pendulum motion 7
3.3 Extending mechanism pendulum During a swing, the length of the pendulum changes to create a profile similar to the profile shown in figure 2.3. The pendulum with extension (double arrow) is shown in figure 3.2. Figure 3.2 Pendulum with elongation The length changes over time and this is shown in figure 3.3. In this figure the different phases can be distinguished and also the clearance above the ground during the return phase. The graph starts when the tip of the leg touches the ground for the first time. Figure 3.3 Extension of length over time 8
The extension has to be done at a high speed, it can only take 1/4 th of a cycle (0.0275s see chapter 2). To create a mechanism which can perform at such a high speed and which can make the required profile, a planetary gear set (8) is used in combination with a conrod (11). The conrod is attached eccentrically to the planetary gear and moves the tip of the leg (9) parallel to the pendulum. This is shown in figure 3.4. The combination of the pendulum with the planetary gear and conrod is shown in figure 3.5. The tip of the leg is has to be light to keep the inertia forces low and has to be stiff for support of the robot. This is like the concept design of the Tech United team [6] Figure 3.4: Extra rod with planetary gearset In the planetary gear (figure 3.4) the sun is driven by a motor which is attached to the robot with its housing. The ring of the gear is also fixed to the robot and therefore the planet rotates around the sun. Via the conrod the gear is coupled with element 12. The bearings at points 8 and 9 are attached to the pendulum and will cause the parallel motion of the tip of the leg to the pendulum. 9
In figure 3.3 can be seen that the tip of the leg has to extend and retract twice during one cycle. This is done by making the diameter of the planet twice the size of the sun (2:1). By connecting the conrod eccentric to the planet, the difference in height between the take off and return phase is created. In figure 3.4 the path of the connecting point is shown. The dashed part is during the take off phase and the continues line is during the return phase. Figure 3.5 Pendulum with planetary gear (8), conrod (10) and the tip of the leg (9) 10
3.4 Assembly drawing The 2 dimensional mechanism shown in figure 3.5 is used as the basis for the 3 dimensional design shown in figure 3.6 and 3.7. The different elements are numbered and are listed below the pictures. Figure 3.6 Side view of leg Nr Description of part Nr Description of part 1 7 Carrier of planetary gears 2 Connection rod, for conrod (2) to pendulum Conrod, from crankshaft to pendulum (12) 8 3 Ring of planetary gear 9 4 Connecting rod, for coupling planetary gears to conrod (8) Sun of planetary gear, with drive shaft attached Planet of planetary gear 10 Conrod, between planetary gear and the tip of the leg (11) Bulkheads, for coupling of the tip of the leg (11) with pendulum (12) Rod, for coupling of the tip of the leg (11) with pendulum (12) Tip of the leg, which moves parallel to the pendulum (12) Pendulum, made with sheet metal 5 6 11 12 11
Figure 3.7 Front view of leg Nr Description of part Nr Description of part 1 Connection rod, for conrod (2) to pendulum Conrod, from crankshaft to pendulum (12) Ring of planetary gear 8 12 Conrod, between planetary gear and the tip of the leg (11) Bulkheads, for coupling of the tip of the leg (11) with pendulum (12) Rod, for coupling of the tip of the leg (11) with pendulum (12) Tip of the leg, which moves parallel to the pendulum (12) Pendulum, made with sheet metal 2 3 9 10 11 6 Connecting rod, for coupling planetary gears to conrod (8) Sun of planetary gear, with drive shaft attached Planet of planetary gear 13 Ring, for connection to the robot 7 Carrier of planetary gears 14 Ring, for coupling both planetary gear rings (3) 4 5 12
As can be seen in figure 3.7 a double gear set is used. They are on both sides of the tip of the leg to create a symmetric support for the connecting rod (4). Three planets in each gear are used to create rotational stiffness. The casing of the pendulum is made conic to create more deformation stiffness. This is especially necessary during the take off phase where the full weight of the robot has to be supported by four legs under an 45 degree angle (see figure 3.8). The left side of the casing (figure 3.7) of the pendulum is not made conic because on this side the motor will be attached. Making this side straight creates more stiffness in the driveshaft. To be able to connect the ring of the gear (3) to the robot four bearings are used, on each side two. Around the driveshaft of the sun (5) a bearing is placed on which the ring can rotate freely. Around the ring a second bearing is attached which makes it possible for the casing of the pendulum (12) to rotate freely around the ring and around the driveshaft. The rings for the planetary gears are coupled with element 14 to create one rigid ring. The connecting rod (10) to keep the tip of the leg (11) in place can slide between two sliders on each side. They are milled for accuracy and are attached to the casing (12) of the leg. The rod (2) for the pendulum motion is placed at the top left in figure 3.6. Element 13 is a supporting ring for shaft of the right planetary gear. This ring is attached to the robot. Figure 3.8 Support at full extension 13
4 Setup of multiple legs in the robot The previous chapter outlined the assembly of one leg. As said in chapter 2 the robot will be supported at 4 points with pairs of 2 legs. The support of the pairs has to remain inside one of the gray areas of figure 2.1. In this chapter the design of the coupled pair of legs will be presented and after that the configuration of all the legs. 4.1 Coupled pair of legs In the leg of figure 3.7 the motor (m1) for the driveshaft is attached on the left side. The coupled leg will be attached to motor m1 on the right side. It will therefore be a reversed version of figure 3.7 and the motor m1 is placed between the two legs. The state of the coupled leg is exactly the opposite, as is mentioned in chapter 2. Schematically this is shown in figure 4.1 with a front view and a top view. Figure 4.1 Top en front views of coupled legs 14
4.2 Multiple couples In combination with figure 2.1, 4 pairs of legs can be positioned in the robot. They are placed to the sides of the robot to create maximum stability. The top view of the robot with actuation of the extension is shown in figure 4.2. The driving of the pendulum is shown in figure 4.3. Figure 4.2 Top view of coupled legs in robot with extension actuation 15
Figure 4.3 Top view coupled legs with actuation of pendulum The dotted lines in figure 4.2 show the path of the tip of a leg, which fully use the available 220mm. The placing of the legs with a similar phase is done in the arrangement shown with the goal to minimize the amount of motors and minimization of the length of the crankshaft. To determine the amount of motors, steering has to be considered. Steering is done by driving the left side legs at a different rate than the right side legs. A difference can be created with a differential, but this would require a complex component with many parts (see [5]). Therefore the difference is created with two separate motors, as can be seen in figure 4.3. The minimization of the length of the crank is done with the coupling of two legs to one crank. The crankshafts on each side need therefore only two cranks. These two aspects and the reflection of the right side to the left creates a stable configuration. 16
To see the difference in height of the actuation of the pendulum motion and the extending motion a side view is shown in figure 4.4. The part which is designated as the robot has the maximum width and can take any form as long as the connection to the 6 motors is available. Figure 4.4 Side view robot with motors for extension a pendulum motion 17
5 Conclusion and remarks The mechanism has a step size of 220 mm per leg and in combination with the parts used; it will be able to attain a high velocity. There is not made use of pneumatic actuation or similar actuators which require time before maximum velocity can be reached. The combination of a pendulum motion and an extension causes that a relatively small mechanism can be used to create the 220 mm step. The combination of coupled legs with 4 supporting areas creates a stable support for the robot and only requires 6 motors for the whole actuation. The robot has a maximum weight of 40kg which will be supported by 4 legs. At maximum stretch of the legs the conic casing will help to support this weight. With the separation of the left and right side it is possible to steer the robot. The design has to be detailed further to be able to determine the exact dimensions of parts and requirements of motors and gears. Simulations with this data can be done with the SAM model shown in figure 3.5. Costs will also have to be considered during detailing, because in the design of the mechanism it is not taken into account which parts are commercially available. 18
6 References [1] Fédération Internationale de Football Association (FIFA), Laws of the Game, 2009/2010 [2] Middle Size Robot League Rules and Regulations for 2009, Version - 13.1 20081212, December 2008 [3] Arkive, Brown hare, http://www.arkive.org/brown-hare/lepus-europaeus/video-06.html, visited December 2009 [4] P.C.J.N. Rosielle, Constructieprincipes voor het nauwkeurig bewegen en positioneren, lecture notes 4007 (TU/e), March 2004 in Dutch [5] T.A.J.M. van de Ven, Concept design of a walking robot for Tech United., August 2009 [6] Tech United team meeting on 8 December, arranged by dr.ir. M.J.G. van de Molengraft 19