Changes between Version 3 and Version 4 of Rehab/KinematicsJointRangesConversionFactors
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 Nov 3, 2016, 9:09:16 PM (2 years ago)
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Rehab/KinematicsJointRangesConversionFactors
v3 v4 4 4 A good introduction to coordinate frames, transformations and kinematics is beyond the scope of this document. There are several good introductory robotics books available. We recommend Spong, M.; Hutchinson, S.; Vidyasagar, M. Robot Modeling and Control; 2006 John Wiley & Sons as we use the variant of the DenavitHartenberg (DH) method that is from this book to establish the coordinate frames. 5 5 6 Figure 1 below shows the Proficio in its zero position. A positive joint motion is based on the right hand rule for each axis.6 DH frames are defined roughly as shown in Figure 1 when the robot is in its zero position (NOT the robot’s home position). Note that the joint range of Joint 3 (Table 2) prevents the Proficio from actually reaching this position. Frames 0 and 1 are located at the intersection of the J1 and J2 axes. Frame 2 is coincident to the J3 axis. The frame 3 origin is coincident to the center of the haptic ball when it points straight up. The DH parameters do not change between left and righthanded configurations. However, the configuration files do contain separate worldtobase transforms for each configuration. These transforms define the origin of the world frame to be at the user’s sternum, 540 mm from the X1Z1 plane along Z0. The diagram shows the locations of the world origin in lefthanded and righthanded robot configurations. A positive joint motion is based on the right hand rule for each axis. 7 7 8 8 {{{ … … 12 12 '''Figure 1: Proficio DH frames''' 13 13 }}} 14 15 14 16 15 Equation 1 below gives the transform between two adjacent DH coordinate frames. The DH parameters that were derived from this equation are located in Table 1 below. Note that c and s stand for cos and sin respectively. … … 70 69 }}} 71 70 72 '''Forward Kinematics for the 4DOF WAM'''71 '''Forward Kinematics for the Proficio''' 73 72 74 The forward kinematics of the 4DOF WAM system is used to determine the end tip location and orientation. These transformations are generated using the parameters in Table 1 and the matrix in Equation 1. 73 The forward kinematics of the Proficio are used to determine the end tip location and orientation. These transformations are generated using the parameters in Table 1 and the matrix in Equation 1. 74 75 The forward kinematics are determined for any frame on the robot by mulitplying all of the transforms up to and including the final frame. To determine the endpoint location and orientation use the following equation: 75 76 76 77 {{{ … … 78 79 {{{ 79 80 #!latex 80 $^{4}T_{tool}=\left[\begin{array}{cccc} 81 u_{x} & v_{x} & w_{x} & P_{x}\\ 82 u_{y} & v_{y} & w_{y} & P_{y}\\ 83 u_{z} & v_{z} & w_{z} & P_{z}\\ 84 0 & 0 & 0 & 1\end{array}\right]$ 81 $^{0}T_{3}=^{0}T_{1}^{1}T_{2}^{2}T_{3}^{3}$ 85 82 }}} 86 83 87 '''Equation 3: Tool frame matrix''' 88 }}} 89 90 You define the frame for your specific endeffector. The forward kinematics are determined for any frame on the robot by mulitplying all of the transforms up to and including the final frame. To determine the tool end tip location and orientation use the following equation: 91 92 {{{ 93 #!div class="center" align="center" 94 {{{ 95 #!latex 96 $^{0}T_{Tool}=^{0}T_{1}^{1}T_{2}^{2}T_{3}^{3}T_{4}^{4}T_{Tool}$ 97 }}} 98 99 '''Equation 4: Tool end tip position and orientation equation for the 4DOF WAM''' 100 }}} 101 102 '''Forward Kinematics for the 7DOF WAM''' 103 104 As with the previous example, you define the frame for your specific endeffector. The forward kinematics are determined for any frame on the robot by mulitplying all of the transforms up to and including the final frame. To determine the end tip location and orientation use the following equation: 105 106 {{{ 107 #!div class="center" align="center" 108 {{{ 109 #!latex 110 $^{0}T_{Tool}=^{0}T_{1}^{1}T_{2}^{2}T_{3}^{3}T_{4}^{4}T_{5}^{5}T_{6}^{6}T_{7}^{7}T_{Tool}$ 111 }}} 112 113 '''Equation 5: Tool end tip position and orientation equation for the 7DOF WAM''' 84 '''Equation 3: Tool end tip position and orientation equation for the Proficio''' 114 85 }}} 115 86 … … 213 184 }}} 214 185 215 == Joint Resolution ==216 {{{217 #!div class="center" align="center"218 '''Table 9: Joint resolution'''219  '''Motor Encoder[[BR]](ME) Cts/Rev''''''Motor/Joint[[BR]]Ratio''''''ME Cts/[[BR]]Joint Rev''''''Joint Encoder[[BR]](JE) Cts/Rev''''''Meters/[[BR]]Joint Rev''''''ME Position[[BR]]Resolution (m)''''''ME Orientation[[BR]]Resolution (rad)''''''JE Position[[BR]]Resolution (m)''''''JE Orientation[[BR]]Resolution (rad)'''220  '''J1'''  4096 42 172,032 1,578,399 6.28 36.5E6 36.5E6 4.0E6 4.0E6221  '''J2'''  4096 28.25 115,712 655,360 6.28 54E6 54E6 9.6E6 9.6E6222  '''J3'''  4096 16.8 68,812 655,360 3.14 45E6 91E6 4.8E6 9.6E6223  '''J4'''  4096 18 73,728 327,680 3.14 42.6E6 85.2E6 9.6E6 19.2E6224  '''J5'''  4096 9.48 38,830 N/A 376.8E3 9.7E6 161.7E6 N/A N/A225  '''J6'''  4096 9.48 38,830 N/A 376.8E3 9.7E6 161.7E6 N/A N/A226  '''J7'''  4096 14.93 61,153 N/A 0 N/A (backlash) 17.5E3 N/A N/A227 }}}