Changes between Version 5 and Version 6 of Burt-Research/KinematicsJointRangesConversionFactors
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- Dec 6, 2017, 5:53:27 PM (7 years ago)
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Burt-Research/KinematicsJointRangesConversionFactors
v5 v6 1 1 = Kinematics, Transmission Ratios, and Joint Ranges = 2 3 == Kinematics ==4 5 * The robot has 3 joints: J1, J2, and J3, shown below. J1 rotates about Z0, J2 rotates about Z1, and J3 rotates about Z2.6 * J3 is able to change between left- and right-hand configurations, denoted J3L and J3R, respectively.7 * J1 and J2 are part of a cable differential system.8 9 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 Denavit-Hartenberg (D-H) method that is from this book to establish the coordinate frames.10 11 2 12 3 === D-H parameters === … … 20 11 '''Figure 1: BURT D-H frames''' 21 12 }}} 13 14 * The robot has 3 joints: J1, J2, and J3, shown below. J1 rotates about Z0, J2 rotates about Z1, and J3 rotates about Z2. 15 * J3 is able to change between left- and right-hand configurations, denoted J3L and J3R, respectively. 16 * J1 and J2 are part of a cable differential system. 17 18 === Forward Kinematics for BURT === 22 19 23 20 Equation 1 below gives the transform between two adjacent D-H coordinate frames. The D-H parameters that were derived from this equation are located in Table 1 below. Note that c and s stand for cos and sin respectively. … … 67 64 68 65 69 '''Forward Kinematics for BURT'''70 71 66 The forward kinematics of BURT 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. 72 67 … … 98 93 }}} 99 94 100 101 == Motor-to-Joint Transformations == 102 '''Motor-to-Joint Position Transformations''' 95 === Transmission ratios === 103 96 104 97 The following transformations show the change in joint positions as a function of motor positions. The input transmission ratios and the differential transmission ratios are calculated from known pulley, pinion, and cable diameters. … … 130 123 }}} 131 124 125 === Transfmormation matrices === 126 132 127 The motor position can also be derived from joint space by taking the inverse of the multiplying matrix. For convenience, they are as follows: 133 128 … … 152 147 }}} 153 148 154 '''Motor-to-Joint Torque Transformations'''155 149 156 150 Similar to the position transformations the following equations determine the joint torque from the motor torque:
