# Changes between Version 5 and Version 6 of Burt-Research/KinematicsJointRangesConversionFactors

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Timestamp:
Dec 6, 2017, 5:53:27 PM (21 months ago)
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• ## Burt-Research/KinematicsJointRangesConversionFactors

 v5 = Kinematics, Transmission Ratios, and Joint Ranges = == Kinematics == * The robot has 3 joints: J1, J2, and J3, shown below. J1 rotates about Z0, J2 rotates about Z1, and J3 rotates about Z2. * J3 is able to change between left- and right-hand configurations, denoted J3L and J3R, respectively. * J1 and J2 are part of a cable differential system. 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. === D-H parameters === '''Figure 1: BURT D-H frames''' }}} * The robot has 3 joints: J1, J2, and J3, shown below. J1 rotates about Z0, J2 rotates about Z1, and J3 rotates about Z2. * J3 is able to change between left- and right-hand configurations, denoted J3L and J3R, respectively. * J1 and J2 are part of a cable differential system. === Forward Kinematics for BURT === 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. '''Forward Kinematics for BURT''' 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. }}} == Motor-to-Joint Transformations == '''Motor-to-Joint Position Transformations''' === Transmission ratios === 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. }}} === Transfmormation matrices === The motor position can also be derived from joint space by taking the inverse of the multiplying matrix. For convenience, they are as follows: }}} '''Motor-to-Joint Torque Transformations''' Similar to the position transformations the following equations determine the joint torque from the motor torque: