Solving Jacobian Matrix of Parallel Manipulators With Linear Driving Limbs by Using CAD Variation Geometric Approach

Abstract

The velocity Jacobian matrix and the force Jacobian matrix are important index for kinematics, singularity and dynamics analyses of parallel manipulators. A novel computer variation geometric approach is proposed for solving the velocity Jacobian matrix and the force Jacobian matrix of parallel manipulators with linear driving limbs, as well as the determinant of Jacobian matrix. First, basic computer variation geometry techniques and definitions are presented for designing the simulation mechanisms, and several simulation mechanisms of parallel manipulators with linear driving limbs are created. Second, some velocity simulation mechanisms are created and the partial derivatives in Jacobian matrix are solved automatically and visualized dynamically. Based on the results of the computer simulation, the velocity Jacobian matrix and force Jacobian matrix are formed and the determinant of Jacobian matrix is solved. Moreover, the simulation results prove that the computer variation geometry approach is fairly quick and straightforward, and is accurate and repeatable. This project is supported by NSFC No. 50575198.

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