Cartesian Dimensional Homogeneous Jacobian Matrix for Performance Evaluation and Optimization of Complex Dof Parallel Manipulator

Kinematic performance indices are used to have an evaluation of the potential efficiency of the robots. Some of these items are designing the optimal structure, trajectory planning, programming, and evaluation of behavior of the robot in positioning and orienting with desired rates or resolution. These indices will be used when the robot has even translational or rotational degrees of freedom (DoF). Due to dimensional incompatibility of the Jacobian entries in the complex DoF’s robots with both types of DoF’s, performance indices such as Jacobian condition index and associate singular values, are not applicable. In this paper, inhomogeneity of Jacobin matrix has been resolved by introducing a new Jacobian matrix which is called Cartesian Jacobian Matrix (CJM). Cartesian Jacobian Matrix maps Cartesian velocity vector of End-Effector (EE) to the joint space velocity vector. As a case study, the suggested method has been used for a Tricept parallel kinematic manipulator. Moreover, considering Local Conditioning Index (LCI) and associated singular values through the workspace have been led to structure optimization of the robot in order to have maximum positioning and orienting rates of EE through the maximum cuboid workspace. The optimization has been performed by Genetic algorithm via GA toolbox of MATLAB 2012 software.