Research on the error transfer characteristics of a 3-DOF parallel tool head

The Jacobian matrix and many other indices based on it are usually used to evaluate the kinematic performance of a parallel manipulator. For the parallel tool head developed based on the 3-DOF parallel manipulator with two rotational degrees of freedom and one translational degree of freedom (2R1T), the error transfer characteristic between the deviation of tool tip and the joint error of each driving shaft is one of the important kinematic performances should be evaluated. However, the original Jacobian matrix of the 2R1T parallel manipulator has the dimensional problem. Thus, it is hard to provide an effective error transfer characteristics evaluation of this type of parallel manipulator by using the original Jacobian matrix and traditional kinematic indices, which no longer have clear physical meaning, and we don't know which joint error of driving shaft in joint space would have greater effect on the motion error of end-effector. In order to solve these problems, by taking a 3-DOF parallel tool head as an object, a novel dimensionless homogeneous error transfer matrix is first formulated. Based on this transfer matrix, an index named ETI is proposed to further evaluate the error transfer characteristics of the 3-DOF parallel tool head. Furthermore, some simulations of contouring error and a straight line motion experiment are given to prove the effectiveness of the theory proposed in this paper.