Manipulators: Execution of prescribed trajectories special link positions and versions of assembly

Abstract A new technique for the kinematical analysis and design of manipulators based on the following principles is proposed: 1. (1) Link positions are determined by subsystems of equations which contain a reduced number of unknowns and may be solved separately. The derivation of such systems of equations may be based: (a) on the modeling of the manipulator by two open chains or (b) on modified closure matrix equations. 2. (2) Special 4 × 4 matrices which describe separately the link geometry and the relative motion of links are applied. 3. (3) All potential configurations which are formed by the manipulator links may be determined using the information on special link positions. 4. (4) Angles of rotation in the joints are determined as functions of the trajectory parameters using a system of six nonlinear equations represented in echelon shape. The above techniques are applied for the kinematical analysis of a Cincinnati Milacron T3 manipulator with six degrees-of-freedom. A computer program for the control of rotations in the joints has been developed based on these techniques, and the results are presented at the end of this paper.