On the numerical kinematic analysis of general parallel robotic manipulators

A systematic two-part approach for the numerical kinematic analysis of general parallel robotic manipulators, is presented. The first part deals with structural analysis. Based on graph theory and the depth first search algorithm, a method for identifying and orienting the dependent kinematic loops of the robot is developed. This method not only facilitates the assignment of the local coordinate systems attached to the robot, but also arranges them in the correct order to allow efficient recursive coordinate transformation. The second part deals with displacement analysis. A set of recursion formulas is developed for computing the forward coordinate transformations, and these formulas are then adopted in a two-phase computational algorithm to obtain the numerical solutions to the direct and inverse kinematics problems. The two-phase algorithm developed is not only insensitive to the initial approximation of the solution vector, but also converges rapidly. It is also useful for finding multiple solutions for the robot as well as for continuous trajectory planning, as shown by the numerical examples presented