On the Kinematic Analysis of Robotic Mechanisms

The kinematic analyses, of manipulators and other robotic devices composed of mechanical links, usually depend on the solution of sets of nonlinear equations. There are a variety of both numerical and algebraic techniques available to solve such systems of equations and to give bounds on the number of solutions. These solution methods have also led to an understanding of how special choices of the various structural parameters of a mechanism influence the number of solutions inherent to the kinematic geometry of a given structure. In this paper, results from studying the kinematic geometry of such systems are reviewed, and the three most useful solution techniques are summarized. The solution techniques are polynomial continuation, Gröbner bases, and elimination. We then discuss the results that have been obtained with these techniques in the solution of two basic problems, namely, the inverse kinematics for serial-chain manipulators, and the direct kinematics of in-parallel platform devices. KEY WORDS—inverse kinematics, direct kinematics, manipulators, in-parallel manipulators, series manipulators, polynomial continuation, characteristic polynomial