Kinematic analysis and singularity representation of spatial five-degree-of-freedom parallel mechanisms

Abstract

This article addresses the kinematic modeling and the determination of the singularity loci of spatial five-degree-of-freedom parallel mechanisms with prismatic or revolute actuators. The architecture of the spatial five-degree-of-freedom parallel mechanisms is first introduced. Then, algorithms are derived for the solution of the inverse kinematic problem for the two types of mechanisms considered here. Two different methods are presented for the derivation of the velocity equations and the corresponding Jacobian matrices are derived. The numerical determination of the workspace boundaries is then briefly discussed. Finally, the determination of the singularity loci is performed, using the velocity equations, and examples are given to illustrate the results. It is shown that the vector formulation of the velocity equations leads to more efficient algorithms for the determination of the singularity loci. Spatial five-degree-of-freedom parallel mechanisms can be used in several robotic applications as well as in flight simulators. The kinematic analysis and the determination of the singularity loci are very important design issues. © 1997 John Wiley & Sons, Inc.