Direct Kinematic Analysis of 3-rs Parallel Mechanisms

This article presents a direct kinematic analysis of 3-RS parallel mechanisms. A 3-RS parallel mechanism consists of a ®xed base and a moving platform connected by three serial chains, with each serial chain containing one passive revolute joint and one passive spherical joint. A variety of 3-RS mechanisms have been proposed in the literature, to overcome the disadvantages of small workspace characteristic of Stewart platforms and other 6±6 parallel mechanisms. We provide a computationally ecient method to solve the direct kinematics problem for general 3-RS mechanisms. By appealing to Sylvester's dialytic elimination method, the direct kinematics problem can be reduced to the solution of a 16th order polynomial equation in a single variable. In our approach the polynomial coecients are represented in terms of convolutions of vectors, which considerably simpli®es the coding of the algorithm, and unlike existing approaches does not rely on symbolic computation software. The method is applied to the direct kinematic analysis of the Eclipse, a novel six d.o.f. 3-RS parallel mechanism designed for ®ve-face machining. Ó 2001 Elsevier Science Ltd. All rights reserved.