Direct kinematic analysis of 3-RS parallel mechanisms

Abstract

This article presents a direct kinematic analysis of 3-RS parallel mechanisms. A 3-RS parallel mechanism consists of a fixed 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 efficient 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 coefficients are represented in terms of convolutions of vectors, which considerably simplifies 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 five-face machining.