THE CONFIGURATION SPACE OF A PARALLEL POLYGONAL MECHANISM

Nir Shvalb (Israel), Moshe Shoham (Israel) and David Blanc (Israel)

Received December 18, 2007; Revised February 8, 2009

Abstract

We study the configuration space  of a parallel polygonal mechanism, and give necessary conditions for the existence of singularities; this shows that generically  is a smooth manifold. In the planar case, we construct an explicit Morse function on  and show how geometric information about the mechanism can be used to identify the critical points.

Keywords and phrases: configuration space, work space, robotics, (planar) mechanism.