Singular configurations of planar parallel manipulators

Abstract

The paper deals with determining singular configurations for a group of 3 DOF planar parallel manipulators whose links form revolute and prismatic pairs. Relations for Jacobian matrix determinants for selected mechanisms are derived. The form of the equations differs depending on the structure of the inner part of the manipulators belonging to the Assur groups of the 3rd class. An analysis of the relations shows that singular configurations occur when Assur points coincide. Due to the approach proposed, singular configurations can be determined using classical kinematic analysis methods, without it being necessary to specify a Jacobian determinant and to define its zeroing conditions. Also a method of determining singular configurations from auxiliary mechanisms' characteristic point trajectory is proposed. The research results make it easier to define the conditions in which singular configurations occur.