Graphical singularity analysis of 3-DOF planar parallel manipulators

This paper introduces a new approach to identify singularities of planar parallel manipulators (PPMs). This method is based on Maxwell's reciprocal figure theory which establishes a duality between self-stress frameworks and reciprocal figures. We use line geometry tools to introduce a new graphical construction called the Mechanism's Line of action Graph (MLG). The MLG is introduced in order to implement Maxwell's Reciprocal Figure theory to mechanisms. In this paper, we show that the configurations where the MLG has a connected reciprocal figure imply a singularity type-II in the mechanism. This singularity analysis tool is also used to trace the singularity loci of the PPM.