Singularity analysis of a planar parallel mechanism with revolute joints based on a geometric approach

Abstract

The singularity is a critical part of a parallel kinematic machine (PKM) in which the degree of freedom decreases or actuator forces conflict with one another to break down the PKM. Therefore, defining and avoiding the region of singularities are essential for safely operating PKMs. This paper proposes a new method for determining the singularity of a planar-type PKM with revolute joints by taking a geometric approach. The main idea of the paper is to use the wrench, not velocity, equation to calculate the Jacobian matrix. In addition, a distinct feature of the proposed method is that it uses perpendicular distances between end-effectors, actuators, and screws to determine singularities based on screw theory. This proposed method can analyze many types of PKMs, including non-redundant as well as redundant ones. The paper considers non-redundant and redundant 5-bar, 6-bar, 3-RRR, and 4-RRR PKMs for case studies. The proposed method is intuitive and simple and thus can be used for analyzing the singularity of various PKMs.