Corank 2 singularities of planar 3-PRR parallel robots

Abstract

Parallel robots are used in various applications like motion simulators, industrial manipulators, machine tools, medical and surgical robots, and haptic devices. The reasons why parallel robots are preferred in such a wide spectrum of applications are that they have higher accuracy, higher stiffness, lower inertia, and larger payload-to-weight ratio compared to conventional series robots. Their biggest disadvantage is the presence of actuation singularities within their workspace. While approaching these singularities, which arise due to the closedloop architecture of the mechanism, the inverse dynamic solution grows unbounded, and the control of the robot is lost. For these reasons, it is of great importance for parallel robots to pass through actuation singularities so that they can use their entire workspace. Although the previous literature has generally focused on corank 1 actuation singularities, the occurrence of actuation singularities with a corank that is greater than one is also possible. The aim of this paper is to analyze corank 2 actuation singularities of planar 3-PRR parallel robots with three degrees of freedom. The loop-closure equation method is applied in the kinematic modeling of the robot. The loop-closure constraints are incorporated into the dynamic model via the use of Lagrange multipliers. The conditions required for the associated singular matrix to be rankdeficient by 2 are found. Keywords: Parallel robot, Singularity, Corank