John F. O’Brien
Constraint singularity, parallel robots, unstable singularity, self-motion, 3-RPS
The constraint singularity is a type of configuration-space singularity in parallel robots that, like the redundant output singularity, allows end-effector motion even with all active joints fixed (unstable motion). However, the constraint singularity cannot be eliminated by swapping active and passive joints, and may fail to be detected by analysis of active joint differential kinematics. A geometric, coordinate-free method of determining the necessary conditions for unstable motion is modified in this paper to find constraint singularities. As opposed to numerical searches, this method requires finding rank deficiency conditions of two sparse matrices. The approach is used to find constraint singularities in the 3-RPS parallel robot.
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