Kinematic Control of Parallel Mechanisms in the Presence of Unstable Singularities

Parallel mechanisms frequently contain an unstable type of singularity that has no counterpart in serial mechanisms. When the mechanism is at or near this type of singularity, it loses the ability to counteract external forces in certain directions which can lead to arbitrary motion. The determination of unstable singular configurations in parallel mechanisms is not trivial, and is usually attempted via exhaustive search of the workspace using the mechanism kinematics. This paper considers the kinematic control of parallel mechanisms in the presence of unstable singularities. Various possible remedies are considered, including passive joint actuation, active external bracing, and passive joint braking. The braking method is explored in detail since it requires less instrumentation and mechanical modification, and does not require a priori information of the singularity locations. Simulation results based on a planar platform and a six-degree-of-freedom machining center are presented to illustrate the approach.