Kinematic sensitivity analysis of the 3-UPU parallel mechanism

This paper addresses the kinematic sensitivity of the three degree-of-freedom 3-UPU parallel mechanism, a mechanism consisting of a fixed base and a moving platform connected by three serial UPU chains. Although a mathematical mobility analysis confirms that the mechanism has three degrees of freedom, hardware prototypes exhibit unexpected large motions of the platform even when the three prismatic joints are locked at arbitrary configurations. Existing mathematical classifications of kinematic singularities also fail to explain the gross motions of the 3-UPU. This paper resolves this apparent paradox. We show that the 3-UPU is highly sensitive to certain minute clearances in the universal joint, and that a careful kinematic sensitivity analysis of the 3-UPU augmented with virtual joints satisfactorily explains the gross motions. Observations with a hardware experimental prototype confirm the results of our sensitivity analysis.