Repeatability Analysis of an Overconstrained Kinematic Coupling Using a Parallel- Mechanism-Equivalent Model

A parallel-mechanism-equivalent model for repeatability analysis of an overconstrained kinematic coupling is proposed. An overconstrained Kelvin-type coupling with one additional support is introduced and used for method illustration. Contact forces of the an overconstrained coupling under a preload are computed with the Moore-Penrose inverse, and the deformations are obtained using the Hertz theory. The coupling is equivalently modeled as a 7-SPS parallel mechanism, the spherical joints of which represent centers of supporting balls and contact points, and prismatic joints are used to simulate the deformations. Therefore, the pose error of the coupling due to a preload is analyzed using the well-appraised incremental method for forward kinematics analysis of parallel mechanisms. The uncertainties of the preload are discussed and a boundary-sampling method is proposed for repeatability analysis. The main contribution of this study lies in the greatly simplified repeatability analysis of overconstrained kinematic couplings by the proposed parallel-mechanism-equivalent model and the boundary-sampling method. Finally, the proposed methods are validated by a case study.