Analytical prediction of singularity sensitivity of the Bennett spatial mechanism to dimensional deviations

This paper investigates the sensitivity of singular configurations in a one-degree-of-freedom Bennett spatial mechanism to geometric deviations. Although the mechanism exhibits exact mobility under strict conditions, practical implementations introduce inaccuracies affecting its kinematic and kinetostatic behaviour. Experiments on a mechatronic prototype reveal increased actuator current near singular configurations, indicating degraded transmission properties. An analytical framework is proposed to interpret this phenomenon. The loop-closure equations are reformulated using a virtual compensation transformation incorporating these deviations. Sensitivity is evaluated through displacement analysis, the smallest singular value, Jacobian conditioning, force-ellipsoid analysis, and a peak-to-baseline force-ellipsoid volume ratio quantifying local force-transmission sensitivity. Results show that deviations significantly modify singular behaviour. While the ideal mechanism approaches rank deficiency with vanishing singular values, geometric deviations regularize the singularity by maintaining finite singular values and increasing actuator demand near critical configurations. The framework supports analysis of over-constrained mechanisms with geometric imperfections.