A New Approach for the Orders of the Bennett-Based Linkages in Mobility Analysis

Among the 3D single-loop overconstrained linkages, quite a number of them are combinations of Bennett linkages. Mobility on the overconstrained linkages including the Bennett-based linkages is known to be one of the difficult topics in kinematics. In the paper, a new approach based on the linear superposition principle for determining the orders of Bennett-based linkages is proposed, and the mobility of some typical Bennett-based linkages is calculated with the Modified Gru¨bler-Kutzbach criterion. In addition, geometric properties of some of the screw systems are employed to identify whether the mobility is global.