The Joint Displacement Method for Multiloop Kinematic Analysis

We present a kinematic formulation, referred to as the joint displacement method. In the kinematic analysis, the closed-loop kinematic chain of interest must be transformed into several open-loop chains by imagining that some joints are relaxed (disconnected), and by replacing them as physical entities with a set of constraint equations. This formulation requires only a minimal number of generalized coordinates, hence it provides a highly efficient approach for real-time kinematic analysis of spatial mechanisms, heretofore unseen in the literature. For example, the Jacobian matrix for the RSCR mechanism is 3 × 3 and the CPU time required to perform Gauss elimination is 182 times shorter than that in the traditional link-coordinate method which requires a 17 × 17 Jacobian matrix. This method is applicable to both single loop and multiloop spatial mechanisms with revolute, cylindrical, translational, spherical and universal joints. A general-purpose computer program that implements the joint displacement method has been developed and tested on a variety of mechanisms.