THE JOINT DISPLACEMENT METHOD FOR MULTILOOP KINEMATIC ANALYSIS

We present a kinematic formulation, referred to as the joint displacem ent method. In the kinematic analysis; the closed-loop kinematic chain of interest must be transformed into several open-loop chains by imag ining that some joints are relaxed (disconnected), and by replacing th em as physical entities with a set of constraint equations. This formu lation requires only a minimal number of generalized coordinates, henc e it provides;a highly efficient approach for real-time kinematic anal ysis of spatial mechanisms, heretofore unseen in the literature. For-e xample, the Jacobian matrix for the RSCR mechanism is 3 x 3 and the CP U time required to perform Gauss elimination is 182 times shorter than that in the traditional link-coordinate method which requires a 17 x 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 t hat implements the joint displacement method has been developed and te sted on a variety of mechanisms.