Inverse kinematic and dynamic analysis of planar path generating adjustable mechanism

Path generating adjustable mechanisms with continuous adjustment have been studied in literature, wherein the synthesis has been commonly based on the position kinematics of the mechanism. Many real life applications would, however, demand that the coupler point traces the path at specified velocity and acceleration, thus necessitating development of inverse velocity and acceleration analyses. Further, the inverse dynamic analysis needs to be carried out from the viewpoint of mechanical design and motion control of the mechanism. In this paper, inverse kinematic and dynamic analysis of a path generating four-bar mechanism with continuous one-parameter adjustment is presented. The kinematic analysis is presented for both, the non-singular and singular configurations of the mechanism. Newton's equations of motion are solved by introducing a set of generalized unknowns, resulting in explicit formulae for all the unknowns. The dynamic analysis approach is general and is applicable to any multi-degree-of-freedom single-loop planar mechanism with revolute joints. Results are presented for illustrative examples and future extension of the presented work is discussed.