A novel algorithm for kinematic and dynamic optimal synthesis of planar four-bar mechanisms with joint clearance †

In practice, clearances in the joints are inevitable due to tolerances and defects arising from design and manufacturing. Moreover, the joints undergo wear and backlash, resulting in poor accuracy and repeatability. This paper presents a novel optimization method for simultaneously kinematic and dynamic synthesis of a planar four-bar linkage with clearance at the joints. It is well-known that in the presence of clearance at a joint, the linkage gains an additional, uncontrollable degree of freedom which is the source of error. Here, we synthesis the path generation problem while controlling the unwanted degrees of freedom by revising the mass distributions of the moving links. An algorithm based on particle swarm optimization method solves this highly nonlinear optimization problem with some constraints. Finally, an example is included to demonstrate the efficiency of the algorithm. The results clearly show that the linear and angular accelerations of the links for the optimal design are very smooth and bounded.