Optimal free-defect synthesis of four-bar linkage with joint clearance using PSO algorithm

This paper presents the design of planar four-bar linkages free of order, branch and circuit defects, for the purpose of path generation, having clearances at one, two, three or all of its joints. Joint clearance is treated as a massless virtual link and its direction is known by the direction of the joint force. A Particle Swarm Optimization based algorithm is given here to solve this highly nonlinear optimization problem with some constraints, namely; the Grashof's and free of the foregoing defects conditions. An example is included in which the optimal problem is solved for different cases; namely planar four-bar linkage having clearances at one, two, three, all of the joints and without clearance. For all the designs, the generated paths, the errors and the directions of the virtual links are plotted and are compared. Finally, we compare the optimal designs with reality.