Finding the optimal characteristic parameters for 3R pseudo-rigid-body model using an improved particle swarm optimizer

Compliant mechanisms have been used in many engineering areas where high precision and sensitivity are required. One of the major challenges of designing compliant mechanisms lies in understanding and analyzing the nonlinear deflections of flexible members. The pseudo-rigid-body model (PRBM) method, which simplifies the modeling of the nonlinear deflection by approximating it as motion of rigid links, has been accepted as one of the most important tools for synthesis and analysis of compliant mechanisms. In this paper, a review of various PRBMs is presented. The 3R PRBM whose characteristic parameters are independent of external loads is discussed in detail. For the purpose of finding the optimal set of the characteristic parameters for the 3R PRBM, a six-dimensional objective function is formulated by combining the approximation errors of both tip point and tip slope for the two extreme load cases, i.e., pure moment load and pure vertical force load. A particle swarm optimizer was employed to conduct a continuous search on the objective function. The resulting 3R PRBM with the optimized characteristic parameters shows better performance in predicting large deflections of cantilever beams over the original 3R PRBM.