Topology optimization of fundamental compliant mechanisms using a novel asymmetric beam flexure

Flexure or compliant mechanisms have found application in many nano/micro and macro devices. They usually provide guided motion via elastic deformation of their flexure beams. A properly designed flexure shall have large bearing to motion direction stiffness ratio in a wide range of the stage displacement. A common approach for achieving such design requirement is to reinforce the constitutive flexure beams via an intermediate rigid element which has been symmetrically placed in the middle of the beam. The objective of the current paper is to investigate if it is possible to improve the performance of such flexures via utilizing the reinforcement rigid element in anasymmetric manner. Based on the principle of virtual work, the differential equations governing the static behavior of an asymmetric reinforced beam (ARB) flexure are derived. By employing the beam constraint model (BCM), closed-form expressions are derived for the end displacements of the beam in terms of the applied end loads. Also, an analytical expression is suggested for the strain energy of an ARB solely in terms of its end displacements. This formula is used to find the strain energy, load-displacement relations, stiffnesses and error motions of parallelogram (P) flexures constituted from ARBs. Results related to the stiffness and error motions are closely verified via finite element simulations. It is observed that in most situations, the best performance corresponds to a P-flexure with asymmetric beams. In addition, contour plots of the ratio of bearing to motion direction stiffness of this P-flexure are presented in terms of the normalized specifications of the system to provide the designers with a convenient tool for proper selection of design parameters. Genetic algorithm is employed along with the concept of ARB flexures to design an optimal P-flexure. Simulation results reveal that the performance index of a sample P -flexure with ARBs is appreciably higher than that of an optimal P -flexure with symmetric reinforced beams. The novel idea presented in this research can be effectively employed to enhance the efficiency of more complicated beam-based flexure modules. (C) 2017 Elsevier Ltd. All rights reserved.