Ground Structure Based Joint Stiffness Controlling Method for Joint Compliant Mechanism Design

Abstract

The object of this study is to develop a topology optimization method for the design of joint compliant mechanism structures. Joint compliant mechanisms are compliant mechanisms consisting of rigid or sufficiently rigid one-dimensional elements and elastic hinge joints. Although continuumbased methods have been successful to configure compliant mechanisms, the optimized mechanisms are usually difficult to manufacture because of their geometric complexities. The ground structure based topology optimization method using beam elements can alleviate the geometric complexity issue, but it is still difficult to actually fabricate the optimized layouts. Existing topology optimization results on compliant mechanisms indicate that optimized compliant mechanisms have very localized eastic deformations to wok as mechanisms. This means that most elastic deformations in compliant mechanisms occur in very localized hinge regions. Therefore, it will be advantageus to find directly the elastic hinge joint locations and stiffnss values by a topology optimization formulation while ground beams are treated only as joint-connecting elements without going through much deformation. Motivated by this observation, we propse a joint stiffness controlling method where gournd beams of given thickness are connected through joint springs at beam joints. The main characteristics of the proposed method are: 1) beam elements are connected by elastic joints, not by rigid ones, 2) instead of geometric dimensions of beam elements, the stiffness of the joints is varied during optimization, 3) the maximum translational and rotational stiffnesses of the joints are assumed to be proportional to those of neighboring beams, and 4) the final topology of a structure is obtained by considering the connectivity of beam elements at the joints. To take manufacturability into account, joint springs are allowed to take on only a few discrete values; a set of pre-manufactured elastic joints having different rotational stiffness are assumed to be available in designing compliant mechanisms. The validity and effectiveness of the proposed design method is investigated by solving a couple of numerical examples including the popular design problems of a micro force converter and micro gripper.