Optimal design of compliant mechanisms.

Abstract

Compliant mechanisms are mechanical devices that rely on elastic deformation to achieve force and motion transmission. Unlike load-bearing structures which are designed to be as stiff as possible, compliant mechanisms are designed to be flexible in order to achieve a specified motion. And unlike conventional mechanisms consisting of several rigid links connected with rigid joints, compliant mechanisms can be designed as single-piece entities that require no assembly. They are especially suited for applications requiring a small range of motion. The challenge in designing compliant mechanisms is to provide adequate flexibility in order to achieve the required motion, but at the same time provide adequate stiffness and mechanical advantage. Development of systematic methods for the synthesis and design of compliant mechanisms is the focus of this dissertation. A new method for designing compliant mechanisms is developed using topology optimization. The compliant mechanism design problem is posed in two parts, one which addresses the motion requirements, and another which addresses the loading requirements. The mutual potential energy is considered as a measure of flexibility, and the strain energy is considered as a measure of stiffness. The conflicting design objectives of maximum flexibility and maximum stiffness are handled via multi-criteria optimization, where the objective function is posed as a ratio of mutual potential energy to strain energy. This problem formulation is implemented using finite elements and solved using the sequential linear programming method. A penalty function on the design variables is introduced to facilitate convergence for large problems. This procedure is capable of handling both two-dimensional and three-dimensional problems, as well as problems with multiple outputs. Results indicate good convergence, and subsequent finite element analysis verifies the functionality of the optimal solution. Furthermore, physical prototypes were fabricated which serve as proof of concept. An investigation into avoiding lumped compliance by distributing the strain energy density uniformly throughout the structure is also made using an optimality criteria method. The results of the topology optimization algorithm demonstrate that it is a viable method for designing compliant mechanisms based on functional specifications, and that both the flexibility and stiffness requirements are handled effectively.