Sparse monolithic compliant mechanisms using continuum structural topology optimization

A formulation for design of continuous, hinge-free compliant mechanisms is developed and examined within a continuum structural topology optimization framework. The formulation makes use of two distinctly different sets of springs, the first of which are artificial springs of relatively large stiffness attached to the input and output ports of the mechanism model, and the second of which are springs attached only to the output port with smaller stiffnesses that represent the resistance of the workpiece as it is manipulated by the mechanism. The proposed formulation involves solving two nested optimization problems. In the inner problem the arrangement of a constrained amount of structural material is optimized to maximize the mechanism’s mutual potential energy in response to a force loading at the input port while working against the stiff artificial springs on the input and output ports. As the relative stiffness of the artificial springs increases, the material continuity of the mechanism also increases to the point where de facto ‘hinge’ regions are eliminated. In the outer problem, the artificial springs are removed and one solves for an appropriate amount of structural material that yields the desired finite deformation compliance characteristics of the mechanism when working against the real workpiece resistance. Different aspects of the proposed formulation are demonstrated on a number of examples and discussed