Many artifacts made by humans are designed to be strong and rigid to keep their shape by resisting deformation. In contrast, nature prefers flexible bodies and tends to accept deformation rather than prevent it except for special applications—bones, teeth, and so forth. A compliant mechanism is a single piece flexible mechanism that depends on elastic deformation of its members to transfer force or motion. Using designs in nature as motivation, this research developed a mathematical, hence computational, framework for design of compliant mechanisms that are suitable for a large range of motion.; Compliant mechanisms here are designed in two stages; (a) topology synthesis and (b) size and shape synthesis. The topology design yields a kinematically feasible configuration to produce the desired output motion under the action of applied input and adequate stiffness to withstand external loading. A multi-objective function is defined as maximizing geometric advantage (= output displacement/input displacement) over strain energy is formulated. Next, the size and shape design is performed to satisfy performance criteria such as stress, buckling constraints, etc. using an objective function that maximizes geometrical advantage. These two design stages are carried out based on geometric nonlinear formulations. This nonlinear formulation is implemented using finite beam element and Newton-Raphson method and solved using sequential linear programming and sequential quadratic programming methods, respectively. The topology design procedure is capable of handling both two-dimensional problems as well as three-dimensional problems that enables us to design more sophisticated mechanisms. Additionally, a parametric study of the effect of design variables on the objective function is carried out and scaling laws are investigated.
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