A mechanism is designed to transform forces and/or displacements from an input to one or multiple outputs. This transformation is essentially ruled by the kinematics, i.e. the defined ratio between input and output displacements. Although the kinematics forms the basis for the design of conventional mechanisms, approaches for the topology and shape optimization of compliant mechanisms do not normally explicitly include the kinematics in their optimization formulation. The kinematics is more or less an outcome of the optimization process. A defined kinematics can only be realized by iteratively adjusting process-specific optimization parameters within the optimization formulation. Moreover, existing approaches normally minimize the strain energy that is stored in the compliant mechanisms according to a defined input and output displacement — although in some applications a certain amount of strain energy is required. This paper presents a new optimization formulation that solves the aforementioned problems. It is based on the principles of designing compliant mechanisms with selective compliance formerly presented by the author. The formulation is derived by means of an intensive workup of the design problem of compliant mechanisms. The method is validated for different design examples ranging from standard single-input/single-output mechanisms (force inverters) to multi-output mechanisms (shape-adaptive structures).

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