Kinematically started efficient position analysis of deformed compliant mechanisms utilizing data of standard joints

Topology optimization of a flexure-based mechanism requires the properties of the mechanism in several deformed configurations. This paper presents a fast and accurate method to compute these configurations. It is generally applicable on mechanisms with complex standard flexure joints. First kinematic equations of the mechanism are derived by allowing the mechanism to move only in the directions for which it is designed. Secondly the configurations of the joints are approximated based on the rotations of the elements by which the joints are modeled. These orientations are obtained by a parameterization based on a priori knowledge of standard flexure joints. Finally, the resulting approximation is used as initial guess to obtain the configuration accurately, after which relevant properties like stiffness can be derived. For a manipulator with three complex joints the computation time was reduced up to a factor of 65 compared to a conventional method. When for optimization purposes an approximation is acceptable, the computation time can be reduced by a factor of 600, using a linear description of the deformation that remains in the first part of the method.