Optimization of release locations for small self-stress large stiffness flexure mechanisms

In overconstrained mechanisms inherent alignment errors cause self-stress. The level of stress can be reduced by inserting flexure releases making the mechanism exactly constrained. The location and orientation of releases can be optimized for a combination of minimum self-stress and maximum stiffness. We compare two methods for optimization in a case study of a four-bar mechanism with three overconstraints. The first method analyzes the kinematics of a mechanism using a multibody modeling approach and a singular value decomposition. The second method lumps the compliance of the mechanism to the joints. It is shown that in order to obtain a mechanism with large stiffness and small self-stress over a range of motion the mechanism must be exactly constrained in special poses. In a special pose an exactly constrained mechanism can become statically and kinematically indeterminate due to an alignment of releases. The singular value decomposition method is a powerful tool to find the special poses and to design exactly constrained configurations. It provides sufficient insight to assist the selection of release locations, without requiring all the stiffness properties of the mechanism.