The primary compliance vector (PCV) captures the dominant kinematic behavior of a compliant mechanism. Its trajectory describes large deformation mechanism behavior and can be integrated in an optimization objective in detailed compliant mechanism design. This paper presents a general framework for the optimization of the PCV path, the mechanism trajectory of lowest energy, using a unified stiffness characterization and piecewise curve representation. We present a meaningful objective formulation for the PCV path that evaluates path shape, location, orientation, and length independently and apply the framework to two design examples. The framework is useful for design of planar and shell compliant mechanisms that traverse a specified mechanism trajectory and that are insensitive to load perturbations.

The primary compliance vector captures the predominant kinematic degree of freedom of a mechanism. Its displacement describes large deformation mechanism behavior and can be an optimization objective in detailed compliant mechanism design. This paper presents a general framework for the optimization of the PCV path of compliant mechanisms using unified stiffness characterization, Fourier descriptors, and surrogate-based optimization. We found a meaningful objective formulation that evaluates PCV path shape independently. Furthermore, we reason that design variables should effect mechanism shape. Lastly, we apply the framework to a design example.