A dynamic compliance matrix method for modeling compliant mechanisms

Lagrange's equation is usually combined with the compliance matrix method to solve the dynamics of compliant mechanisms that belongs to a time-domain approach. In contrast, we introduce a dynamic compliance matrix method (DCM) for both kinetostatics and vibration analyses of small-deformation compliant mechanisms in the frequency domain. We discuss in detail under what preconditions the so-called dynamic compliance matrix is valid and how it can be correctly transferred between flexure building blocks. Then, we propose a generalized procedure for the dynamic compliance modeling of serial-parallel chains by virtue of mechanical networks. In essence, such a new concept of DCM has a similar modeling process to traditional static compliance matrix method by mass grounding, but it enables both kinetostatic and dynamic modeling of compliant mechanisms in a pseudo-static way switched by setting the circular frequency to zero as needed. It relies on a matrix summation operation without the requirements of internal force analysis and kinematic calculation, hence is modeling-concise and programming-friendly for complex serial-parallel compliant mechanisms. Two case studies are presented to validate the proposed DCM and discuss its application scopes.