compliant mechanisms, mechanical engineering, flexure hinge, precision positioning stage, compliance matrix, flexible manipulator, dynamic analysis, pseudo-static model


This paper presents a pseudo-static modeling methodology for dynamic analysis of distributed compliant mechanisms to provide accurate and efficient solutions. First, a dynamic stiffness matrix of the flexible beam is deduced, which has the same definition and a similar form as the traditional static compliance/stiffness matrix but is frequency-dependent. Second, the pseudo-static modeling procedure for the dynamic analysis is implemented in a statics-similar way. Then, all the kinematic, static and dynamic performances of compliant mechanisms can be analyzed based on the pseudo- static model. The superiority of the proposed method is that when it is used for the dynamic modeling of compliant mechanisms, the traditional dynamic modeling procedures, such as the calculation of elastic and kinetic energies as well as using the Lagrange’s equation, are avoided and the dynamic modeling is converted to a statics-similar problem. Comparison of the proposed method with an elastic-beam-based model in previous literature and finite element analysis for an exemplary XY precision positioning stage reveals its high accuracy and easy operation.

Original Publication Citation

"Ling, M., Howell, L.L., Cao, J., Jian, Z., “A Pseudo-Static Model for Dynamic Analysis on Frequency Domain of Distributed Compliant Mechanisms,” Journal of Mechanisms and Robotics, Vol 10, 051011-1 to 051011-10, doi: 10.1115/1.4040700, 2018."

Document Type

Peer-Reviewed Article

Publication Date



ASME: Journal of Mechanisms and Robotics




Ira A. Fulton College of Engineering


Mechanical Engineering

University Standing at Time of Publication

Full Professor