Compliant mechanism; flexure hinge; flexible manipulator; transfer matrix method


Kinematic and static analyses of compliant mechanisms are crucial at the early stage of design, and it can be difficult and laborsome for complex configurations with distributed compliance. In this paper, a general and concise kinematic/static modeling method of flexure-hinge-based compliant mechanisms with arbitrary serial-parallel substructures is presented to provide accurate and efficient solutions by combining the matrix displacement method with the transfer matrix method. The transition between the elemental stiffness matrix and the transfer matrix of the flexure hinge and the flexible beam is straightforward, enabling the condensation of a hybrid serial-parallel substructure into one equivalent element simple. Then, the static model of the whole compliant mechanism can be easily established based on the equlibrium equation of the nodal force. The input/output force-displacement relations and the Jacobian matrix are further built for single-DOF and multi-DOF compliant mechanisms based on the modeling method. Comparison of the proposed method with finite element analysis and experiment for two exemplary mechanisms reveals good prediction accuracy, suggesting its feasibility for fast performance evaluation and parameter optimization at the initial stage of design.

Original Publication Citation

"Ling, M., Cao, J. Howell, L.L., Zeng, M., “Kinetostatic Modeling of Complex Compliant Mechanisms with Serial-Parallel Substructures: A Semi-Analytical Matrix Displacement Method,” Mechanism and Machine Theory, Vol. 125, pp. 169-184,, 2018."

Document Type

Peer-Reviewed Article

Publication Date





Ira A. Fulton College of Engineering


Mechanical Engineering

University Standing at Time of Publication

Full Professor