Static and dynamic analysis of flexure hinge mechanisms using the weak-form quadrature element method

Flexure hinges are critical components in compliant mechanisms since they can achieve smooth precision motion without backlash and friction. A quadrature element modeling method is extended to model compliant mechanisms. Flexure hinges are regarded as the Timoshenko beam. The elemental mass and stiffness matrices are formulated with a weak-form quadrature element method, which is distinguished by integral and differential quadrature. One quadrature element is able to model a circular flexure hinge. Two benchmark examples are investigated to verify the proposed approach in the comparison of the static and dynamic behavior. The calculation results demonstrate that the proposed approach is of high computational efficiency and accuracy.

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