Abstract
Analytical compliance model is vital to the flexure- based compliant mechanism in its mechanical design and motion control. The matrix is a common and effective approach in the compliance modeling while it is not well developed for the closed-loop serial and parallel compliant mechanisms and is not applicable to the situation when the external loads are applied on the flexure members. Concise and explicit analytical compliance models of the serial flexure-based compliant mechanisms under arbitrary loads are derived by using the matrix method. An equivalent method is proposed to deal with the situation when the external loads are applied on the flexure members. The external loads are transformed to concentrated forces applied on the rigid links, which satisfy the equations of static equilibrium and also guarantee that the deformations at the displacement output point remain unchanged. Then the matrix method can be still adopted for the compliance analysis of the compliant mechanism. Finally, several specific examples and an experimental test are given to verify the effectiveness of the compliance models and the force equivalent method. The research enriches the matrix method and provides concise analytical compliance models for the serial compliant mechanism.
Highlights
Compared with conventional mechanisms, flexure-based compliant mechanisms can provide motions without friction, backlash, and wear [1]
The matrix is a common and effective approach in the compliance modeling while it is not well developed for the closed-loop serial and parallel compliant mechanisms and is not applicable to the situation when the external loads are applied on the flexure members
This paper focuses on the analytical compliance modeling of the serial flexure-based compliant mechanisms under arbitrary external loads
Summary
Flexure-based compliant mechanisms can provide motions without friction, backlash, and wear [1]. N Lobontiu, et al [10], formulated an analytical compliance model for the planar compliant mechanisms with single-axis flexure hinges based on the Castigliano’s displacement theorem. Compared with the Castigliano’s theorem, the matrix method is more simple and effective for the analytical compliance modeling of the compliant mechanism. When the compliant mechanism is inserted into the dual-stage for accuracy compensation within a long stroke [22], the deformations of the flexure members under inertial forces and gravity cannot be calculated by using the matrix method. According to the relative positional relationship between the applied loads and the displacement output point, concise and explicit compliance models of the open- and closed-loops serial compliant mechanisms are derived based on the matrix method. Several specific examples are given to illustrate the effectiveness of the proposed method
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