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Mechanical Sciences An open-access journal for theoretical and applied mechanics
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Volume 5, issue 2
Mech. Sci., 5, 67–78, 2014
https://doi.org/10.5194/ms-5-67-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
Mech. Sci., 5, 67–78, 2014
https://doi.org/10.5194/ms-5-67-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 12 Dec 2014

Research article | 12 Dec 2014

A function for characterizing complete kinetostatic behaviors of compliant bistable mechanisms

G. Li and G. Chen G. Li and G. Chen
  • School of Mechatronics, Xidian University, Xi'an, Shaanxi 710071, China

Abstract. In this paper, a straightforward and accurate numerical modeling (a rational function called "tri-root bistable function") are proposed to represent the complete nonlinear bistable force-displacement characteristics. The rational function has a cubic polynomial numerator and quadratic polynomial denominator. With three different kinds of compliant bistable mechanisms, the tri-root bistable function is proved effective and accurate, and that it is capable of capturing the key features of a bistable kinetostatic curve accurately with fewer parameters. Then, for the classic fully-compliant bistable mechanism, six closed-form equations are presented and used to describe the relationships between the tri-root bistable function parameters and the mechanism's design parameters, which are achieved using a multi-variable nonlinear regression. The regression analysis is validated by nonlinear finite element analysis. Finally, a fully-compliant statically balanced mechanism consisting of three different classic fully-compliant bistable mechanisms is illustrated to show the capability of the proposed method in designing compliant multi-stable mechanisms.

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Short summary
A rational function called tri-root bistable function are proposed to represent the complete nonlinear bistable force-displacement characteristics. The function has a cubic polynomial numerator and quadratic polynomial denominator. For the classic fully-compliant bistable mechanism, six closed-form equations are used to describe the relationships between the function parameters and the mechanism's design parameters, which are achieved using a multi-variable nonlinear regression.
A rational function called tri-root bistable function are proposed to represent the complete...
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