A numerical method for static analysis of pseudo-rigid-body model of compliant mechanisms

Abstract

This paper presents a numerical method for analyzing the pseudo-rigid-body model of compliant mechanisms based on finite elements and the principle of minimum potential energy. The proposed method represents the links of pseudo-rigid-body model with truss elements. As a result, the pseudo-rigid-body model is modeled into a compliant system that consists of finite elements and springs. The static equilibrium position of the pseudo-rigid-body model can be obtained by minimizing the potential energy function of this compliant system. A comparison between the proposed method and the MinPE method is presented. Lastly, a case study is provided to demonstrate the application of this method in the automated analysis of pseudo-rigid-body models. This numerical method paves the way for introducing the topology optimization techniques into the synthesis of flexure-based compliant mechanisms.

Keywords

Compliant mechanism topology optimization pseudo-rigid-body model static analysis principle of minimum potential energy

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References

Huang

Tang

. A compliant parallel xy micromotion stage with complete kinematic decoupling. IEEE Trans Autom Sci Eng 2012; 9: 538–553.

Ananthasuresh

Kota

Kikuchi

. Strategies for systematic synthesis of compliant MEMS. Proceedings of the 1994 ASME winter annual meeting, symposium on MEMS: dynamics systems and control 1994; vol 2, Chicago, IL: ASME, pp. 677–686.

Frecker

Ananthasuresh

Nishiwaki

. Topological synthesis of compliant mechanisms using multi-criteria optimization. ASME J Mech Des 1997; 119: 238–245.

Sigmund

. On the design of compliant mechanisms using topology optimization*. J Struct Mech 1997; 25: 493–524.

Zhang

. Topology optimozation of compliant mechanisms. Chin J Mech Eng 2003; 39: 47–51.

Howell

. Compliant mechanisms, New York: John Wiley & Sons, Inc, 2001.

Kim

Kota

Moon

. An instant center approach toward the conceptual design of compliant mechanisms. ASME J Mech Des 2006; 128: 542–550.

Howell

Midha

. A loop-closure theory for the analysis and synthesis of compliant mechanisms. ASME J Mech Des 1996; 118: 121–125.

Howell LL. A generalized loop-closure theory for the analysis and synthesis of compliant mechanisms. PhD Thesis, Purdue University, 1993.

10.

Aten

Zirbel

Jensen

. A numerical method for position analysis of compliant mechanisms with more degrees of freedom than inputs. ASME J Mech Des 2011; 133: 061009–061009.

11.

Avilés

Ajuria

Victoria Hormaza

. A procedure based on finite elements for the solution of nonlinear problems in the kinematic analysis of mechanisms. Finite Elem Anal Des 1996; 22: 305–327.

12.

Avilés

Ajuria

Gómez-Garay

. Comparison among nonlinear optimization methods for the static equilibrium analysis of multibody systems with rigid and elastic elements. Mech Mach Theory 2000; 35: 1151–1168.

13.

Vanderplaats

. Numerical optimization techniques for engineering design: with applications, New York: McGraw-Hill, 1984.