A Generalized Constraint Model for Two-Dimensional Beam Flexures

To utilize beam flexures in constraint-based flexure mechanism design, it is important to develop a qualitative and quantitative understanding of their constraint characteristics in terms of stiffness and error motions. This paper provides a highly generalized yet accurate closed-form load-displacement model for two-dimensional beam flexures, taking into account the nonlinearities arising from load equilibrium applied in the deformed configuration. In particular, stiffness and error motions are parametrically quantified in terms of elastic, load-stiffening, kinematic, and elastokinematic effects. The proposed beam constraint model incorporates any general loading conditions, boundary conditions, initial curvature, and beam shape. The accuracy and effectiveness of the proposed beam constraint model is verified extensively by non-linear Finite Elements Analysis.© 2009 ASME

[1]  L. Rubin,et al.  Instruments and Experiences: Papers on Measurement and Instrument Design , 1988 .

[2]  A. Midha,et al.  Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms , 1995 .

[3]  Shorya Awtar,et al.  Constraint-based design of parallel kinematic XY flexure mechanisms , 2007 .

[4]  Shorya Awtar,et al.  Characteristics of Beam-Based Flexure Modules , 2007 .

[5]  J. E. Plainevaux,et al.  Etude des déformations d’une lame de suspension élastique , 1956 .

[6]  Larry L. Howell,et al.  Evaluation of equivalent spring stiffness for use in a pseudo-rigid-body model of large-deflection compliant mechanisms , 1996 .

[7]  Stuart T. Smith,et al.  Flexures: Elements of Elastic Mechanisms , 2000 .

[8]  Michael Curt Elwenspoek,et al.  Comb-drive actuators for large displacements , 1996 .

[9]  A. Slocum,et al.  Precision Machine Design , 1992 .

[10]  Shorya Awtar,et al.  Elastic Averaging in Flexure Mechanisms: A Muliti-Beam Parallelogram Flexure Case-Study , 2006 .

[11]  Jonathan B. Hopkins,et al.  Design of parallel flexure systems via Freedom and Constraint Topologies (FACT) , 2007 .

[12]  Saša Zelenika,et al.  Analytical and experimental characterisation of high-precision flexural pivots subjected to lateral loads , 2002 .

[13]  J. A. Haringx.  The cross-spring pivot as a constructional element , 1949 .

[14]  K. E. Bisshopp,et al.  Large deflection of cantilever beams , 1945 .

[15]  Kjell Mattiasson,et al.  Numerical results from large deflection beam and frame problems analysed by means of elliptic integrals , 1981 .