Theoretical and experimental investigation of performance characteristics and design aspects of cross-spring pivots

Abstract Cross-spring pivots have been widely employed over the last decades in a broad variety of precision engineering applications due to the high motion repeatability achieved thanks to the absence of stick slip and clearance. In this paper, the non-linear effect of the anticlastic curvature of the leaf-springs is considered for the accurate analytical modeling of the elasto-kinematic behavior of cross-spring pivots. Finite element analyses (FEA), based on a non-linear thin-shell model, are carried out in order to compare them with the analytical results for the main performance parameters of this type of device, i.e. center-shift, rotational stiffness and stress in the leaf-springs. Furthermore, an experimental setup is built to assess the applicability limits of both models. Finally, remarkable performance aspects of cross-spring pivots are discussed aiming for design improvements.

[1]  Simon Henein,et al.  FLEXURE PIVOT FOR AEROSPACE MECHANISMS , 2007 .

[2]  Phil Mellor,et al.  2D shape optimization of leaf-type crossed flexure pivot springs for minimum stress , 2015 .

[3]  Y. Fung,et al.  A BOUNDARY LAYER PHENOMENON IN THE LARGE DEFLEXION OF THIN PLATES , 1955 .

[4]  Frédéric Barlat,et al.  Anticlastic curvature in draw-bend springback , 2005 .

[5]  Tien-Fu Lu,et al.  Review of circular flexure hinge design equations and derivation of empirical formulations , 2008 .

[6]  Wh Wittrick The Theory of Symmetrical Crossed Flexure Pivots , 1948 .

[7]  R. Pomeroy The effect of anticlastic bending on the curvature of beams , 1970 .

[8]  Larry L. Howell,et al.  Compound joints: Behavior and benefits of flexure arrays , 2016 .

[9]  Saša Zelenika,et al.  Optimized cross-spring pivot configurations with minimized parasitic shifts and stiffness variations investigated via nonlinear FEA , 2017 .

[10]  Spencer P. Magleby,et al.  Cylindrical cross-axis flexural pivots , 2018 .

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

[12]  Shusheng Bi,et al.  Modeling of cross-spring pivots subjected to generalized planar loads , 2012 .

[13]  Shusheng Bi,et al.  Design and experiment of generalized triple-cross-spring flexure pivots applied to the ultra-precision instruments. , 2014, The Review of scientific instruments.

[14]  Shusheng Bi,et al.  Stiffness and stress characteristics of the generalized cross-spring pivot , 2010 .

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

[16]  Shusheng Bi,et al.  An effective pseudo-rigid-body method for beam-based compliant mechanisms , 2010 .

[17]  Larry L. Howell,et al.  Lattice flexures: Geometries for stiffness reduction of blade flexures , 2016 .

[18]  Qiaoling Meng,et al.  A novel analytical model for flexure-based proportion compliant mechanisms , 2014 .

[19]  Lena Zentner,et al.  General design equations for the rotational stiffness, maximal angular deflection and rotational precision of various notch flexure hinges , 2017 .

[20]  David Zhang,et al.  Closed-form compliance equations of filleted V-shaped flexure hinges for compliant mechanism design , 2010 .

[21]  Nicolae Lobontiu,et al.  Two-axis flexure hinges with axially-collocated and symmetric notches , 2003 .

[22]  Min Young Kim,et al.  Cartwheel flexure-based compliant stage for large displacement driven by a stack-type piezoelectric element , 2007, 2007 International Conference on Control, Automation and Systems.

[23]  Zhao Hongzhe,et al.  Accuracy characteristics of the generalized cross-spring pivot , 2010 .

[24]  Hai-Jun Su,et al.  The modeling of cartwheel flexural hinges , 2009 .

[25]  P. Nelson,et al.  Balancing a retroreflector to minimize rotation errors using a pendulum and quadrature interferometer. , 2015, Applied optics.

[26]  J. P. Meijaard,et al.  Refinements of Classical Beam Theory for Beams with a Large Aspect Ratio of Their Cross-Sections , 2011 .

[27]  Dannis Michel Brouwer,et al.  Large deflection stiffness analysis of parallel prismatic leaf-spring flexures taking into account shearing, constrained warping and anticlastic curving effects , 2013 .

[28]  Lena Zentner,et al.  The influence of asymmetric flexure hinges on the axis of rotation , 2011 .

[29]  Shusheng Bi,et al.  Quasi-constant rotational stiffness characteristic for cross-spring pivots in high precision measurement of unbalance moment , 2016 .