Analysis of the center of rotation in primitive flexures: Uniform cantilever beams with constant curvature

Abstract Precision of rotation is a fundamental characteristic of primitive flexures, especially when compliant mechanisms are designed for micro-scale applications. In case of single leaf flexures, distributed compliance allows flexible beams to undergo large deflections. Nevertheless, the center of rotation changes its position during such deflections. In this paper, large deflection analysis is performed on cantilever beams with uniform cross section and constant curvature, subjected to end-moment loads. Analytical expressions to determine the position of the center of rotation of the flexure are derived. The center of rotation refers to the displacement of the free-end section of the beam, occurring when the flexure, due to the external load application, moves from its neutral configuration to the deformed one. Several examples are considered and the analytical solutions are compared to the results obtained by finite element analysis. A final example focuses on the determination of the pseudo-rigid body model.

[1]  Pietro Valdastri,et al.  Modeling of a compliant joint in a Magnetic Levitation System for an endoscopic camera , 2012 .

[2]  Bijan Shirinzadeh,et al.  A new design of piezoelectric driven compliant-based microgripper for micromanipulation , 2009 .

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

[4]  Kyungwoo Lee.  Large deflections of cantilever beams of non-linear elastic material under a combined loading , 2002 .

[5]  Shusheng Bi,et al.  A Novel Family of Leaf-Type Compliant Joints: Combination of Two Isosceles-Trapezoidal Flexural Pivots , 2009 .

[6]  Yanling Tian,et al.  A flexure-based mechanism and control methodology for ultra-precision turning operation , 2009 .

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

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

[9]  Nicola Pio Belfiore,et al.  Inverse kinetostatic analysis of compliant four-bar linkages , 2013 .

[10]  Bijan Shirinzadeh,et al.  Development of a high precision flexure-based microgripper , 2009 .

[11]  Robert McIntyre Fowler,et al.  Flex-16: A Large-Displacement Monolithic Compliant Rotational Hinge , 2014 .

[12]  Bijan Shirinzadeh,et al.  Design and analysis of a novel flexure-based 3-DOF mechanism , 2014 .

[13]  J. Herder,et al.  Large deflection analysis of cantilever beam under end point and distributed loads , 2014 .

[14]  Xianmin Zhang,et al.  Input coupling analysis and optimal design of a 3-DOF compliant micro-positioning stage , 2008 .

[15]  J. Lang,et al.  A curved-beam bistable mechanism , 2004, Journal of Microelectromechanical Systems.

[16]  S. Baglio,et al.  Investigation on Mechanically Bistable MEMS Devices for Energy Harvesting From Vibrations , 2012, Journal of Microelectromechanical Systems.

[17]  Nicola Pio Belfiore,et al.  Functional Synthesis of a New Class of Micro Electro-Mechanical Systems , 2014 .

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

[19]  Yu Jingjun,et al.  Analysis of Rotational Precision for an Isosceles-Trapezoidal Flexural Pivot , 2008 .

[20]  Shafaat A. Bazaz,et al.  Design, simulation and testing of electrostatic SOI MUMPs based microgripper integrated with capacitive contact sensor , 2011 .

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

[22]  David Zhang,et al.  Dynamic modelling of a flexure-based mechanism for ultra-precision grinding operation , 2011 .

[23]  L. Tsai,et al.  Modeling of Flexural Beams Subjected to Arbitrary End Loads , 2002 .

[24]  Yue-Qing Yu,et al.  A pseudo-rigid-body 2R model of flexural beam in compliant mechanisms , 2012 .

[25]  Hai-Jun Su,et al.  A stiffness model for control and analysis of a MEMS hexapod nanopositioner , 2014 .

[26]  Hai-Jun Su,et al.  A Pseudorigid-Body 3R Model for Determining Large Deflection of Cantilever Beams Subject to Tip Loads , 2009 .

[27]  Nicolae Lobontiu,et al.  Corner-Filleted Flexure Hinges , 2001 .

[28]  Nicolae Lobontiu,et al.  Parabolic and hyperbolic flexure hinges: flexibility, motion precision and stress characterization based on compliance closed-form equations , 2002 .

[29]  Yong Mo Moon,et al.  DESIGN OF LARGE-DISPLACEMENT COMPLIANT JOINTS , 2005 .

[30]  Marco Balucani,et al.  Design, optimization and construction of MEMS-based micro grippers for cell manipulation , 2013, 2013 International Conference on System Science and Engineering (ICSSE).

[31]  Shusheng Bi,et al.  A Family of Butterfly Flexural Joints: Q-LITF Pivots , 2012 .

[32]  Liu Wangyu,et al.  Analysis of the displacement of distributed compliant parallel-guiding mechanism considering parasitic rotation and deflection on the guiding plate , 2014 .

[33]  Marco Balucani,et al.  The development of a MEMS/NEMS-based 3 D.O.F. compliant micro robot , 2010, 19th International Workshop on Robotics in Alpe-Adria-Danube Region (RAAD 2010).

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

[35]  Q. Yang,et al.  A Monolithic Compliant Piezoelectric-Driven Microgripper: Design, Modeling, and Testing , 2013, IEEE/ASME Transactions on Mechatronics.

[36]  Marco Balucani,et al.  MEMS-Based Conjugate Surfaces Flexure Hinge , 2015 .

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

[38]  X. Pei,et al.  ADLIF: a new large-displacement beam-based flexure joint , 2011 .

[39]  Simon Henein,et al.  Short Communication: Flexure delicacies , 2012 .

[40]  Li Chen,et al.  An integral approach for large deflection cantilever beams , 2010 .

[41]  Tie-bang Xie,et al.  A micro-displacement stage for scanning white-light interferometry , 2005 .

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

[43]  B. Nelson,et al.  Monolithically Fabricated Microgripper With Integrated Force Sensor for Manipulating Microobjects and Biological Cells Aligned in an Ultrasonic Field , 2007, Journal of Microelectromechanical Systems.

[44]  B. Shvartsman,et al.  Large deflections of a cantilever beam subjected to a follower force , 2007 .

[45]  F. Virginia Rohde.  Large deflections of a cantilever beam with uniformly distributed load , 1953 .

[46]  Yves Bellouard.  Microrobotics: Methods and Applications , 2009 .

[47]  Ma Li.  Integrating positioning X-Y stage based on bulk micromachining , 2009 .

[48]  Yanling Tian,et al.  A flexure-based five-bar mechanism for micro/nano manipulation , 2009 .

[49]  Larry L. Howell,et al.  A compliant contact-aided revolute joint , 2005 .

[50]  Yong-Mo Moon,et al.  Bio-mimetic design of finger mechanism with contact aided compliant mechanism , 2007 .

[51]  Yanling Tian,et al.  Analysis of parasitic motion in parallelogram compliant mechanism , 2010 .

[52]  Paolo Gallina,et al.  A novel MEMS device for the multidirectional mechanical stimulation of single cells: Preliminary results , 2014 .

[53]  Stuart T. Smith,et al.  ELLIPTICAL FLEXURE HINGES , 1997 .

[54]  C. Lakshmana Rao,et al.  Large deflection of constant curvature cantilever beam under follower load , 2010 .

[55]  John C. Ziegert,et al.  Hybrid bi-directional flexure joint , 2014 .