0
Research Papers

Modeling Large Spatial Deflections of Slender Bisymmetric Beams in Compliant Mechanisms Using Chained Spatial-Beam Constraint Model

[+] Author and Article Information
Guimin Chen

School of Electro-Mechanical Engineering,
Xidian University,
Xi'an, Shaanxi 710071, China
e-mail: guimin.chen@gmail.com

Ruiyu Bai

School of Electro-Mechanical Engineering,
Xidian University,
Xi'an, Shaanxi 710071, China

1Corresponding author.

Manuscript received June 18, 2015; final manuscript received January 20, 2016; published online March 10, 2016. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 8(4), 041011 (Mar 10, 2016) (9 pages) Paper No: JMR-15-1148; doi: 10.1115/1.4032632 History: Received June 18, 2015; Revised January 20, 2016

Modeling large spatial deflections of flexible beams has been one of the most challenging problems in the research community of compliant mechanisms. This work presents a method called chained spatial-beam constraint model (CSBCM) for modeling large spatial deflections of flexible bisymmetric beams in compliant mechanisms. CSBCM is based on the spatial-beam constraint model (SBCM), which was developed for the purpose of accurately predicting the nonlinear constraint characteristics of bisymmetric spatial beams in their intermediate deflection range. CSBCM deals with large spatial deflections by dividing a spatial beam into several elements, modeling each element with SBCM, and then assembling the deflected elements using the transformation defined by Tait–Bryan angles to form the whole deflection. It is demonstrated that CSBCM is capable of solving various large spatial deflection problems either the tip loads are known or the tip deflections are known. The examples show that CSBCM can accurately predict large spatial deflections of flexible beams, as compared to the available nonlinear finite element analysis (FEA) results obtained by ansys. The results also demonstrated the unique capabilities of CSBCM to solve large spatial deflection problems that are outside the range of ansys.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Sen, S. , and Awtar, S. , 2013, “ A Closed-Form Nonlinear Model for the Constraint Characteristics of Symmetric Spatial Beams,” ASME J. Mech. Des., 135(3), p. 031003. [CrossRef]
Howell, L. L. , Magleby, S. P. , and Olsen, B. M. , 2013, Handbook of Compliant Mechanisms, Wiley, New York.
Hoover, A. M. , and Fearing, R. S. , 2009, “ Analysis of Off-Axis Performance of Compliant Mechanisms With Applications to Mobile Millirobot Design,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), St. Louis, MO, Oct. 10–15, pp. 2770–2776.
Chen, G. , Zhang, S. , and Li, G. , 2013, “ Multistable Behaviors of Compliant Sarrus Mechanisms,” ASME J. Mech. Rob., 5(2), p. 021005. [CrossRef]
Howell, L. L. , 2001, Compliant Mechanisms, Wiley, New York.
Su, H. J. , 2009, “ A Pseudorigid-Body 3R Model for Determining Large Deflection of Cantilever Beams Subject to Tip Loads,” ASME J. Mech. Rob., 1(2), p. 021008. [CrossRef]
Yu, Y.-Q. , Feng, Z.-L. , and Xu, Q.-P. , 2012, “ A Pseudo-Rigid-Body 2R Model of Flexural Beam in Compliant Mechanisms,” Mech. Mach. Theory, 55(9), pp. 18–23. [CrossRef]
Midha, A. , Her, I. , and Salamon, B. , 1992, “ Methodology for Compliant Mechanisms Design: Part I—Introduction and Large-Deflection Analysis,” 18th Annual ASME Design Automation Conference, Scottsdale, AZ, Sept. 13–16, pp. 29–38.
Campanile, L. F. , and Hasse, A. , 2008, “ A Simple and Effective Solution of the Elastica Problem,” Proc. Inst. Mech. Eng., Part C, 222(12), pp. 2513–2516. [CrossRef]
Banerjee, A. , Bhattacharya, B. , and Mallik, A. K. , 2008, “ Large Deflection of Cantilever Beams With Geometric Non-Linearity: Analytical and Numerical Approaches,” Int. J. Non-Linear Mech., 43(5), pp. 366–376. [CrossRef]
Tolou, N. , and Herder, J. L. , 2009, “ A Seminalytical Approach to Large Deflections in Compliant Beams Under Point Load,” Math. Probl. Eng., 2009, p. 910896. [CrossRef]
Lan, C. C. , 2008, “ Analysis of Large-Displacement Compliant Mechanisms Using an Incremental Linearization Approach,” Mech. Mach. Theory, 43(5), pp. 641–658. [CrossRef]
Kimball, C. , and Tsai, W. , 2002, “ Modeling of Flexural Beams Subjected to Arbitrary Ends Loads,” ASME J. Mech. Des., 124(2), pp. 223–235. [CrossRef]
Holst, G. L. , Teichert, G. H. , and Jensen, B. D. , 2011, “ Modeling and Experiments of Buckling Modes and Deflection of Fixed-Guided Beams in Compliant Mechanisms,” ASME J. Mech. Des., 133(5), p. 051002. [CrossRef]
Kim, C. , and Ebenstein, D. , 2011, “ Curve Decomposition for Large Deflection Analysis of Fixed-Guided Beams With Application to Statically Balanced Compliant Mechanisms,” ASME J. Mech. Rob., 4(4), p. 041009. [CrossRef]
Zhang, A. , and Chen, G. , 2013, “ A Comprehensive Elliptic Integral Solution to the Large Deflection Problems of Thin Beams in Compliant Mechanisms,” ASME J. Mech. Rob., 5(2), p. 021006. [CrossRef]
Saxena, A. , and Kramer, S. N. , 1998, “ A Simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End Forces and Moments,” ASME J. Mech. Des., 120(3), pp. 392–400. [CrossRef]
Ma, F. , and Chen, G. , 2014, “ Chained Beam-Constraint-Model (CBCM): A Powerful Tool for Modeling Large and Complicated Deflections of Flexible Beams in Compliant Mechanisms,” ASME Paper No. DETC2014-34140.
Chen, G. , and Ma, F. , 2015, “ Kinetostatic Modeling of Fully Compliant Bistable Mechanisms Using Timoshenko Beam Constraint Model,” ASME J. Mech. Des., 137(2), p. 022301. [CrossRef]
Shoup, T. E. , and McLarnan, C. W. , 1971, “ A Survey of Flexible Link Mechanisms Having Lower Pairs,” J. Mech., 6(1), pp. 97–105. [CrossRef]
Choueifati, J. G. , 2007, “ Design and Modeling of a Bistable Spherical Compliant Mechanism,” Ph.D. thesis, University of South Florida, Tampa, FL.
Parlaktaş, V. , and Tanık, E. , 2011, “ Partially Compliant Spatial Slider–Crank (RSSP) Mechanism,” Mech. Mach. Theory, 46(5), pp. 593–606. [CrossRef]
Tanık, E. , and Parlaktaş, V. , 2011, “ A New Type of Compliant Spatial Four-Bar (RSSR) Mechanism,” Mech. Mach. Theory, 46(11), pp. 1707–1718. [CrossRef]
Smith, C. L. , and Lusk, C. P. , 2011, “ Modeling and Parameter Study of Bistable Spherical Compliant Mechanisms,” ASME Paper No. DETC2011-47397.
Rasmussen, N. O. , Wittwer, J. W. , Todd, R. H. , Howell, L. L. , and Magleby, S. P. , 2006, “ A 3D Pseudo-Rigid-Body Model for Large Spatial Deflections of Rectangular Cantilever Beams,” ASME Paper No. DETC2006-99465.
Ramirez, I. , and Lusk, C. P. , 2011, “ Spatial Beam Large Deflection Equations and Pseudo-Rigid-Body Model for Axisymmetric Cantilever Beams,” ASME Paper No. DETC2011-47389.
Chimento, J. , Lusk, C. P. , and Alqasimi, A. , 2014, “ A 3-D Pseudo-Rigid Body Model for Rectangular Cantilever Beams With an Arbitrary Force End-Load,” ASME Paper No. DETC2014-34292.
Chase, R. P., Jr. , Todd, R. H. , Howell, L. L. , and Magleby, S. P. , 2011, “ A 3-D Chain Algorithm With Pseudo-Rigid-Body Model Elements,” Mech. Based Des. Struct. Mach., 39(1), pp. 142–156. [CrossRef]
Hao, G. , Kong, X. , and Reuben, R. L. , 2011, “ A Nonlinear Analysis of Spatial Compliant Parallel Modules: Multi-Beam Modules,” Mech. Mach. Theory, 46(5), pp. 680–706. [CrossRef]
Awtar, S. , Slocum, A. H. , and Sevincer, E. , 2007, “ Characteristics of Beam-Based Flexure Modules,” ASME J. Mech. Des., 129(6), pp. 625–639. [CrossRef]
Hao, G. , 2013, “ Simplified PRBMs of Spatial Compliant Multi-Beam Modules for Planar Motion,” Mech. Sci., 4(2), pp. 311–318. [CrossRef]
Chen, G. , and Howell, L. L. , 2009, “ Two General Solutions of Torsional Compliance for Variable Rectangular Cross-Section Hinges in Compliant Mechanisms,” Precis. Eng., 33(3), pp. 268–274. [CrossRef]
Sen, S. , 2013, “ Beam Constraint Model: Generalized Nonlinear Closed-Form Modeling of Beam Flexures for Flexure Mechanism Design,” Ph.D. dissertation, The University of Michigan, Ann Arbor, MI.

Figures

Grahic Jump Location
Fig. 1

Three-dimensional deflection of a spatial cantilever beam subject to combined force and moment loads at its free end (the sign convention for forces and moments follows the right-hand rule)

Grahic Jump Location
Fig. 2

Discretization of the spatial beam and the coordinates of the nodes with respect to the fixed coordinate frame

Grahic Jump Location
Fig. 3

Tait–Bryan angles for ith SBCM element (the sign convention for the angles follows the right-hand rule)

Grahic Jump Location
Fig. 4

The deflected configurations of the beam subject to pure end forces

Grahic Jump Location
Fig. 5

The deflected configurations of the beam subject to pure end moments

Grahic Jump Location
Fig. 6

Deflected configurations for the beam subject to combined loads

Grahic Jump Location
Fig. 7

Deflected configurations for the beam subject to combined loads

Grahic Jump Location
Fig. 8

Circular-guided spatial compliant mechanism

Grahic Jump Location
Fig. 10

Deflected configurations of the beam at different crank angles

Grahic Jump Location
Fig. 11

Driving torque Tin versus crank angle ϕ

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In