Research Papers

Nonlinear Analytical Modeling and Characteristic Analysis of a Class of Compound Multibeam Parallelogram Mechanisms

[+] Author and Article Information
Guangbo Hao

School of Engineering-Electrical
and Electronic Engineering,
University College Cork,
Cork, Ireland
e-mail: G.Hao@ucc.ie

Haiyang Li

School of Engineering-Electrical
and Electronic Engineering,
University College Cork,
Cork, Ireland

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received June 3, 2014; final manuscript received January 5, 2015; published online April 6, 2015. Assoc. Editor: Anupam Saxena.

J. Mechanisms Robotics 7(4), 041016 (Nov 01, 2015) (9 pages) Paper No: JMR-14-1123; doi: 10.1115/1.4029556 History: Received June 03, 2014; Revised January 05, 2015; Online April 06, 2015

This paper deals with nonlinear analytical models of a class of compound multibeam parallelogram mechanisms (CMPMs) along with the static characteristic analysis. The CMPM is composed of multiple compound basic parallelogram mechanisms (CBPMs) in an embedded parallel arrangement. First, nonlinear analytical models for the CBPM are derived using the free-body diagram method through appropriate approximation strategies. The nonlinear analytical models of the CMPM are then derived based on the modeling results of the CBPM. Nonlinear finite element analysis (FEA) comparisons, experimental testing, and detailed stiffness analysis for the CBPM are finally carried out. It is shown that the analytical primary motion model agrees with both the FEA model and the testing result very well but the analytical parasitic motion model deviates from the FEA model over the large primary motion/force. It is also shown from the analytical characteristic analysis that the primary translational stiffness increases with the primary motion but the parasitic motion stiffness decreases with the primary motion, and the stiffness ratio of the parasitic motion stiffness to the primary translation stiffness also decreases with the primary motion. It is found that the larger the beam slenderness ratio is, the larger the stiffness or stiffness ratio is, and the more apparent the change of the stiffness or stiffness ratio is. The varied stiffness ratio indicates the mobility change of the CBPM.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Howell, L. L., 2001, Compliant Mechanisms, Wiley, New York.
Awtar, S., Slocum, A. H., and Sevincer, E., 2007, “Characteristics of Beam-Based Flexure Modules,” ASME J. Mech. Des., 129(6), pp. 624–639. [CrossRef]
Trease, B. P., Moon, Y.-M., and Kota, S., 2005, “Design of Large-Displacement Compliant Joints,” ASME J. Mech. Des., 127(6), pp. 788–798. [CrossRef]
Hubbard, N. B., Wittwer, J. W., Kennedy, J. A. L., Wilcox, D., and Howell, L. L., 2004, “A Novel Fully Compliant Planar Linear-Motion Mechanism,” ASME Paper No. DETC2004-57008. [CrossRef]
Zhao, H. Z., Bi, S. S., and Yu, J. J., 2012, “A Novel Compliant Linear-Motion Mechanism Based on Parasitic Motion Compensation,” Mech. Mach. Theory, 50, pp. 15–28. [CrossRef]
Li, Y., Xiao, S., Xi, L., and Wu, Z., 2014, “Design, Modeling, Control and Experiment for a 2-DOF Compliant Micro-Motion Stage,” Int. J. Precis. Eng. Manuf., 15(4), pp. 735–744. [CrossRef]
Howell, L. L., DiBiasio, C. M., Cullinan, M. A., Panas, R., and Culpepper, M. L., 2010, “A Pseudo-Rigid-Body Model for Large Deflections of Fixed-Clamped Carbon Nanotubes,” ASME J. Mech. Rob., 2(3), p. 034501. [CrossRef]
Yong, Y. K., Moheimani, S. O. R., Kenton, B. J., and Leang, K. K., 2012, “Invited Review Article: High-Speed Flexure-Guided Nanopositioning: Mechanical Design and Control Issues,” Rev. Sci. Instrum., 83(12), p. 121101. [CrossRef] [PubMed]
Awtar, S., 2004, “Analysis and Synthesis of Planer Kinematic XY Mechanisms,” Sc.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Zelenika, S., and De Bona, F., 2002, “Analytical and Experimental Characterization of High-Precision Flexural Pivots Subjected to Lateral Loads,” Precis. Eng., 26(4), pp. 381–388. [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]
Su, H., 2009, “A Pseudo-Rigid-Body 3R Model for Determining Large Deflection of Cantilever Beams Subject to Tip Loads,” ASME J. Mech. Rob., 1(2), p. 021008. [CrossRef]
Chen, G., Xiong, B., and Huang, X., 2011, “Finding the Optimal Characteristic Parameters for 3R Pseudo-Rigid-Body Model Using an Improved Particle Swarm Optimizer,” Precis. Eng., 35(3), pp. 505–511. [CrossRef]
Hao, G., 2014, “Extended Nonlinear Analytical Models of Compliant Parallelogram Mechanisms: Third-Order Models,” Trans. Can. Soc. Mech. Eng., 39(1) (in press).


Grahic Jump Location
Fig. 1

Four types of parallelogram based leaf-type CTJs

Grahic Jump Location
Fig. 2

A CBPM with actual geometry, loading and displacement indication

Grahic Jump Location
Fig. 4

Parasitic translational displacement along the X-axis

Grahic Jump Location
Fig. 5

Primary translational displacement along the Y-axis

Grahic Jump Location
Fig. 6

Parasitic rotational yaw about the Z-axis

Grahic Jump Location
Fig. 7

Testing rig for the primary motion

Grahic Jump Location
Fig. 8

Parasitic translational stiffness (kx) along the X-axis

Grahic Jump Location
Fig. 9

Primary translational stiffness (ky) along the Y-axis

Grahic Jump Location
Fig. 10

Parasitic rotational stiffness (kr) about the Z-axis

Grahic Jump Location
Fig. 11

Stiffness ratio: kx/ky

Grahic Jump Location
Fig. 12

Stiffness ratio: kr/ky




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