Research Papers

A Family of Butterfly Flexural Joints: Q-LITF Pivots

[+] Author and Article Information
Xu Pei

e-mail: peixu@buaa.edu.cn

Shusheng Bi

School of Mechanical Engineering and Automation,
Beihang University,
Beijing 100191, R.P. China

1Corresponding author.

Contributed by the Design Innovation and Devices of ASME for publication in the Journal of Mechanical Design. Manuscript received October 18, 2011; final manuscript received September 24, 2012; published online November 15, 2012. Assoc. Editor: Alexander Slocum.

J. Mech. Des 134(12), 121005 (Nov 15, 2012) (8 pages) doi:10.1115/1.4007917 History: Received October 18, 2011; Revised September 24, 2012

The typical leaf-type isosceles-trapezoidal flexural (LITF) pivot consists of two flexural beams and two rigid-bodies. The single LITF pivot has the small range of motion and relatively large center shift. However, the vacancy in the pivot point makes LITF pivots much easier to be cascaded than other commonly used flexure joints. The performances of LITF pivots will be greatly improved by connecting them together in series. This paper presents an innovative design of LITF pivots. The single LITF pivot is regarded as a basic configurable module, and four of them can be used to construct new types of flexure joint, which are referred to here as quadri-LITF (Q-LITF) pivot. Ten types of Q-LITF pivots are synthesized in this paper. Compared with a single LIFT pivot, the stroke of a Q-LITF pivot is larger, and stiffness of the mechanism becomes smaller. The center-shift of the Q-LIFT pivot can be optimized by tuning geometric parameters of its single LITF modules. Based on the pseudorigid-body (PRB) model of the single LITF pivot, the method for analyzing the Q-LITF pivots is proposed. One type of the Q-LITF pivots is selected as an example to demonstrate the proposed method for the Q-LITF pivot analysis. The comparison between the results of PRB model analysis and the finite element analysis (FEA) shows the feasibility and efficiency of the analysis procedure.

Copyright © 2012 by ASME
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Awtar, S., and Slocum, A. H., 2007, “Constraint-Based Design of Parallel Kinematic XY Flexure Mechanisms,” ASME J. Mech. Des., 129(8), pp. 816–830. [CrossRef]
Her, I., and Chang, J. C., 1994, “A Linear Scheme for the Displacement Analysis of Micropositioning Stages With Flexure Hinges,” ASME J. Mech. Des., 116, pp. 770–776. [CrossRef]
Onillon, E., Henein, S., and Theurillat, P., 2003, “Small Scanning Mirror Mechanism,” Proceedings of the 2003 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 1129–1133.
Ouyang, P. R., Zhang, W. J., Gupta, M. M., 2008, “A New Compliant Mechanical Amplifier Based on a Symmetric Five-Bar Topology,” ASME J. Mech. Des., 130(10), p. 104501. [CrossRef]
KrishnanG., and AnanthasureshG. K., 2008, “Evaluation and Design of Displacement-Amplifying Compliant Mechanisms for Sensor Applications,” ASME J. Mech. Des., 130(10), p. 102304. [CrossRef]
Howell, L. L., and Midha, A., 1994, “A Method for the Design of Compliant Mechanisms With Small-Length Flexural Pivots,” ASME J. Mech. Des., 116(11), pp. 280–290. [CrossRef]
Howell, L. L., 2001, Compliant Mechanisms, Wiley, New York.
TseytlinY.M., 2006, Structural Synthesis in Precision Elasticity, Springer, New York.
Trease, B., Moon, Y., and Kota, S., 2005, “Design of Large-Displacement Compliant Joints,” ASME J. Mech. Des., 127, pp. 788–798. [CrossRef]
Smith, S. T., and Chetwynd, D. G., 1992, Foundations of Ultraprecision Mechanism Design, Gordon and Breach Science, New York.
Jensen, B. D., and Howell, L. L., 2002, “The Modeling of Cross-Axis Flexural Pivots,” Mech. Mach. Theory, 37, pp. 461–476. [CrossRef]
Smith, S. T., 2000, Flexures: Elements of Elastic Mechanisms, Gordon and Breach Science, New York.
Goldfarb, M., and Speich, J. E., 2000, “A Well-Behaved Revolute Flexure Joint for Compliant Mechanism Design,”ASME J. Mech. Des., 121(3), pp. 424–429. [CrossRef]
Henein, S., Spanoudakis, P., Droz, S., Myklebust, L. I., and Onillon, E., 2003, “Flexure Pivot for Aerospace Mechanisms,” 10th European Space Mechanisms and Tribology Symposium, San Sebastian, Spain.
Pei, X., Yu, J. J., Zong, G. H., Bi, S. S., and Yu, Z. W., 2008, “Analysis of Rotational Precision for an Isosceles-Trapezoidal Flexural Pivot,” ASME J. Mech. Des., 130(5), p. 052302. [CrossRef]
Pei, X., Yu, J. J., Zong, G. H., and Bi, S. S., 2008, “The Stiffness Model of Leaf-Type Isosceles-Trapezoidal Flexural Pivots,” ASME J. Mech. Des., 130(8), p. 082303. [CrossRef]
Awtar, S., and Slocum, A. H., 2007, “Characteristics of Beam-Based Flexure Modules,” ASME Journal of Mechanical Design, 129(6), pp. 625–639. [CrossRef]
Pei, X., Yu, J. J., Zong, G. H., and Bi, S. S., 2009, “A Novel Family of Leaf-Type Compliant Joints: Combination of Two Isosceles-Trapezoidal Flexural Pivots” ASME Journal of mechanisms and robotics., 1(2), p. 021005. [CrossRef]
Pei, X., and Yu, J. J., “ADLIF: A New Large-Displacement Beam-Based Flexure Joint,” Mech. Sci., 2011(2), 183–188.


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Fig. 2

A LITF pivot and equivalent four-bar model, pin-joint model

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Fig. 1

Leaf-type flexure joint. (a) A LITF pivot (consisting of two flexural beams and two rigid-bodies); (b) ADLIF [19], a double-LITF pivot (consisting of two LITF pivots); (c) butterfly flexural pivot [14], a Q-LITF pivot (consisting of four LITF pivots)

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Fig. 3

The four-bar PRB model for case TI

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Fig. 4

The four-bar PRB model for case TII

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Fig. 5

Cascade of two D-LITF Pivots. IE indicates intermediate element; S indicates stand; ME indicates moveable element. (a) Select two pivots and (b) make the virtual centers coincident, then combine them.

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Fig. 6

The butterfly flexural pivot. (a) Embodiment; (b) schematic; and (c) PRB model

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Fig. 11

Center-shift results comparison

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Fig. 7

Experimental setup and the butterfly pivot

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Fig. 8

Moment–displacement results for butterfly pivot

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Fig. 9

Stress results for butterfly pivot

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Fig. 10

Center-shift results for butterfly pivot

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Fig. 12

Center-shifts of ten types of Q-LITF pivot



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