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Research Papers

Virtual Chain Approach for Mobility Analysis of Multiloop Deployable Mechanisms

[+] Author and Article Information
Hailin Huang

Department of Mechanical and
Biomedical Engineering,
City University of Hong Kong,
Tat Chee Avenue, Kowloon, Hong Kong 999077, China
e-mail: haihuang@cityu.edu.hk

Zongquan Deng

School of Mechatronics Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: denzq@hit.edu.cn

Xiaozhi Qi

Shenzhen Graduate School,
Harbin Institute of Technology,
Shenzhen 518055, China
e-mail: ixiaozhiq@163.com

Bing Li

Professor
e-mail: libing.sgs@hit.edu.cn

Shenzhen Graduate School,
Harbin Institute of Technology,
Shenzhen 518055, China

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 27, 2013; final manuscript received July 12, 2013; published online September 24, 2013. Assoc. Editor: Larry L. Howell.

J. Mech. Des 135(11), 111002 (Sep 24, 2013) (9 pages) Paper No: MD-13-1101; doi: 10.1115/1.4025383 History: Received February 27, 2013; Revised July 12, 2013

In this paper, we present a virtual chain approach for the mobility analysis of multiloop deployable mechanisms. First, the relative motion of the links of single-loop units in multiloop mechanisms are analyzed using the equivalent motion of certain types of open-loop virtual kinematic chains; these kinematic chains comprise some types of joints connected in series by flexible links. This reveals that the links in these virtual chains are not rigid when the mechanism is moving. The parameters of these virtual kinematic chains (such as the link length, the twist angle of two adjacent revolute joint axes, and so on) are variable. By using this approach that involves equivalent kinematic chains, the multiloop mechanisms can be considered equivalent to single-loop mechanisms with flexible links; the closure equations of such multiloop mechanisms can also be derived. The analytical procedures are explained using examples of multiloop mechanisms in which Myard mechanisms as used as the basic single-loop units. A prototype is also fabricated to demonstrate the feasibility of the proposed multiloop mechanism. The proposed method yields a more intuitive and straightforward insight into the mobility of complicated multiloop mechanisms.

Copyright © 2013 by ASME
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References

Hailin, H., Zongquan, D., and Bing, L., 2012, “Mobile Assemblies of Large Deployable Mechanisms,” JSME J. Space Eng., 5(1), pp. 1–14. [CrossRef]
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Zongquan, D., Hailin, H., Bing, L., and Rongqiang, L., 2012, “Synthesis of Deployable/Foldable Single Loop Mechanisms With Revolute Joints,” ASME J. Mech. Robot., 3(3), p. 031006. [CrossRef]
Chen, Y., 2003, “Design of Structural Mechanism,” Ph.D. dissertation, University of Oxford, Oxford, UK.
Song, C., and Chen, Y., 2011, “A Spatial 6R Linkage Derived from Subtractive Goldberg 5R Linkages,” Mech. Mach. Theory, 46(8), pp. 1097–1106. [CrossRef]
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Myard, F. E., 1931, “Contribution à la Géométrie des Systèmes Articulés,” Bull. Soc. Math. France, 59, pp. 183–210.
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Figures

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Fig. 1

D–H model of the Myard linkage

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Fig. 2

Threefold-symmetric Bricard linkage [15]

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Fig. 3

Values of θ versus ϕ of the threefold-symmetric Bricard linkage for a set of α in a complete period [15]

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Fig. 4

3-Myard threefold-symmetric Bricard mechanism

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Fig. 5

Coordinate system in the Myard unit

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Fig. 6

Equivalent single-loop mechanism of the 3-Myard multiloop mechanism

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Fig. 7

CAD model of the 3-Myard multiloop deployable mechanism (a) deployed configuration (b) mid configuration, and (c) folded configuration

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Fig. 8

CAD model of the 4-Myard multi-loop deployable mechanism (a) deployed configuration, (b) mid configuration, (c) folded configuration

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Fig. 9

CAD model of the 6-Myard multiloop deployable mechanism (a) deployed configuration, (b) mid configuration, (c) folded configuration

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Fig. 10

Conceptual model of one module of a double-layer deployable structure

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Fig. 11

Equivalent replacement of two kinematic chains with identical mobility

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Fig. 12

Extension of basic deployable modules using polygonal connectors (a) hexagonal connector, (b) square connector, (c) triangular connector

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Fig. 13

Prototype of double-layer deployable mechanism (a) deployed configuration (b) mid configuration, and (c) folded configuration

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Fig. 14

Models of plane-symmetric Bricard linkage and its equivalent joint (a) D–H model and (b) physical model

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Fig. 15

CAD model of 4-plane-symmetric Bricard multiloop mechanism (a) deployed configuration (b) mid configuration and (c) folded configuration

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Fig. 16

The 4-plane-symmetric Bricard multiloop mechanism and its equivalent single-loop mechanism (a) physical model and equivalent model and (b) top view of the mechanism

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Fig. 17

CAD model of 6-plane-symmetric Bricard multiloop mechanism (a) deployed configuration, (b) mid configuration, and (c) folded configuration

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Fig. 18

CAD models of larger mobile assemblies of 6 R plane-symmetric Bricard mechanisms (a) General mid configuration and (b) folded configuration

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