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Research Papers

Mobility Analysis of Symmetric Deployable Mechanisms Involved in a Coplanar 2-Twist Screw System

[+] Author and Article Information
Bing Li

State Key Laboratory of Robotics
and System (HIT),
Harbin 150001, China;
Shenzhen Graduate School,
Harbin Institute of Technology,
Shenzhen 518055, China
e-mail: libing.sgs@hit.edu.cn

Hailin Huang

State Key Laboratory of Robotics
and System (HIT),
Harbin 150001, China;
Shenzhen Graduate School,
Harbin Institute of Technology,
Shenzhen 518055, China
e-mail: dwenhcil@gmail.com

Zongquan Deng

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

1Corresponding author.

Manuscript received September 30, 2014; final manuscript received April 3, 2015; published online August 18, 2015. Assoc. Editor: Byung-Ju Yi.

J. Mechanisms Robotics 8(1), 011007 (Aug 18, 2015) (9 pages) Paper No: JMR-14-1273; doi: 10.1115/1.4030373 History: Received September 30, 2014

In this paper, an intuitive approach for the mobility analysis of deployable mechanisms involved in a special screw system with two coplanar twist vectors is proposed. First, the coplanar screw system with a pair of parallel/concurrent zero pitch screws is analyzed, and the intuitive allowable mobility set for the screw system is described. Next, kinematic chains containing the coplanar screw system are enumerated. The proposed approach is used to explain the mobility of the deployable Bennett mechanism, Myard mechanism, and Bricard mechanism; some novel deployable mechanisms could be found based on the analysis. Furthermore, it is shown that the proposed approach can be applied to the mobility analysis of multiloop deployable mechanisms and is found to be more intuitive than the traditional approach, which provides a straightforward insight into the mobility of complicated mechanisms.

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Figures

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Fig. 1

Two coplanar screw systems: (a) concurrent axes and (b) parallel axes

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Fig. 2

Kinematic chain representations of coplanar screw systems with two twists: (a) concurrent axes and (b) parallel axes

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Fig. 3

Symmetric Bennett mechanism

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Fig. 4

Geometry of the second subchain of deployable Bennett mechanism

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Fig. 5

CAD model of a deployable Bennett mechanism: (a) deployed configuration, (b) general configuration, and (c) folded configuration

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Fig. 6

CAD model of the deployable Bennett-extended 6R mechanism: (a) deployed configuration, (b) general configuration, and (c) folded configuration

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Fig. 7

Geometric model of the deployable Bennett-extended 6R mechanism

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Fig. 8

Bennett-extended 3R1S mechanism

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Fig. 9

CAD model of deployable Bennett-extended 3R1S mechanism: (a) deployed configuration, (b) general configuration, and (c) folded configuration

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Fig. 10

Theoretical Myard mechanism

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Fig. 11

CAD model of deployable Myard mechanism: (a) deployed configuration, (b) general configuration, and (c) folded configuration

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Fig. 12

CAD model of deployable Myard-extended 7R mechanism: (a) deployed configuration, (b) general configuration, and (c) folded configuration

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Fig. 13

Symmetric open-loop kinematic chains comprising multiple coplanar screw systems: (a) chain 1, (b) chain 2, and (c) chain 3

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Fig. 14

CAD model of deployable 4R1S mechanism: (a) deployed configuration, (b) general configuration, and (c) folded configuration

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Fig. 15

Threefold-symmetric Bricard mechanism

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Fig. 16

CAD model of threefold-symmetric Bricard mechanism: (a) deployed configuration, (b) general configuration, and (c) folded configuration

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Fig. 17

Plane-symmetric Bricard mechanism

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Fig. 18

CAD model of plane-symmetric Bricard mechanism: (a) deployed configuration, (b) general configuration, and (c) folded configuration

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Fig. 19

CAD model of a multiloop deployable mechanism constructed from two plane-symmetric Bricard mechanisms: (a) general configuration and (b) folded configuration

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Fig. 20

Intuitive illustration of the mobility of two plane-symmetric-Bricard multiloop mechanism

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Fig. 21

CAD models of a multiloop deployable mechanism constructed from three general plane-symmetric Bricard mechanisms: (a) single-loop mechanism, (b) deployed configuration, and (c) folded configuration

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Fig. 22

Intuitive illustration of the mobility of a multiloop deployable mechanism constructed from three general plane-symmetric Bricard mechanisms

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Fig. 23

3-Myard threefold-symmetric Bricard mechanism: (a) theoretical model and (b) CAD model

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Fig. 24

CAD model for four-plane-symmetric Bricard multiloop mechanism: (a) deployed configuration and (b) folded configuration

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Fig. 25

Equivalent model of the four-plane-symmetric Bricard multiloop mechanism

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