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Research Papers: Design of Mechanisms and Robotic Systems

Design and Mobility Analysis of Large Deployable Mechanisms Based on Plane-Symmetric Bricard Linkage

[+] Author and Article Information
Xiaozhi Qi

State Key Laboratory of Robotics
and System (HIT),
Shenzhen Graduate School,
Harbin Institute of Technology,
Shenzhen, Guangdong 518055, China
e-mail: ixiaozhiq@163.com

Hailin Huang

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

Zhihuai Miao

State Key Laboratory of Robotics
and System (HIT),
Shenzhen Graduate School,
Harbin Institute of Technology,
Shenzhen, Guangdong 518055, China
e-mail: miaozhihuai@hitsz.edu.cn

Bing Li

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

Zongquan Deng

State Key Laboratory of Robotics
and System (HIT),
School of Mechatronics Engineering,
Harbin Institute of Technology,
Harbin, Heilongjiang 150001, China
e-mail: denzq@hit.edu.cn

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 1, 2016; final manuscript received October 13, 2016; published online November 14, 2016. Assoc. Editor: Massimo Callegari.

J. Mech. Des 139(2), 022302 (Nov 14, 2016) (11 pages) Paper No: MD-16-1476; doi: 10.1115/1.4035003 History: Received July 01, 2016; Revised October 13, 2016

In this paper, a class of large deployable mechanisms constructed by plane-symmetric Bricard linkages is presented. The plane-symmetric Bricard linkage is a closed-loop overconstrained spatial mechanism composed of six hinge-jointed bars, which has one plane of symmetry during its deployment process. The kinematic analysis of the linkage is presented from the perspectives of geometric conditions, closure equations, and degree-of-freedom. The results illustrate that the linkage has one degree-of-freedom and can be deployed from the folded configuration to one rectangle plane. Therefore, the plane-symmetric Bricard linkage can be used as a basic deployable unit to construct larger deployable mechanisms. Four plane-symmetric Bricard linkages can be assembled into a quadrangular module by sharing the vertical bars of the adjacent units. The module is a multiloop deployable mechanism and has one degree-of-freedom. The singularity analysis of the module is developed, and two methods to avoid singularity are presented. A large deployable mast, deployable plane truss, and deployable ring are built with several plane-symmetric Bricard linkages. The deployment properties of the large deployable mechanisms are analyzed, and computer-aided design models for typical examples are built to illustrate their feasibility and validate the analysis and design methods.

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Figures

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Fig. 1

Plane-symmetric Bricard linkage model: (a) model construction process and (b) CAD model

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Fig. 2

Theoretical model of a plane-symmetric Bricard linkage

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Fig. 3

CAD models of three configurations: (a) bifurcation configuration, (b) first configuration, and (c) second configuration

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Fig. 4

Transitions of plane-symmetric Bricard linkage with multiple configurations: (a), (e), and (i) are folded configurations; (c) and (g) are bifurcation configurations

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Fig. 5

Deployment process of the linkage with θ1=π→π/2: (a) folded configuration, (b) mid-deployed configuration, and (c) deployed configuration

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Fig. 6

β and θ1 for different α

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Fig. 7

Equivalent joint of the plane-symmetric Bricard linkage

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Fig. 8

Curves of the instantaneous rotation radius and angle (the filled circles represent the vertical links, the empty circles represent the virtual rotation joints, and the line segments represent the virtual links)

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Fig. 9

Quadrangular deployable module assembled by four plane-symmetric Bricard linkages: (a) folded configuration and (b) mid-deployed configuration

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Fig. 10

Schematic diagrams of a quadrangular deployable module: (a) folded configuration, (b) singular configuration, (c) asymmetric configuration, and (d) deployed configuration

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Fig. 11

Kinematic singularity of a quadrangular module: (a) singularity configuration, (b) asymmetric configuration, and (c) deployed configuration

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Fig. 12

Variation of singularity with changing α

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Fig. 13

Methods of avoiding singularity: (a) Bevel gear pair and (b) Myard linkage

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Fig. 14

Deployment schematic diagram of a deployable mast

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Fig. 15

CAD model of a deployable mast containing nine quadrangular modules: (a) folded configuration, (b) mid-deployed configuration, and (c) deployed configuration

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Fig. 16

Deployment schematic diagram of a deployable plane truss

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Fig. 17

CAD model of a deployable plane truss containing 16 quadrangular modules: (a) folded configuration, (b) mid-deployed configuration, and (c) deployed configuration

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Fig. 18

Deployment schematic diagram of a hexagonal deployable module with δ=120 deg

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Fig. 19

CAD model of a hexagonal deployable module: (a) folded configuration, (b) mid-deployed configuration, and (c) deployed configuration

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Fig. 20

Deployment schematic diagram of a deployable ring with δ=150 deg

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Fig. 21

CAD model of a deployable ring containing 12 units: (a) folded configuration, (b) mid-deployed configuration, and (c) deployed configuration

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Fig. 22

Curves of deployment dimension of deployable mast and plane truss with angle θ

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Fig. 23

Kinematic simulation of a large deployable ring mechanism: (a) θ=0 deg, (b) θ=15 deg, (c) θ=30 deg, (d) θ=45 deg, (e) θ=60 deg, (f) θ=75 deg, and (g) θ=90 deg

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Fig. 24

Curves of deployment diameter for a deployable ring with angle θ

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Fig. 25

Deployable mesh-reflector antenna

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