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Research Papers

A Rolling 8-Bar Linkage Mechanism

[+] Author and Article Information
Yaobin Tian

School of Mechanical, Electronic
and Control Engineering,
Beijing Jiaotong University,
No. 3 Shangyuancun, Haidian District,
Beijing 100044, China
e-mail: 09116325@bjtu.edu.cn

Yan-An Yao

School of Mechanical, Electronic
and Control Engineering,
Beijing Jiaotong University,
No. 3 Shangyuancun, Haidian District,
Beijing 100044, China
e-mail: yayao@bjtu.edu.cn

Jieyu Wang

School of Mechanical,
Electronic and Control Engineering,
Beijing Jiaotong University,
No. 3 Shangyuancun, Haidian District,
Beijing 100044, China
e-mail: 12121333@bjtu.edu.cn

1Corresponding author.

Manuscript received May 23, 2013; final manuscript received October 26, 2014; published online March 11, 2015. Assoc. Editor: Xilun Ding.

J. Mechanisms Robotics 7(4), 041002 (Nov 01, 2015) (11 pages) Paper No: JMR-13-1099; doi: 10.1115/1.4029117 History: Received May 23, 2013; Revised October 26, 2014; Online March 11, 2015

In this paper, a rolling mechanism constructed by a spatial 8-bar linkage is proposed. The eight links are connected with eight revolute joints, forming a single closed-loop with two degrees of freedom (DOF). By kinematic analysis, the mechanism can be deformed into planar parallelogram or spherical 4-bar mechanism (SFM) configuration. Furthermore, this mechanism can be folded onto a plane at its singularity positions. The rolling capability is analyzed based on the zero-moment-point (ZMP) theory. In the first configuration, the mechanism can roll along a straight line. In the second configuration, it can roll along a polygonal region and change its rolling direction. By alternatively choosing one of the two configurations, the mechanism has the capability to roll along any direction on the ground. Finally, a prototype was manufactured and some experiments were carried out to verify the functions of the mechanism.

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Figures

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Fig. 1

The hybrid Bricard linkage: (a) the planar expanded state and (b) a general folded state

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Fig. 2

General position of the 8-bar linkage: (a) 3D model and (b) sketch of the mechanism

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Fig. 3

The singularity position when θ1 = 90 deg and θ2 = 180 deg

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Fig. 4

Rotational motion about line BF

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Fig. 5

Rotational motions about line HD

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Fig. 6

The singularity position when θ1 = 180 deg and θ2 = 90 deg

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Fig. 7

Rotational motions about line CG

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Fig. 8

Rotational motions about line AE

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Fig. 9

(a) SFM configuration and (b) PPM configuration

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Fig. 10

(a) A general view of the PPM and (b) the projected view on the yz plane

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Fig. 11

(a) Sketch of the SFM and (b) the simplified sketch of the SFM

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Fig. 12

The symmetrical plane CSG

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Fig. 13

(a) The curves of r when θ2 = 150 deg, ((b)) the curves of r when θ2 = 135 deg, the two dashed triangles in (a), (b) are the edges of links AB and BC

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Fig. 14

Schematic of the PPM

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Fig. 15

The curves of yzmp when the PPM moves to the right with w ≤ 0

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Fig. 16

A rolling cycle to the right: (a) the PPM is in its initial state (θ1 = 90 deg), (b) the PPM begins to roll about point C, (c) point E is touches the ground and link CE becomes a new supporting link, and (d) the PPM returns to the initial state

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Fig. 17

The curves of yzmp when the PPM moves to the right with α < 0

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Fig. 18

Initial state of the SFM

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Fig. 19

(a) The curves of ZMP when the SFM moves to the right with ω ≤ 0 (the black solid lines are the supporting edges of SFM), (b) the curves of xZMP and yZMP with ω = −270 deg/s, and (c) the curves of xZMP and yZMP with ω = −360 deg/s

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Fig. 20

The curves of yzmp when the SFM moves to the right with α < 0

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Fig. 21

Rolling directions

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Fig. 22

Rolling on the ground with barriers

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Fig. 23

Prototype of the 8-bar linkage

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Fig. 24

Deformations of the 8-bar linkage

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Fig. 25

Folding states at the first singularity position (the total sizes of each state are (a) 260 mm × 200 mm × 130 mm, (b) 260 mm × 200 mm × 260 mm, and (c) 200 mm × 200 mm × 260 mm)

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Fig. 26

Folding states at the second singularity position (the total sizes of each state are (a) 300 mm × 300 mm × 80 mm and (b) 300 mm × 300 mm × 160 mm)

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Fig. 27

Rolling experiment of the PPM

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Fig. 28

Rolling experiment of the SFM when θ2 ≈150 deg

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Fig. 29

Rolling experiment of the SFM when θ2 ≈ 200 deg

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