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Research Papers

An Approach for Computing the Transmission Index of Full Mobility Planar Multiloop Mechanisms

[+] Author and Article Information
Xingwei Zhao

Chair of Mechatronics and Machine Dynamics,
Technical University of Berlin,
Berlin 10587, Germany
e-mail: wangmxtju@aliyun.com

Haitao Liu

Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
Tianjin University,
Tianjin 300072, China
e-mail: liuht@tju.edu.cn

Huafeng Ding

School of Mechanical Engineering and
Electronic Information,
China University of Geosciences,
Wuhan 430074, China
e-mail: dhf@ysu.edu.cn

Lu Qian

Institute of Automatic Control and
Complex Systems,
University of Duisburg-Essen,
Duisburg 47057, Germany
e-mail: qianluzxw@gmail.com

1Corresponding author.

Manuscript received June 6, 2016; final manuscript received April 18, 2017; published online June 14, 2017. Assoc. Editor: Yuefa Fang.

J. Mechanisms Robotics 9(4), 041017 (Jun 14, 2017) (10 pages) Paper No: JMR-16-1164; doi: 10.1115/1.4036718 History: Received June 06, 2016; Revised April 18, 2017

An approach for the force/motion transmissibility analysis of full mobility planar multiloop mechanisms (PMLM) is proposed in this paper by drawing on the duality of twist space and wrench space. By making a comparison study, it is concluded that the velocity model of a full mobility planar multiloop mechanism can be expressed in the same form as that of a full mobility planar parallel mechanism (PPM). Thereby, a set of dimensionally homogeneous transmission indices is proposed, which can be employed for precisely representing the closeness to different types of singularities as well as for dimensional optimization. A 3-RRR parallel mechanism and a full mobility planar multiloop mechanism for face-shovel excavation are taken as examples to demonstrate the validity and effectiveness of the proposed approach.

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Figures

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Fig. 1

Full mobility planar parallel mechanism

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Fig. 2

Full mobility planar multiloops mechanism

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Fig. 3

Comparison study on the velocity model of PPMs and PMLMs

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Fig. 4

Definitions of characteristic lengths of a MLPM

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Fig. 5

Schematic diagram of a 3-RRR planar mechanism

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Fig. 6

Variations of ηs and ηp versus φ from 0 deg to 140 deg at x=0 and y=0

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Fig. 7

Variations of σmin(J) and σmin(T*) versus φ from 0 deg to 140 deg at x=0 and y=0

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Fig. 8

Distribution of ηs given φ  = 60 deg

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Fig. 9

Distribution of ηp given φ  = 60 deg

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Fig. 10

Schematic diagram of a face-shovel excavation arm

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Fig. 11

Variations of ηs and ηp versus φ from 20 deg to 160 deg at x=0 and y=0

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Fig. 12

Variations of σmin(J) and σmin(T*) versus φ from 20 deg to 160 deg at x=0 and y=0

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Fig. 13

Distribution of ηs given φ  = 70 deg

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Fig. 14

Distribution of ηp given φ  = 70 deg

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Fig. 15

Distribution of ηs given φ  = 120 deg

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Fig. 16

Distribution of ηp given φ  = 120 deg

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Fig. 17

Distribution of ηs given φ  = 160 deg

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Fig. 18

Distribution of ηp given φ  = 160 deg

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Fig. 19

Four independent closed loops of the excavation arm

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