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Research Papers

Mobility, Singularity, and Kinematics Analyses of a Novel Spatial Parallel Mechanism

[+] Author and Article Information
Fugui Xie

The State Key Laboratory of Tribology and
Institute of Manufacturing Engineering,
Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China;
Beijing Key Laboratory of
Precision/Ultra-Precision
Manufacturing Equipments and Control,
Tsinghua University,
Beijing 100084, China;
Fraunhofer-Institut fuer Werkzeugmaschinen und
Umformtechnik (IWU),
Reichenhainer Str. 88,
Chemnitz D-09126, Germany
e-mail: xiefg@mail.tsinghua.edu.cn

Xin-Jun Liu

The State Key Laboratory of Tribology and
Institute of Manufacturing Engineering,
Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China;
Beijing Key Laboratory of
Precision/Ultra-Precision Manufacturing
Equipments and Control,
Tsinghua University,
Beijing 100084, China
e-mail: xinjunliu@mail.tsinghua.edu.cn

Xuan Luo

The State Key Laboratory of Tribology and
Institute of Manufacturing Engineering,
Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China

Markus Wabner

Fraunhofer-Institut fuer Werkzeugmaschinen und
Umformtechnik (IWU),
Reichenhainer Str. 88,
Chemnitz D-09126, Germany

1Corresponding authors.

Manuscript received June 13, 2016; final manuscript received September 25, 2016; published online October 27, 2016. Assoc. Editor: Marc Gouttefarde.

J. Mechanisms Robotics 8(6), 061022 (Oct 27, 2016) (10 pages) Paper No: JMR-16-1171; doi: 10.1115/1.4034886 History: Received June 13, 2016; Revised September 25, 2016

A spatial parallel kinematic mechanism (PKM) with five degrees of freedom (DoFs) and three limbs is proposed in this paper. To investigate the characteristics of the proposed mechanism's DoFs, mobility analysis based on a line graph method and Grassmann line geometry is carried out. The results show that the mobile platform can rotate about a fixed point at the base and translate in a specific plane (i.e., three rotations and two translations). Therefore, the mobile platform can be located at an arbitrary point in the space and has flexible orientational capability. The orientation of the mobile platform is described by using tilt-and-torsion (T&T) angles, and the kinematics model is established with this precondition. Within the process of kinematics modeling, parasitic motion of the mobile platform is analyzed, and singularity configurations are also disclosed. On this basis, four working modes with different configurations are identified, and one of them is focused on and investigated in detail. The proposed PKM has good potential to be used in the development of movable machine centers. The kinematic analysis is very helpful for the understanding of the concept and the potential applications.

Copyright © 2016 by ASME
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Figures

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Fig. 1

A spatial parallel kinematic mechanism: (a) CAD model and (b) kinematic scheme

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Fig. 2

Intersection between line vectors

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Fig. 3

Line vector and couple are perpendicular

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Fig. 4

Relationship between couples

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Fig. 5

Motion and constraint line graphs for the first limb

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Fig. 6

Motion line graph for the second limb

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Fig. 7

Motion line graph for the mobile platform of the proposed PKM

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Fig. 8

Potential application cases: (a) large translational capability and (b) large workspace

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Fig. 9

Definitions of the azimuth angle φ and the tilt angle θ

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Fig. 10

Parasitic motion distribution: (a) in all the directions and (b) without singularity

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Fig. 11

Distributions of the first input in all the directions

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Fig. 12

Distributions of angle ξ : (a) in all the directions and (b) without singularity

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Fig. 13

Distributions of μ2 : (a) in all the directions and (b) without singularity

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Fig. 14

Distributions of μ3 : (a) in all the directions and (b) without singularity

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Fig. 15

Working modes: (a) under T&T angles and (b) relationship between φ and θ

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Fig. 16

Active inputs of the second limb: (a) L2−4=|B4P2| and (b) L2−5=|B5C2|

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