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Research Papers

Kinematic Optimization of a Five Degrees-of-Freedom Spatial Parallel Mechanism With Large Orientational Workspace

[+] 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 Lab of Precision/Ultra-Precision
Manufacturing Equipments and Control,
Tsinghua University,
Beijing 100084, China;
Fraunhofer-Institut fuer Werkzeugmachinen und
Umformtechnik (IWU),
Reichenhainer Str. 88,
Chemnitz D-09126, Germany

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 Lab of Precision/Ultra-Precision
Manufacturing Equipments and Control,
Tsinghua University,
Beijing 100084, China
e-mail: xinjunliu@mail.tsinghua.edu.cn

Jinsong Wang

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 Werkzeugmachinen und
Umformtechnik (IWU),
Reichenhainer Str. 88,
Chemnitz D-09126, Germany

1Corresponding author.

Manuscript received November 4, 2016; final manuscript received June 15, 2017; published online August 4, 2017. Assoc. Editor: Clement Gosselin.

J. Mechanisms Robotics 9(5), 051005 (Aug 04, 2017) (9 pages) Paper No: JMR-16-1341; doi: 10.1115/1.4037254 History: Received November 04, 2016; Revised June 15, 2017

This paper deals with the kinematic optimization of a five degrees-of-freedom (DoFs) spatial parallel mechanism with three kinematic chains. Inspired by the structure of the icosahedron, the base of the discussed mechanism has been designed into a compact and light-weight frame. Due to the potential advantages, this mechanism is used as a movable plug-in module in a multi-axis machine center to process large-scale parts with rotary contour surfaces. To derive its optimal parameters, kinematic optimization based on the motion/force transmissibility is carried out. The parameter design space (PDS) is generated first. Then, the performance evaluation index (i.e., local transmission index (LTI)) is derived sequentially. On this basis, the good transmission positioning workspace (GTPW) for a given orientation is defined by constraining the value of LTI with a certain metric. Thereafter, the atlases of the GTPW and the optimal region satisfying the workspace constraint are derived in the PDS. Within this region, a set of optimal parameters without dimension are selected. Consequently, the cuboid workspaces within GTPWs are identified in detail. By using the ratio between required workspace in application and the derived cuboid workspaces, optimal geometric parameters with dimension are derived. Workspace analysis results show that, for an arbitrary orientation between the vertical and horizontal directions, there is always a cuboid workspace within GTPW larger than required workspace. In addition, the orientational capability of the mechanism can reach more than 90 deg, and the flexible 2DoFs rotations can also be realized. The work in this paper is very helpful to the development of a mobile machining module.

Copyright © 2017 by ASME
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Figures

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Fig. 1

A spatial parallel mechanism: (a) computer-aided design model and (b) kinematic scheme

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Fig. 2

DoF and constraint analysis of the first limb

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Fig. 3

A spatial parallel mechanism: (a) vertical model and (b) horizontal model

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Fig. 4

An icosahedron: (a) three-dimensional model and (b) selected faces

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Fig. 5

Application in processing parts with rotary contour surfaces

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Fig. 6

Definitions of the azimuth angle φ and the tilt angle θ

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Fig. 7

PDS: (a) three-dimensional view and (b) planar view

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Fig. 8

Working modes of the spatial mechanism in a projection plane

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Fig. 9

GTPW atlases (φ=270 deg): (a) θ=0 deg, (b) θ=30 deg, (c) θ=60 deg, and (d) θ=90 deg

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Fig. 10

Optimal region when GTPWφ=270 deg,θ≥0.6

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Fig. 11

Relationship between GTPWφ=270 deg,θ and θ

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Fig. 12

Cuboid positioning workspace within GTPW (φ=270 deg and θ=0 deg, 30 deg, 60 deg, 80 deg, 90 deg)

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Fig. 13

Distributions of GTOW when (x = 0 mm, y = 0 mm, z = −440 mm, and z = −120 mm)

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Fig. 14

Definition of the parameter (φ′, θ′)

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Fig. 15

GTSC around the reference axis (φ=270 deg and θ=60 deg)

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Fig. 16

Distribution of θmin′ as the reference (φ=270 deg,θ) changes

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