Cartesian Parallel Manipulators With Pseudoplanar Limbs

[+] Author and Article Information
Chung-Ching Lee

Department of Tool and Die Making, National Kaohsiung University of Applied Sciences, 415 Chien Kung Road, Kaohsiung 80782, Taiwan, R.O.Ccclee@cc.kuas.edu.tw

Jacques M. Hervé

 Ecole Centrale Paris, Grande Voie des Vignes, F-92295 Chatenay-Malabry, Francejherve@ecp.fr

J. Mech. Des 129(12), 1256-1264 (Dec 18, 2006) (9 pages) doi:10.1115/1.2779892 History: Received May 25, 2006; Revised December 18, 2006

Based on the Lie-group-algebraic properties of the displacement set, the three-degree-of-freedom (3DOF) pseudoplanar motion often termed Y motion for brevity is first introduced. Then, all possible general architectures of the mechanical generators of a given Y subgroup are obtained by implementing serial arrays of 1DOF Reuleaux pairs or hinged parallelograms. In total, five distinct mechanical generators of Y motion are revealed and seven ones having at least one parallelogram are also derived from them. In order to avoid the singularity that may occur in the limbs, all singular postures of Y-motion generators are also located by detecting the possible linear dependency of the joint twists and the group dependency of displacement sets. The parallel layout of three 4DOF limbs including Y-motion generators with orthogonal planes make up a Cartesian translational parallel manipulator, which produces a motion set of spatial translations. The 3DOF translation of the moving platform is directly controlled by the three 1DOF translations in three orthogonal prismatic fixed joints.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 5

Transitory infinitesimal singularity of HPHY-motion generator

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Figure 6

Transitory infinitesimal singularity of PHHY-motion generator

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Figure 7

PPP linkage and its corresponding wrong generator of Y motion

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Figure 8

Finite singularity of PPH and PHPY-motion generators

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Figure 9

Permanent finite singularity with two coaxial H pairs: wrong generators of Y motion

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Figure 10

Transitory finite singularity of Y-motion generators with two coaxial H pairs

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Figure 11

A general architecture of Cartesian parallel manipulator

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Figure 12

Cartesian parallel manipulators with idle H pairs: working like a Cartesian 3‐(PPP)

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Figure 13

Cartesian parallel manipulators without idle pairs

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Figure 14

Three illustrations of Cartesian parallel manipulators

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Figure 1

A general generator of {Y(w,p)}

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Figure 2

Y-motion generators with 1 DOF lower pairs

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Figure 3

Y-motion generators with hinged parallelograms

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Figure 4

A HHH(RRR) chain with transitory infinitesimal singularity




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