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RESEARCH PAPERS

Linear Property of the Screw Surface of the Spatial RPRP Linkage

[+] Author and Article Information
Chintien Huang

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwanchuang@mail.ncku.edu.tw

Han-Tsung Tu

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan

J. Mech. Des 128(3), 581-586 (Jul 08, 2005) (6 pages) doi:10.1115/1.2181602 History: Received January 06, 2005; Revised July 08, 2005

This paper investigates the screw surface of the RPRP linkage, an overconstrained linkage with mobility one. The screw surface is a ruled surface containing screws for displacing the coupler of the RPRP linkage from one reference position to all reachable positions. In this paper, two types of RPRP linkages, in folded and unfolded forms, are constructed by using hexahedrons in accordance with Delassus’ criteria. It is shown that the screw surfaces of both types of RPRP linkages can be represented by screw systems of the second order. These novel finite screw systems are obtained by intersecting two 3-systems corresponding to the finite displacements of the RP and PR dyads. The intersection of finite screw systems is conducted by employing the intersection operation of vector subspaces of the six-dimensional vector space.

FIGURES IN THIS ARTICLE
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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

General arrangement of the RPRP linkage

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Figure 3

The unfolded RPRP linkage

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Figure 4

Top view of the folded RPRP linkage

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Figure 5

Top view of the unfolded RPRP linkage

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Figure 6

Basis screws of the PR dyad displacements

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Figure 7

Basis screws of the RP dyad displacements

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Figure 8

Joint screws of the folded RPRP linkage

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Figure 9

Basis screws of the RPRP 2-system

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Figure 10

Joint screws of the unfolded RPRP linkage

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Figure 11

The fourth special 2-system

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Figure 2

The folded RPRP linkage

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