Research Papers

Position and Orientation Characteristic Equation for Topological Design of Robot Mechanisms

[+] Author and Article Information
Ting-Li Yang

 SINOPIC Jinling Petrochemical Corporation, Room 402, Building 6, The 4th Suo-Jin-Cun Village, Nanjing 210042, P.R.C.yangtl@public1.ptt.js.cn

An-Xin Liu

 PLA University of Science and Technology, Nanjing 210007, P.R.C.liuanxin@public1.ptt.js.cn

Qiong Jin

 Southeast University, Nanjing 210096, P.R.C.qjin@hotmail.com

Yu-Feng Luo

 Nanchang University, Nanchang 330029, P.R.C.yfluo@ncu.edu.cn

Hui-Ping Shen

 Jiangsu Polytechnic University, Changzhou 213016, P.R.C.shp65@126.com

Lu-Bin Hang

 Shanghai Jiaotong University, Shanghai 200030, P.R.C.hanglb@sjtu.edu.cn

J. Mech. Des 131(2), 021001 (Dec 30, 2008) (17 pages) doi:10.1115/1.2965364 History: Received October 02, 2006; Revised June 04, 2008; Published December 30, 2008

This paper presents the explicit mapping relations between topological structure and position and orientation characteristic (POC) of mechanism motion output. It deals with (1) the symbolic representation and the invariant property of the topological structure of the mechanism, (2) the matrix representation of POC of mechanism motion output, and (3) the POC equations of serial and parallel mechanisms and the corresponding symbolic operation rules. The symbolic operation involves simple mathematic tools and fewer operation rules and has clear geometrical meaning, so it is easy to use. The POC equations cannot only be used for structural analysis of the mechanism (such as determining POC of the relative motion between any two links of a mechanism and the rank of single-loop kinematic chain and calculating the full-cycle DOF of a mechanism, etc.) but can be used for structural synthesis of the mechanism as well (e.g., structural synthesis of the rank-degenerated serial mechanism, the over constrained single-loop mechanism, and the rank-degenerated parallel mechanism, etc.).

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Single-open chain (i.e., SOC)

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Figure 2

Basic dimensional constraint types (27-28)

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Figure 3

Three overconstrained kinematic chains

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Figure 4


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Figure 5

Velocity output of kinematic pair

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Figure 6

Velocity analysis for serial mechanism (SOC)

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Figure 7

SOC{−R∥R∥R−} and its equivalent SOC

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Figure 9

SOC{−R∥R∥R−R∥R∥R−} and its equivalent SOC

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Figure 12

3T-0R parallel mechanism

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Figure 13

The delta mechanism

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Figure 14

A type of 1T-3R parallel mechanism

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Figure 15

3-UPU parallel mechanism

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Figure 16

3−SOC{−R⊥P−S−} parallel mechanism




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