Research Papers

A General Degree of Freedom Formula for Parallel Mechanisms and Multiloop Spatial Mechanisms

[+] Author and Article Information
Ting-Li Yang

 SINOPIC Jinling Petrochemical Corporation, Nanjing, China; Changzhou University, Changzhou, Chinayangtl@126.com

Dong-Jin Sun

 SINOPIC Jinling Petrochemical Corporation, Nanjing, Chinasundj@126.com

J. Mechanisms Robotics 4(1), 011001 (Feb 03, 2012) (17 pages) doi:10.1115/1.4005526 History: Received June 19, 2010; Revised October 21, 2011; Published February 03, 2012; Online February 03, 2012

Based on the position and orientation characteristic (POC) set and the POC equations for serial mechanisms and parallel mechanisms proposed by authors, this paper presents a novel general degree of freedom (DOF) formula which is totally different from approaches based on the screw theory and the displacement group. It can be used to determine the full-cycle DOF of parallel mechanisms (PMs) and multiloop spatial mechanisms using symbolic “union” and “intersection” operations for POC sets. These operations involve only several rules and only simple mathematical tools (vector algebra, theory of sets, etc.) are used. Furthermore, criteria for determination of the inactive joints and selection of the actuating joints are proposed. The presented approach is illustrated with several examples.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Six basic dimension constraint types

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Figure 2

Output velocity of kinematic pairs

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Figure 3


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Figure 4


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Figure 5

Topology structure of a PM and its jth independent loop

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Figure 6

A (3T-0R) parallel mechanism

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Figure 7

A (3T-0R) parallel mechanism with inactive joints

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Figure 8

A (1T-3R) parallel mechanism

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Figure 9

A three-loop spatial mechanism

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Figure 10

A parallel mechanism with two branches



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