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Research Papers

Classification of 3T1R Parallel Manipulators Based on Their Wrench Graph

[+] Author and Article Information
Semaan Amine

Department of Mechanical Engineering,
Beirut Arab University,
P.O. Box 115020,
Riad El Solh,
Beirut 11072809, Lebanon
e-mail: s.amin@bau.edu.lb

Ossama Mokhiamar

Department of Mechanical Engineering,
Beirut Arab University,
P.O. Box 115020,
Riad El Solh,
Beirut 11072809, Lebanon;
Department of Mechanical Engineering,
Alexandria University,
El-Chatby,
Alexandria 21544, Egypt
e-mail: ossama.mokhiamar@bau.edu.lb

Stéphane Caro

Institut de Recherche en Communications et
Cybernétique de Nantes,
UMR CNRS No. 6597,
1 rue de la Noë,
Nantes 44321, France
e-mail: stephane.caro@irccyn.ec-nantes.fr

1Corresponding author.

Manuscript received March 10, 2016; final manuscript received November 7, 2016; published online December 2, 2016. Assoc. Editor: Jian S. Dai.

J. Mechanisms Robotics 9(1), 011003 (Dec 02, 2016) (10 pages) Paper No: JMR-16-1064; doi: 10.1115/1.4035188 History: Received March 10, 2016; Revised November 07, 2016

This paper presents a classification of 3T1R parallel manipulators (PMs) based on the wrench graph. By using the theory of reciprocal screws, the properties of the three-dimensional projective space, the wrench graph, and the superbracket decomposition of Grassmann–Cayley algebra, six typical wrench graphs for 3T1R parallel manipulators are obtained along with their singularity conditions. Furthermore, this paper shows a way in which each of the obtained typical wrench graphs can be used in order to synthesize new 3T1R parallel manipulator architectures with known singularity conditions and with an understanding of their geometrical properties and assembly conditions.

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Figures

Grahic Jump Location
Fig. 1

Two 3T1R PMs [19]: (a) 4-R¯`R`R¯R¯R` and (b) 4-R¯`R`R`R¯R¯

Grahic Jump Location
Fig. 2

The Quadrupteron PM

Grahic Jump Location
Fig. 3

Actuation singularity of the Quadrupteron PM

Grahic Jump Location
Fig. 4

A 2-PRRU-PRRR-PRPP PM

Grahic Jump Location
Fig. 8

Simplified design AA of a 4-RPUR PM

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