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Research Papers: Mechanisms and Robotics

# Synthesis and Design of a Novel 3T1R Fully-Parallel Manipulator

[+] Author and Article Information
Oscar Salgado

Department of Mechanical Engineering, University of the Basque Country, Alameda de Urquijo s/n Bilbao 48013, Spainoscar.salgado@ehu.es

Oscar Altuzarra

Department of Mechanical Engineering, University of the Basque Country, Alameda de Urquijo s/n Bilbao 48013, Spainoscar.altuzarra@ehu.es

Víctor Petuya

Department of Mechanical Engineering, University of the Basque Country, Alameda de Urquijo s/n Bilbao 48013, Spainvictor.petuya@ehu.es

Alfonso Hernández

Department of Mechanical Engineering, University of the Basque Country, Alameda de Urquijo s/n Bilbao 48013, Spaina.hernandez@ehu.es

Also known as Schönflies motion.

The nomenclature used in the paper is as follows: ${RL,rl}$ denotes the rotational motion subgroup defined by a point $L$ located in its axis and a unit vector $rl$ defining its direction; ${Tu}$ denotes the translational motion subgroup defined in the direction of unit vector $u$; ${Xe}$ means the Schönflies motion subgroup, where unit vector $e$ defines the direction of its rotational axis; and ${D}$ defines the group of rigid-body displacements.

Under the term ${Xe}⋅{RL,rl}$ will be enclosed any 5-DOF 3T2R displacement belonging to the five-dimensional subset of rigid-body displacements, 5-DOF 3T2R displacement that will be identical to the ${Xe}⋅{RL,rl}$ bond.

Single-headed arrows mean allowed directions of pure translation, and double-headed ones the feasible directions of the angular velocities, which can define either a pure rotation or a screw displacement.

NIASA-Neff & Associates Inc.

Fagor Automation® .

J. Mech. Des 130(4), 042305 (Mar 03, 2008) (8 pages) doi:10.1115/1.2839005 History: Received November 06, 2006; Revised April 23, 2007; Published March 03, 2008

## Abstract

In this paper a new topology of four degrees-of-freedom 3T1R fully-parallel manipulator is presented, which is defined only using lower kinematic pairs. The paper starts with a complete type synthesis of different topologies of fully-parallel manipulators that can perform the so-called Schönflies motion, based on the Theory of Groups of Displacements. After imposing some practical requirements, the different possibilities of manipulators are reduced to only one topology of fully-parallel and fully-symmetrical parallel manipulator. Then, the kinematic analysis of the manipulator is shown, including the closed-form resolution of both forward and inverse position problems, the velocity and the singularity analysis. Finally, a prototype of the manipulator is presented, which is intended to be used in pick and place applications.

###### FIGURES IN THIS ARTICLE
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Copyright © 2008 by American Society of Mechanical Engineers
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## Figures

Figure 1

Examples of 4-DOF 3T1R fully-parallel manipulator: (a) 4-P̱Pa2RR; (b) 4-ṞPa2RR

Figure 2

Examples of 4-DOF 3T1R fully-parallel manipulator: (a) 4-ṞRCR; (b) 4-ṞRRRR

Figure 3

4-DOF parallel manipulator

Figure 4

3T2R {Xe}⋅{Re} bond generated by each P̱RPaRR limb

Figure 5

3T1R {Xk} motion pattern of the manipulator

Figure 6

inverse kinematic singularity

Figure 7

Forward kinematic singularity with an uncontrolled instantaneous translational motion along the 12(i−j) direction

Figure 8

Forward kinematic singularity with an uncontrolled instantaneous screw motion along the Z-axis direction

Figure 9

CATIA model of the parallel manipulator

Figure 10

CATIA model of the P̱RPaRR limb

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