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Technical Briefs

A Formula That Produces a Unique Solution to the Forward Displacement Analysis of a Quadratic Spherical Parallel Manipulator: The Agile Eye

[+] Author and Article Information
Xianwen Kong

Department of Mechanical Engineering, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UKx.kong@hw.ac.uk

Clément M. Gosselin

Département de Génie Mécanique, Université Laval, Pavillon Adrien-Pouliot, 1065 Avenue de la médicine, Québec, QC, G1V 0A6, Canadagosselin@gmc.ulaval.ca

J. Mechanisms Robotics 2(4), 044501 (Aug 30, 2010) (4 pages) doi:10.1115/1.4002077 History: Received May 31, 2009; Revised May 12, 2010; Published August 30, 2010; Online August 30, 2010

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a quadratic spherical parallel manipulator: the Agile Eye. An alternative formulation of the kinematic equations of the Agile Eye is proposed. The singularity analysis of the Agile Eye is then dealt with. After an alternative solution to the FDA has been presented, a formula is revealed that produces a unique current solution to the FDA for a given set of inputs. A regular cube in the input-space, which is singularity free, is also proposed for the Agile Eye. This work will facilitate the control of the Agile Eye.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

A quadratic spherical parallel manipulator: the Agile Eye. (a) CAD model, (b) kinematic model.

Grahic Jump Location
Figure 2

Current solution to the FDA of the Agile Eye (θ1=30 deg, θ2=30 deg, and θ3=30 deg)

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