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Research Papers

Forward Displacement Analysis of a Linearly Actuated Quadratic Spherical Parallel Manipulator

[+] 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 Gosselin

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

James M. Ritchie

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

In general, this may not happen in practice due to link interference.

J. Mechanisms Robotics 3(1), 011007 (Jan 06, 2011) (6 pages) doi:10.1115/1.4003079 History: Received July 19, 2010; Revised November 15, 2010; Published January 06, 2011; Online January 06, 2011

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a linearly actuated quadratic spherical parallel manipulator. An alternative formulation of the kinematic equations of the quadratic spherical parallel manipulator is proposed. The singularity analysis of the quadratic spherical parallel manipulator is then dealt with. A new type of singularity of parallel manipulators—leg actuation singularity—is identified. If a leg is in a leg actuation singular configuration, the actuated joints in this leg cannot be actuated even if the actuated joints in other legs are released. A formula is revealed that produces a unique current solution to the FDA for a given set of inputs. The input space is also revealed for the quadratic spherical parallel manipulator in order to guarantee that the robot works in the same assembly mode. This work may facilitate the control of the quadratic spherical parallel manipulator.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 2

Singularity-free regions of the LAQSPM (−π/2<ϕ3≤π/2)

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Figure 3

Leg actuation singular configuration of the LAQSPM

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Figure 4

Current solution to the FDA of the LAQSPM (ϕ1=18.83 deg, ϕ2=26.10 deg, and ϕ3=18.83 deg)

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Figure 5

Input space of the LAQSPM

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Figure 6

Manipulation of the LAQSPM in the virtual reality environment

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