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Research Papers

An Approach for Acceleration Analysis of Lower Mobility Parallel Manipulators

[+] Author and Article Information
Haitao Liu

School of Mechanical Engineering, Tianjin University, Tianjin 300072, China

Tian Huang1

School of Mechanical Engineering, Tianjin University, Tianjin 300072, Chinahtiantju@public.tpt.tj.cn

Derek G. Chetwynd

School of Engineering, The University of Warwick, Coventry CV4 7AL, UK

1

Corresponding author.

J. Mechanisms Robotics 3(1), 011013 (Feb 10, 2011) (8 pages) doi:10.1115/1.4003271 History: Received December 22, 2009; Revised December 05, 2010; Published February 10, 2011; Online February 10, 2011

This paper presents a new approach to the velocity and acceleration analyses of lower mobility parallel manipulators. Building on the definition of the “acceleration motor,” the forward and inverse velocity and acceleration equations are formulated such that the relevant analyses can be integrated under a unified framework that is based on the generalized Jacobian. A new Hessian matrix of serial kinematic chains (or limbs) is developed in an explicit and compact form using Lie brackets. This idea is then extended to cover parallel manipulators by considering the loop closure constraints. A 3-P RS parallel manipulator with coupled translational and rotational motion capabilities is analyzed to illustrate the generality and effectiveness of this approach.

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Copyright © 2011 by American Society of Mechanical Engineers
Topics: Manipulators
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References

Figures

Grahic Jump Location
Figure 1

Hessian matrix Hi of the ith limb

Grahic Jump Location
Figure 2

Hessian matrix H of a parallel manipulator

Grahic Jump Location
Figure 3

Schematic diagram of Sprint Z3 head

Grahic Jump Location
Figure 4

Variations versus time of (a) velocity and (b) acceleration of the actuated joints, (c) linear velocity and (d) acceleration of the reference point, and (e) angular velocity and (f) acceleration of the platform. Note that the system symmetries are always reflected within these graphs and so no significant data is hidden.

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