Research Papers

A General Approach for Geometric Error Modeling of Lower Mobility Parallel Manipulators

[+] Author and Article Information
Haitao Liu

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

Tian Huang

School of Mechanical Engineering, Tianjin University, Tianjin 300072, Chinahtiantju@public.tpt.tj.cn; th@eng.warwick.ac.uk

Derek G. Chetwynd

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

J. Mechanisms Robotics 3(2), 021013 (Apr 20, 2011) (13 pages) doi:10.1115/1.4003845 History: Received April 15, 2010; Revised September 24, 2010; Published April 20, 2011; Online April 20, 2011

This paper presents a general and systematic approach for geometric error modeling of lower mobility manipulators. The approach can be implemented in three steps: (1) development of a linear map between the pose error twist and source errors within an individual limb using the homogeneous transformation matrix method; (2) formulation of a linear map between the pose error twist and the joint error intensities of a lower mobility parallel manipulator; and (3) combination of these two models. The merit of this approach lies in that it enables the source errors affecting the compensatable and uncompensatable pose accuracy of the platform to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for the accuracy improvement achievable by suitable measures, i.e., component tolerancing in design, manufacturing and assembly processes, and kinematic calibration. Three typical and well-known parallel manipulators are taken as examples to illustrate the generality and effectiveness of this approach.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 2

The ith limb of an f-DOF parallel mechanism with joint errors

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Figure 3

Schematic diagram of the Sprint Z3 head

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Figure 4

Schematic diagram of the Tricept robot

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Figure 6

Geometric errors of Rja−1,i relative to Rja,i

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Figure 7

Two frames with geometric errors

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Figure 8

A parallelogram joint with joint errors

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Figure 1

Schematic diagram of an f-DOF parallel mechanism

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Figure 5

Schematic diagram of the Delta robot



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