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Technical Brief

On the Solution Set for Positive Wire Tension With Uncertainty in Wire-Actuated Parallel Manipulators

[+] Author and Article Information
Leila Notash

Mem. ASME
Department of Mechanical and Materials Engineering,
Queen University,
Kingston, ON K7P 2S4, Canada
e-mail: leila.notash@queensu.ca

Manuscript received September 30, 2015; final manuscript received January 15, 2016; published online March 25, 2016. Assoc. Editor: Raffaele Di Gregorio.

J. Mechanisms Robotics 8(4), 044506 (Mar 25, 2016) (9 pages) Paper No: JMR-15-1288; doi: 10.1115/1.4032593 History: Received September 30, 2015; Revised January 15, 2016

The solution for positive wire tension vector in the presence of uncertainties in design parameters and error in data is investigated for parallel manipulators. The minimum 2-norm non-negative solution and enclosures for the vector of wire tensions are formulated utilizing the perturbed and the interval forms of Jacobian matrix and platform wrench. Methodologies for calculating the minimum 2-norm non-negative solution set of wire tension vector, for interval Jacobian matrix and interval external wrench, are presented. Example parallel manipulators are simulated to investigate the implementation and effectiveness of these methodologies while relating their results.

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Figures

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Fig. 1

Four-wire parallel manipulators with (a) 2DOF and (b) 3DOF

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Fig. 2

Parameters of planar wire-actuated parallel manipulators

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Fig. 4

Bounds of solution and solution set for example 2 (a) τcorrr using three parameters and (b) τtotr

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Fig. 3

Bounds of solution and solution sets for example 1: τcorrr using (a) six parameters; (b) three parameters; (c) two parameters; (d) convex hull of vertices; and (e) τtotr

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