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Research Papers

Motion Analysis of Manipulators With Uncertainty in Kinematic Parameters

[+] Author and Article Information
Vahid Nazari

Department of Mechanical and
Materials Engineering,
Queen's University,
Kingston, ON K7L 3N6, Canada
e-mail: v.nazari@queensu.ca

Leila Notash

Department of Mechanical and
Materials Engineering,
Queen's University,
Kingston, ON K7L 3N6, Canada
e-mail: leila.notash@queensu.ca

1Corresponding author.

Manuscript received March 16, 2015; final manuscript received September 6, 2015; published online November 24, 2015. Assoc. Editor: Raffaele Di Gregorio.

J. Mechanisms Robotics 8(2), 021014 (Nov 24, 2015) (9 pages) Paper No: JMR-15-1060; doi: 10.1115/1.4031657 History: Received March 16, 2015; Revised September 06, 2015; Accepted September 18, 2015

In this article, a novel method for characterizing the exact solution for interval linear systems is presented. In the proposed method, the entries of the interval coefficient matrix and interval right-hand side vector are formulated as linear functions of two or three parameters. The parameter groups for two- and three-parameter cases are identified. The exact solution is characterized using the solution sets corresponding to the parameter groups. The parametric method is then employed in the motion analysis of manipulators considering the uncertainty in kinematic parameters. Example manipulators are used to show the implementation of the method and the effect of uncertainty in the motion performance.

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Figures

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Fig. 1

Two degrees-of-freedom planar serial manipulator

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Fig. 2

(a) One-parameter solution set, solid line, and the exact solution, dashed lines, (b) one of two-parameter solution sets represented with solid lines, (c) all two-parameter solution sets, dashed lines, (d) one of three-parameter solution sets, solid lines, and (e) two-parameter solution set in Eq. (20) when θ1=(π/6) (rad), θ2=(π/4) (rad), and the radius of uncertainty is (π/180) (rad)

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Fig. 3

(a) Two-parameter solution set, dotted lines, and the exact solution, solid lines, and (b) three-parameter solution set

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Fig. 4

(a) A 3DOF spherical manipulator with RRP layout, (b) a reconfigurable planar parallel manipulator with PPRPR layout, and (c) zero configuration of the legs of the parallel manipulator

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Fig. 5

Exact solution of the joints in spherical manipulator with RRP layout

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Fig. 6

Exact solution, hatched and filled areas; and feasible solution, filled area, for the joints of leg 3 of parallel manipulator of Fig. 4(b) with the first and second prismatic joints locked

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