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RESEARCH PAPERS

Sensitivity Analysis of the Orthoglide: A Three-DOF Translational Parallel Kinematic Machine

[+] Author and Article Information
Stéphane Caro

Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN) UMR 6597 CNRS, École Centrale de Nantes, Université de Nantes, École des Mines de Nantes 1, rue de la Noë-44321 Nantes, FranceStephane.Caro@irccyn.ec-nantes.fr

Philippe Wenger, Fouad Bennis, Damien Chablat

Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN) UMR 6597 CNRS, École Centrale de Nantes, Université de Nantes, École des Mines de Nantes 1, rue de la Noë-44321 Nantes, France

J. Mech. Des 128(2), 392-402 (Jun 08, 2005) (11 pages) doi:10.1115/1.2166852 History: Received November 17, 2004; Revised June 08, 2005

In this paper, two complementary methods are introduced to analyze the sensitivity of a three-degree-of-freedom (3-DOF) translational parallel kinematic machine (PKM) with orthogonal linear joints: the Orthoglide. Although these methods are applied to a particular PKM, they can be readily applied to 3-DOF Delta-Linear PKM such as ones with their linear joints parallel instead of orthogonal. On the one hand, a linkage kinematic analysis method is proposed to have a rough idea of the influence of the length variations of the manipulator on the location of its end-effector. On the other hand, a differential vector method is used to study the influence of the length and angular variations in the parts of the manipulator on the position and orientation of its end-effector. Besides, this method takes into account the variations in the parallelograms. It turns out that variations in the design parameters of the same type from one leg to another have the same effect on the position of the end-effector. Moreover, the sensitivity of its pose to geometric variations is a minimum in the kinematic isotropic configuration of the manipulator. On the contrary, this sensitivity approaches its maximum close to the kinematic singular configurations of the manipulator.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Basic kinematic architecture of the Orthoglide

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Figure 2

Morphology of the ith leg of the Orthoglide

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Figure 3

Cartesian workspace, Cu, points Q1 and Q2

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Figure 4

Mean of sensitivity of px throughout Cu

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Figure 5

Mean of sensitivity of py throughout Cu

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Figure 6

Mean of sensitivity of pz throughout Cu

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Figure 7

Mean of sensitivity of p throughout Cu

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Figure 8

Sensitivity of px to the variations in the 1st leg

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Figure 9

Sensitivity of py to the variations in the 1st leg

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Figure 10

Sensitivity of p to the variations in the 1st leg

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Figure 11

Global sensitivity of p, px, py, and pz

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Figure 12

Sensitivity of px in the isotropic configuration

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Figure 13

Sensitivity of p in the isotropic configuration

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Figure 14

Q2 configuration, sensitivity of px

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Figure 15

Q2 configuration, sensitivity of p

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Figure 16

Variations in O−Ai chain

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Figure 17

Variations in Ai−Bi chain

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Figure 18

Variations in Bi−Bij−Cij chain

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Figure 19

Variations in Cij−Ci−P chain

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Figure 20

Variations in the ith parallelogram

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Figure 21

Sensitivity of the position of the end-effector along Q1Q2: (a) to dimensional variations and (b) to angular variations

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Figure 22

Sensitivity of the orientation of the end-effector along Q1Q2: (a) to dimensional variations and (b) to angular variations

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Figure 23

Maximum position (a) and orientation (b) errors of the end-effector along Q1Q2

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Figure 24

Repartition of the position error (a) and the orientation error (b) of the end-effector in Q1 configuration

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Figure 25

Repartition of the position error (a) and the orientation error (b) of the end-effector in the isotropic configuration

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Figure 26

Repartition of the position error (a) and the orientation error (b) of the end-effector in Q2 configuration

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