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Research Papers

Sensitivity Analysis of 3-RP R Planar Parallel Manipulators

[+] Author and Article Information
Stéphane Caro

Institut de Recherche en Communications et Cybernétique de Nantes, UMR CNRS No. 6597 1 rue de la Noë, 44321 Nantes, Francestephane.caro@irccyn.ec-nantes.fr

Nicolas Binaud

Institut de Recherche en Communications et Cybernétique de Nantes, UMR CNRS No. 6597 1 rue de la Noë, 44321 Nantes, Francenicolas.binaud@irccyn.ec-nantes.fr

Philippe Wenger

Institut de Recherche en Communications et Cybernétique de Nantes, UMR CNRS No. 6597 1 rue de la Noë, 44321 Nantes, Francephilippe.wenger@irccyn.ec-nantes.fr

J. Mech. Des 131(12), 121005 (Nov 10, 2009) (13 pages) doi:10.1115/1.4000216 History: Received January 30, 2009; Revised October 05, 2009; Published November 10, 2009; Online November 10, 2009

This paper deals with the sensitivity analysis of 3-RP R planar parallel manipulators (PPMs). First, the sensitivity coefficients of the pose of the manipulator moving platform to variations in the geometric parameters and in the actuated variables are expressed algebraically. Moreover, two aggregate sensitivity indices are determined, one related to the orientation of the manipulator moving platform and another one related to its position. Then, a methodology is proposed to compare 3-RP R PPMs with regard to their dexterity, workspace size and sensitivity. Finally, the sensitivity of a 3-RP R PPM is analyzed in detail and four 3-RP R PPMs are compared as illustrative examples.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

3-RP R manipulator

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Figure 2

The 3-RP R manipulator under study with ϕ=−π/8, p=[−0.3,−0.1]T, R1=0.6 m, and R2=0.25 m

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Figure 3

Singularity locus of the 3-RP R PPM within a region of the workspace delimited with x∊[−2,2], y∊[−2,2], and ϕ∊[−2,2]

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Figure 4

Section of the workspace of the 3-RP R PPM delimited with the Type-II singularities for a given orientation ϕ, i.e., ϕ=−π/8

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Figure 5

The percentage of Ws, in which (a) νϕqi<3 rad/m; (b) νϕqi<6 rad/m and qi={Ai,ρi,Ci}, i=1,2,3

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Figure 6

The percentage of Ws, in which (a) νpqi<1.5; (b) νpqi<3 and qi={Ai,ρi,Ci}, i=1,2,3

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Figure 7

νϕ and νp isocontours throughout Ws

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Figure 8

Distribution of νϕ and νp throughout Ws

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Figure 9

Distribution of the (a) orientation and (b) positioning errors of the MP for a given pose of the latter: ϕ=π/8 and p=[0.25,0.4]

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Figure 10

(a) |δϕ|mean and (b) ‖δp‖2mean isocontours throughout Ws

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Figure 11

The four 3-RP R manipulators under study with ϕ=0 and p=[1,1.5]T: (a) and (b) nondegenerate manipulators and (c) and (d) degenerate manipulators

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Figure 12

Maximal regular dextrous workspace of (a) M1, (b) M2, (c) M3, and (d) M4

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Figure 13

RDW radius of M1, M2, M3, and M4

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Figure 16

Distribution of νϕ and νp throughout the RDW of M1, M2, M3, and M4

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Figure 14

νϕ isocontours of (a) M1, (b) M2, (c) M3, and (d) M4

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Figure 15

νp isocontours of (a) M1, (b) M2, (c) M3, and (d) M4

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