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Research Papers

Computing the Configuration Space for Tracing Paths Between Assembly Modes

[+] Author and Article Information
Mónica Urízar1

Department of Mechanical Engineering, University of the Basque Country, Alameda de Urquijo s/n, 48013 Bilbao, Spainmonica.urizar@ehu.es

Víctor Petuya

Department of Mechanical Engineering, University of the Basque Country, Alameda de Urquijo s/n, 48013 Bilbao, Spainvictor.petuya@ehu.es

Oscar Altuzarra

Department of Mechanical Engineering, University of the Basque Country, Alameda de Urquijo s/n, 48013 Bilbao, Spainoscar.altuzarra@ehu.es

Erik Macho

Department of Mechanical Engineering, University of the Basque Country, Alameda de Urquijo s/n, 48013 Bilbao, Spainerik.macho@ehu.es

Alfonso Hernández

Department of Mechanical Engineering, University of the Basque Country, Alameda de Urquijo s/n, 48013 Bilbao, Spaina.hernandez@ehu.es

1

Corresponding author.

J. Mechanisms Robotics 2(3), 031002 (Jun 21, 2010) (11 pages) doi:10.1115/1.4001734 History: Received April 21, 2009; Revised February 08, 2010; Published June 21, 2010; Online June 21, 2010

In this paper, the authors present a general methodology for computing the configuration space for three-degree-of-freedom parallel manipulators so that the relation between input and output variables can be easily assessed. Making use of an entity called the reduced configuration space, all solutions of the direct kinematic problem in parallel manipulators are solved. The graphical representation of this entity enables the location of the direct kinematic solutions to be analyzed so as to make use of a wider operational workspace by means of path planning. A descriptive study is presented regarding the diverse possible paths that allow changing between direct kinematic solutions, thus, enlarging the manipulator’s range of motion.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Positional discretization algorithm for the planar kinematic chains RP̱R, RṞR, and P̱RR

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Figure 2

(a) Planar parallel manipulator RP̱R-2PṞR and (b) software representation

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Figure 3

Workspace with constant input α3=170 deg and singular curves

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Figure 4

Two possible configurations for the pose p

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Figure 5

WM and DKP solutions in the joint space

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Figure 6

Reduced configuration space representing output variable φ

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Figure 7

Reduced configuration space representing output variable x

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Figure 8

Interpolation process for obtaining the DKP solutions

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Figure 9

Four DKP solutions for inputs L1=4, α2=21 deg, and α3=170 deg

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Figure 10

Two DKP solutions for inputs L1=3, α2=45 deg, and α3=170 deg

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Figure 11

Reduced configuration space and joint space associated with different α3 values

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Figure 12

DKP solutions for cases: (a) α3=170 deg and (b) α3=160 deg

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Figure 13

Paths encircling cusp points for inputs L1=2.8, α2=0 deg, and α3=160 deg

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Figure 14

Nonsingular solution changing encircling cusp point c1

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Figure 15

(a) Planar parallel manipulator ṞRR-2P̱RR with triangular platform and (b) software representation

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Figure 16

(a) Reduced configuration space for α1=24 deg and (b) joint space for α1=24 deg

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Figure 17

Transition between solutions 2 and 4 encircling a double point

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Figure 18

(a) Planar parallel manipulator ṞRR-2P̱RR and (b) software representation

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Figure 19

(a) Reduced configuration space for constant α1=70 deg and (b) four DKP solutions

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Figure 20

Evolution of disjoint surfaces to a linking surface varying α1

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Figure 21

Reduced configuration space for constant α1=60 deg

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Figure 22

Transition between solutions p0 and p7 along the linking surface

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