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Research Papers

Planning Nonsingular Transitions Between Solutions of the Direct Kinematic Problem From the Joint Space

[+] Author and Article Information
Erik Macho1

Department of Mechanical Engineering, Faculty of Engineering in Bilbao,  University of the Basque Country, Bilbao 48013, Spainerik.macho@ehu.es

Victor Petuya

Department of Mechanical Engineering, Faculty of Engineering in Bilbao,  University of the Basque Country, Bilbao 48013, Spainvictor.petuya@ehu.es

Oscar Altuzarra

Department of Mechanical Engineering, Faculty of Engineering in Bilbao,  University of the Basque Country, Bilbao 48013, Spainoscar.altuzarra.@ehu.es

Alfonso Hernandez

Department of Mechanical Engineering, Faculty of Engineering in Bilbao,  University of the Basque Country, Bilbao 48013, Spaina.hernandez@ehu.es

1

Corresponding author.

J. Mechanisms Robotics 4(4), 041005 (Sep 17, 2012) (9 pages) doi:10.1115/1.4007306 History: Received April 20, 2011; Revised May 14, 2012; Published September 17, 2012; Online September 17, 2012

The aim of this paper is to describe a general and systematic methodology to make controllable transitions between different solutions of the direct kinematic problem (DKP) from the joint space. This work is focused on parallel manipulators and the goal is the usage of just the input variables domain. This way, such transitions can be made controlling all the inputs simultaneously at all times. To do so, it is necessary to analyze the locus of direct kinematics singularities, where different direct kinematic solutions coalesce. It is necessary to specify which portions of such a locus specifically affect each solution. This analysis requires obtaining the locus of triple coalescence singularities. Having done this, all the information can be processed in order to obtain several maps in the joint space. Finally, it will establish the strategy on how to use these maps to connect desired solutions, including the application to a representative example.

Copyright © 2012 by American Society of Mechanical Engineers
Topics: Manipulators , Motion
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References

Figures

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Figure 1

Crossing the singularity loci

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Figure 2

Joint space. Loci of cusps and singular solutions.

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Figure 3

Singularity loci associated with each solution in the joint space

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Figure 4

Solution with positive direct Jacobian in the region of two solutions

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Figure 5

Encircling the loci of cusps

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Figure 6

Joint space solution maps

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Figure 7

3-RP R planar parallel manipulator

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Figure 8

Joint space. Solutions and singularities.

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Figure 9

Joint space solution maps

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Figure 10

Nonsingular transition from solution p1 to solution p2

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Figure 11

Joint space internal views

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Figure 12

Constant input joint space and solutions

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Figure 13

Solutions separated by Jacobian sign

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Figure 14

Joint space solution maps for positive Jacobian solutions

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Figure 15

Joint space solution maps for negative Jacobian solutions

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Figure 16

Nonsingular transition from solution n1 to solution n2

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