This paper analyzes the multiplicity of the solutions to forward kinematics of two classes of analytic robots: 2RPR-PR robots with a passive leg and 3-RPR robots with nonsimilar flat platform and base. Since their characteristic polynomials cannot have more than two valid roots, one may think that triple solutions, and hence nonsingular transitions between different assembly modes, are impossible for them. However, the authors show that the forward kinematic problems of these robots always admit quadruple solutions and obtain analytically the loci of points of the joint space where these solutions occur. Then, it is shown that performing trajectories in the joint space that enclose these points can produce nonsingular transitions, demonstrating that it is possible to design simple analytic parallel robots with two and three degrees-of-freedom (DOF) and the ability to execute these transitions.
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December 2015
Research-Article
Performing Nonsingular Transitions Between Assembly Modes in Analytic Parallel Manipulators by Enclosing Quadruple Solutions
Adrián Peidró,
Adrián Peidró
Systems Engineering
and Automation Department,
Miguel Hernández University,
Elche 03202, Spain
e-mail: apeidro@umh.es
and Automation Department,
Miguel Hernández University,
Elche 03202, Spain
e-mail: apeidro@umh.es
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José María Marín,
José María Marín
Department of Mechanical Engineering
and Energy,
Miguel Hernández University,
Elche 03202, Spain
e-mail: jmarin@umh.es
and Energy,
Miguel Hernández University,
Elche 03202, Spain
e-mail: jmarin@umh.es
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Arturo Gil,
Arturo Gil
Systems Engineering
and Automation Department,
Miguel Hernández University,
Elche 03202, Spain
e-mail: arturo.gil@umh.es
and Automation Department,
Miguel Hernández University,
Elche 03202, Spain
e-mail: arturo.gil@umh.es
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Óscar Reinoso
Óscar Reinoso
Systems Engineering
and Automation Department,
Miguel Hernández University,
Elche 03202, Spain
e-mail: o.reinoso@umh.es
and Automation Department,
Miguel Hernández University,
Elche 03202, Spain
e-mail: o.reinoso@umh.es
Search for other works by this author on:
Adrián Peidró
Systems Engineering
and Automation Department,
Miguel Hernández University,
Elche 03202, Spain
e-mail: apeidro@umh.es
and Automation Department,
Miguel Hernández University,
Elche 03202, Spain
e-mail: apeidro@umh.es
José María Marín
Department of Mechanical Engineering
and Energy,
Miguel Hernández University,
Elche 03202, Spain
e-mail: jmarin@umh.es
and Energy,
Miguel Hernández University,
Elche 03202, Spain
e-mail: jmarin@umh.es
Arturo Gil
Systems Engineering
and Automation Department,
Miguel Hernández University,
Elche 03202, Spain
e-mail: arturo.gil@umh.es
and Automation Department,
Miguel Hernández University,
Elche 03202, Spain
e-mail: arturo.gil@umh.es
Óscar Reinoso
Systems Engineering
and Automation Department,
Miguel Hernández University,
Elche 03202, Spain
e-mail: o.reinoso@umh.es
and Automation Department,
Miguel Hernández University,
Elche 03202, Spain
e-mail: o.reinoso@umh.es
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 4, 2015; final manuscript received August 25, 2015; published online October 15, 2015. Assoc. Editor: Charles Kim.
J. Mech. Des. Dec 2015, 137(12): 122302 (11 pages)
Published Online: October 15, 2015
Article history
Received:
February 4, 2015
Revised:
August 25, 2015
Citation
Peidró, A., María Marín, J., Gil, A., and Reinoso, Ó. (October 15, 2015). "Performing Nonsingular Transitions Between Assembly Modes in Analytic Parallel Manipulators by Enclosing Quadruple Solutions." ASME. J. Mech. Des. December 2015; 137(12): 122302. https://doi.org/10.1115/1.4031653
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