Singularity analysis of closed-loop kinematic chains

Gosselin, Clément; Ángeles, Jorge

doi:10.1109/70.56660

Cited by 1,546 publications

(926 citation statements)

References 22 publications

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“…It was shown in [38] that the Stewart-Gough platforms have very simple type I singularities, as matrix S is singular only when any of the leg lengths is zero. This, in practice, can never happen due to joint limits.…”

Section: Kinematics and Singularities Of Stewart-gough Platformsmentioning

confidence: 99%

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Singularity-Invariant Leg Rearrangements in Stewart–Gough Platforms

Borràs

Thomas

Torras

2010

Advances in Robot Kinematics: Motion in Man and Machine

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A la meva família, pel seu recolzament incondicional. AgraïmentsM'agradaria expressar la meva sincera gratitud al professor Federico Thomas.La seva inestimable guia al llarg d'aquests 4 anys m'ha permès no només realitzar aquesta tesi, sinó aprendre queés la recerca i a estimar la professió a través del seu entusiasme en els projectes però també de la seva mirada crítica, sempre constructiva.També voldria agrair a la professora Carme Torras el temps que m'ha dedicat, al llarg de tots els treballs que hem fet junts, pels seus punts de vista sovint diferents que m'han donat més perspectiva i per deixar-me aprendre de la seva professionalitat i versatilitat.La Maria Alberich també mereix el meu agraïment, per haver-me presentat al Federico, i mostrar-me el camí cap a l'Institut i el món de la investigació, així com també pels seus consells al llarg d'aquest temps, des de la carrera fins avui. Finalment, també vull agrair a tots els companys de l'Institut de Robòtica i Informàtica Industrial, pel bon ambient, els bons moments, les opinions compartides i el recolzament moral i professional. I a la meva família i al Joan, per estar sempre al meu costat. AbstractThe Stewart-Gough platform was first introduced by E. Gough in 1954 and, since then, it has been used for many applications thanks to its great stiffness, accuracy and robustness in comparison with serial manipulators. It has triggered the research on parallel manipulators and continues to be the center of many researches because, despite its simple geometry, its analysis translates into challenging mathematical problems. One of the most challenging ones is the geometric interpretation of its singularities, that is, those positions where the platform loses stiffness. A complete geometric characterization of these unstable poses is still an open problem.The present thesis provides new insight into this problem from a completely new approach: finding singularity-invariant leg rearrangements.Finding all the transformations that leave the solution of a problem invariant does not solve it, but it provides a lot of information that contribute to its resolution. In the Stewart-Gough platform context, this indirect approach consists in the characterization of all the leg rearrangements that leave the platform singularity locus invariant. Such singularity-invariant leg rearrangements are shown to be a powerful tool to obtain kinematically equivalent manipulators, to help to visualize at a glance the complexity of its kinematics and to provide a common and original framework for the study of both pose-dependent singularities and architectural singularities of Stewart-Gough platforms.The thesis analyzes all the rigid components that a Stewart-Gough platform can contain on a case-by-case basis. Then, it is shown how some of the most simple components admit any leg rearrangement that preserves the lines and planes that their attachments define. On the contrary, other more complex components only admit rearrangements that preserve some extra geometric constrains. This appare...

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Section: Kinematics and Singularities Of Stewart-gough Platformsmentioning

confidence: 99%

“…The most accepted classification of Stewart-Gough platform singularities was introduced in 1990 by Gosselin and Angeles [38] using this formulation and consists in three categories:…”

Section: Kinematics and Singularities Of Stewart-gough Platformsmentioning

confidence: 99%

Singularity-Invariant Leg Rearrangements in Stewart–Gough Platforms

Borràs

Thomas

Torras

2010

Advances in Robot Kinematics: Motion in Man and Machine

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“…The definition of singular configurations adopted here corresponds to the definition of (Gosselin and Angeles 1990). For serial singular configurations the analysis is not adequate if the mechanism is near to self-locking.…”

Section: Known Limitationsmentioning

confidence: 99%

Analytical method for the kinetostatic analysis of the second-class RRR Assur group allowing for friction in the kinematic pairs

Durango¹,

Calle²,

Ruiz³

2010

J. Braz. Soc. Mech. Sci. & Eng.

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“…It is clear that the objective function is established as the sum of the square of the Cartesian position error between the desired workspace vertex and the tip of the end-effector, plus the square of the angular position error between the desired orientation and the end-effector orientation. Hence, the objective function can be described in (2). The vertex positions of the desired dexterous workspace are chosen as…”

Section: Objective Functionmentioning

confidence: 99%

“…The dimensional synthesis and workspace are two main characteristics which define a mechanism. They are the most studied issues in the field [2] [3]. The dimensional synthesis of a mechanism can be developed with graphical, analytical and numerical methods [4], [5].…”

Section: Introductionmentioning

confidence: 99%

Optimum Design of Parallelogram Five-bar Manipulator for Dexterous Workspace by using ELEMAEF in Differential Evolution

Villarreal-Cervantes¹,

Cruz-Mucio²,

Portilla-Flores³

2014

Appl. Math. Inf. Sci.

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Abstract:The kinematic design of mechanism is an important stage in the design methodology. A dexterous workspace for a manipulator is an outstanding characteristic that must be considered in it. Hence, a mono-objective constraint optimization problem (MOCOP) for the kinematic design of a manipulator with three revolute joints (3R robot), that fulfils a defined dexterous workspace, is formulated. The MOCOP is solved by proposing a mechanism in the differential evolution (DE) algorithm called exhaustive local exploitation mechanism with adaptive scale factor (ELEMAEF). This mechanism exhaustively exploits a local region in the search space with the information of the base and the difference vectors of good trial vector, in an attempt to generate better individuals in the same direction. In addition, the ELEMAEF guides the evolution of the population toward a better zone without sacrificing the search capabilities of the DE algorithm. A comparison of the DE algorithm with and without the ELEMAEF for this particular design problem is presented. The use of the ELEMAEF gives a superior performance in the DE algorithm.

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Singularity analysis of closed-loop kinematic chains

Cited by 1,546 publications

References 22 publications

Singularity-Invariant Leg Rearrangements in Stewart–Gough Platforms

Singularity-Invariant Leg Rearrangements in Stewart–Gough Platforms

Analytical method for the kinetostatic analysis of the second-class RRR Assur group allowing for friction in the kinematic pairs

Optimum Design of Parallelogram Five-bar Manipulator for Dexterous Workspace by using ELEMAEF in Differential Evolution

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