Kinematics of a Hybrid Series-Parallel Manipulation System

Waldron, Kenneth J.; Raghavan, Madhusudan; Roth, Bernard

doi:10.1115/1.3153039

Cited by 172 publications

(53 citation statements)

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“…4.16(a), that avoids the double-ball-joints in the base, is kinematically equivalent to the octahedral manipulator. This particular arrangement of joints is also known as the triple arm mechanism [101]. …”

Section: Application To the Implementation Of An Octahedral Manipulatormentioning

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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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: Application To the Implementation Of An Octahedral Manipulatormentioning

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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“…Actually, the different real roots of this equation for s 1,5 correspond to the different ways in which the octahedron can be assembled. Note that two other equivalent conditions could be derived for s 2,6 and s 3,4 by decomposing the octahedron into different sets of bananas. Octahedral manipulator and associated notation.…”

Section: Octahedronmentioning

confidence: 99%

“…An octahedron can be decomposed into two bananas. In these two bananas, the squared edge lengths s 1,6 and s 3,4 are unknown, but for each banana s 1,6 and be expressed as a function of s 3,4 . Equating both solutions for s 3,4 a closure condition for the original octahedron in terms of s 1,6 is thus obtained.…”

Section: Octahedronmentioning

confidence: 99%

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The octahedral manipulator revisited

Rojas

Borràs

Thomas

2012

2012 IEEE International Conference on Robotics and Automation

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Abstract-In most practical implementations of the GoughStewart platform, the octahedral form is either taken as it stands or is approximated. The kinematics of this particular instance of the Gough-Stewart platform, commonly known as the octahedral manipulator, has been thoughtfully studied. It is well-known, for example, that its forward kinematics can be solved by computing the roots of an octic polynomial and its singularities have a simple geometric interpretation in terms of the intersection of four planes in a single point. In this paper, using a distance-based formulation, it is shown how these properties can be derived without relying neither on variable eliminations nor trigonometric substitutions. Moreover, thanks to this formulation, a family of platforms kinematically equivalent to the octahedral manipulator is obtained. Herein, two Gough-Stewart parallel platforms are said to be kinematically equivalent if there is a one-to-one correspondence between their squared leg lengths for the same configuration of their moving platforms with respect to their bases. If this condition is satisfied, it can be shown that both platforms have the same assembly modes and their singularities, in the configuration space of the moving platform, are located in the same place.

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“…Lee and Shah (1988) addressed various possible applications of the mechanism. Waldron et al (1989) studied an ARTISAN manipulator. Clavel (1988) proposed the DELTA.…”

Section: Introductionmentioning

confidence: 99%