The Stewart Platform of General Geometry Has 40 Configurations

Raghavan, Madhusudan

doi:10.1115/1.2919188

Cited by 290 publications

(129 citation statements)

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“…Determining the pose of the manipulator platform from the linear actuators' lengths (also known as direct kinematics problem) generally leads to a system of algebraic equations that has at most 40 different solutions [1][2][3][4][5][6][7][8]. This number of solutions can be further reduced by introducing additional constraints, for example, combinatorial or planarity constraints [9].…”

Section: Introductionmentioning

confidence: 99%

On the Direct Kinematics Problem of Parallel Mechanisms

Seibel

Schulz

Schlattmann

2018

Journal of Robotics

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The direct kinematics problem of parallel mechanisms, that is, determining the pose of the manipulator platform from the linear actuators' lengths, is, in general, uniquely not solvable. For this reason, instead of measuring the lengths of the linear actuators, we propose measuring their orientations and, in most cases, also the orientation of the manipulator platform. This allows the design of a low-cost sensor system for parallel mechanisms that completely renounces length measurements and provides a unique solution of their direct kinematics.

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Section: Introductionmentioning

confidence: 99%

On the Direct Kinematics Problem of Parallel Mechanisms

Seibel

Schulz

Schlattmann

2018

Journal of Robotics

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“…For the general case, it was proved that the maximum number of assembly modes was 40 [61,82,86] . In fact, a 40th degree polynomial allowing to calculate (numerically) all possible assembly modes was found by Husty in 1994 [47].…”

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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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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“…This method has been responsible for the first solutions of many long-standing problems in Kinematics. For example, using them, Tsai and Morgan first showed that the inverse kinematics of the general 6R manipulator has sixteen solutions [22], Raghavan showed that the direct kinematics of the general Stewart-Gough platform can have forty solutions [23], and Wampler et al solved nine-point path synthesis problems for four-bar linkages [24].…”

Section: Introductionmentioning

confidence: 99%

Multi-loop Position Analysis via Iterated Linear Programming

Porta

Ros²,

Thomas³

2006

Robotics: Science and Systems II

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Abstract-This paper presents a numerical method able to isolate all configurations that an arbitrary loop linkage can adopt, within given ranges for its degrees of freedom. The procedure is general, in the sense that it can be applied to single or multiple intermingled loops of arbitrary topology. It is also complete, meaning that all possible solutions get accurately bounded, irrespectively of whether the analyzed linkage is rigid or mobile. The problem is tackled by formulating a system of linear, parabolic, and hyperbolic equations, which is here solved by a new strategy exploiting its structure. The method is conceptually simple, geometric in nature, and easy to implement, yet it provides solutions at the desired accuracy in short computation times.

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The Stewart Platform of General Geometry Has 40 Configurations

Cited by 290 publications

References 0 publications

On the Direct Kinematics Problem of Parallel Mechanisms

On the Direct Kinematics Problem of Parallel Mechanisms

Singularity-Invariant Leg Rearrangements in Stewart–Gough Platforms

Multi-loop Position Analysis via Iterated Linear Programming

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