A Redundant Spatial Stewart-Gough Platform with a Maximal Forward Kinematics Solution Set

Husty, Manfred L.; Mielczarek, Sonja; Hiller, Manfred

doi:10.1007/978-94-017-0657-5_16

Cited by 20 publications

(27 citation statements)

References 2 publications

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“…The cubic in the base coincides with the one appearing in [48], whereas the cubic in the platform is not given explicitly there. In [48], the authors propose to add additional legs to obtain redundant manipulators. Instead, here legs are substituted by other legs satisfying the one-to-one correspondence between the base and platform cubics defined by (7.11).…”

Section: Singularity-invariant Leg Rearrangement Rulesmentioning

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: Singularity-invariant Leg Rearrangement Rulesmentioning

confidence: 99%

“…Until the moment, no other similar concept to singularity-invariant leg rearrangements has been found in the literature, except for [48,74], where the authors solve the problem of obtaining redundant legs to a manipulator without modifying its kinematics.…”

Section: Summary Of Open Problems and Related Workmentioning

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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“…which yields R Ω and R Π , respectively. Then R Π splits up and can only vanish w.c. for P [5] = 0. It can easily be seen that the coefficients of the linear homogeneous polynomial P = 0 in the unknowns e 1 , e 2 cannot vanish w.c.. …”

Section: Part [G]mentioning

confidence: 99%

“…. , M 6 is not architecturally singular, then at least a one-parametric set of legs exists, which can be attached to the given manipulator without changing the forward kinematics [5,9] and the singularity set [2] of the manipulator. Moreover, it was shown that in general the base anchor points M i as well as the corresponding platform anchor points m i are located on planar cubic curves C and c, respectively.…”

Section: Types Of Self-motionsmentioning

confidence: 99%

Basic Result on Type II DM Self-Motions of Planar Stewart Gough Platforms

Nawratil

2011

Mechanisms, Transmissions and Applications

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“…The method applied in the proof of [28] can also be used here to prove the continuous flexibility of Chasles' framework for any n directly, i.e. not via infinitesimal flexibility.…”

Section: (B) Chasles' Body-bar Frameworkmentioning

confidence: 99%

On the flexibility and symmetry of overconstrained mechanisms

Stachel

2014

Phil. Trans. R. Soc. A.

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In kinematics, a framework is called overconstrained if its continuous flexibility is caused by particular dimensions; in the generic case, a framework of this type is rigid. Famous examples of overconstrained structures are the Bricard octahedra, the Bennett isogram, the Grünbaum framework, Bottema's 16-bar mechanism, Chasles’ body–bar framework, Burmester's focal mechanism or flexible quad meshes. The aim of this paper is to present some examples in detail and to focus on their symmetry properties. It turns out that only for a few is a global symmetry a necessary condition for flexibility. Sometimes, there is a hidden symmetry, and in some cases, for example, at the flexible type-3 octahedra or at discrete Voss surfaces, there is only a local symmetry. However, there remain overconstrained frameworks where the underlying algebraic conditions for flexibility have no relation to symmetry at all.

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A Redundant Spatial Stewart-Gough Platform with a Maximal Forward Kinematics Solution Set

Cited by 20 publications

References 2 publications

Singularity-Invariant Leg Rearrangements in Stewart–Gough Platforms

Singularity-Invariant Leg Rearrangements in Stewart–Gough Platforms

Basic Result on Type II DM Self-Motions of Planar Stewart Gough Platforms

On the flexibility and symmetry of overconstrained mechanisms

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