Planar Stewart Gough platforms with a type II DM self-motion

Nawratil, Georg

doi:10.1007/s00022-012-0106-6

Cited by 7 publications

(8 citation statements)

References 29 publications

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“…In recent publications [43,44,45,46] of the author, it was shown, that based on the geometrickinematic approach of redundancy, amazing new results can be achieved in the field of self-motions of SG platforms. In this section we give a short overview of these results.…”

Section: Recent Results On Sg Platforms With Self-motionsmentioning

confidence: 99%

“…3). Based on these necessary conditions, the author [46] was able to determine all planar SG platforms (fulfilling Assumption 1 and 2) with a type II DM self-motion. These manipulators are either generalizations of type 1 Bricard octahedra (12-dimensional solution set) or special polygon platforms (cf.…”

Section: Assumption 2 For Guaranteeing a General Case We Assume Thamentioning

confidence: 99%

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Review and Recent Results on Stewart Gough Platforms with Self-Motions

Nawratil

2012

AMM

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Abstract. In Section 1, we give a review on Stewart Gough (SG) platforms with self-motions and the related Borel Bricard problem. Moreover, in Section 2, we report about recent results achieved by the author on this topic (SG platforms with type II DM self-motions). In context of these results, we also present two new theorems in Section 3, which open the way for addressed future work. In Section 4, we give some final remarks on planar SG platforms with type I DM self-motions and formulate a central conjecture.

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Section: Recent Results On Sg Platforms With Self-motionsmentioning

confidence: 99%

Section: Assumption 2 For Guaranteeing a General Case We Assume Thamentioning

confidence: 99%

Review and Recent Results on Stewart Gough Platforms with Self-Motions

Nawratil

2012

AMM

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“…A generalization of the self-motions of Type 1 Bricard octahedra was obtained by the author in [29]. These planar hexapods with so-called Type 2 DM (=Darboux-Mannheim) self-motions do not possess the global symmetry property any longer, but their self-motions are still line-symmetric ones (cf.…”

Section: Hexapodal Self-motions Viewed Under the Aspect Of Symmetrymentioning

confidence: 99%

On the Self-Mobility of Point-Symmetric Hexapods

Nawratil

2014

Symmetry

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In this article, we study necessary and sufficient conditions for the self-mobility of point symmetric hexapods (PSHs). Specifically, we investigate orthogonal PSHs and equiform PSHs. For the latter ones, we can show that they can have non-translational self-motions only if they are architecturally singular or congruent. In the case of congruency, we are even able to classify all types of existing self-motions. Finally, we determine a new set of PSHs, which have so-called generalized Dietmaier self-motions. We close the paper with some comments on the self-mobility of hexapods with global/local symmetries.

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“…One can easily produce examples of mobile infinity-pods by taking congruent base and platform anchor points, with legs of the same length, or by having all base or platform points aligned. There are also other examples of mobile infinity-pods, as the one discovered by Husty and Karger in [KH98,Kar08a], or those described in [Naw11,Naw13,HMH02].…”

Section: Introductionmentioning

confidence: 96%

A new line-symmetric mobile infinity-pod

Gallet¹,

Schicho²

2021

Preprint

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We construct parallel manipulators with one degree of freedom and admitting infinitely many legs lying on a curve of degree ten and genus six. Our technique relies upon a duality between the spaces parametrizing all the possible legs and all the possible configurations of a manipulator. Before describing our construction, we show how this duality helps explaining several known phenomena regarding mobility of parallel manipulators.

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Planar Stewart Gough platforms with a type II DM self-motion

Cited by 7 publications

References 29 publications

Review and Recent Results on Stewart Gough Platforms with Self-Motions

Review and Recent Results on Stewart Gough Platforms with Self-Motions

On the Self-Mobility of Point-Symmetric Hexapods

A new line-symmetric mobile infinity-pod

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