Half-turns and line symmetric motions

Selig, J. M.; Husty, Manfred L.

doi:10.1016/j.mechmachtheory.2010.10.001

Cited by 32 publications

(26 citation statements)

References 14 publications

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“…The For solution E it was already shown by the author in [18] that the self-motion is a line-symmetric motion. This follows directly from the property e 0 = f 0 = 0 under consideration of the result given by Selig and Husty [23].…”

Section: Discussing Solutions A-fmentioning

confidence: 73%

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

Nawratil

2011

J. Geom.

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Due to previous publications of the author, it is already known that one-parametric self-motions of general planar Stewart Gough platforms can be classified into two so-called Darboux Mannheim (DM) types (I and II). Moreover, the author also proved the necessity of three conditions for obtaining a type II DM self-motion. Based on this result we determine in the article at hand, all general planar Stewart Gough platforms with a type II DM self-motion. This is an important step in the solution of the famous Borel Bricard problem.Mathematics Subject Classification. 53A17, 70B15.

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Section: Discussing Solutions A-fmentioning

confidence: 73%

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

Nawratil

2011

J. Geom.

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“…In [4] it was shown that this equation characterises line-symmetric motions, moreover, line-symmetric motions were shown to lie in the intersection of the Study quadric with a 5-plane.…”

Section: Line-symmetry and Translationsmentioning

confidence: 99%

Some Mobile Overconstrained Parallel Mechanisms

Selig

2017

Advances in Robot Kinematics 2016

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The Griffis-Duffy platform is an example of an overconstrained parallel mechanism. Although it has 6 SS legs joining its platform to its base it is still mobile. In this work similar structures are found but with different types of legs. The key to finding these structures is a pair of theorems concerning 3 degree-of-freedom mechanisms subjected to a translation or a half-turn. Although these results are not new concise statements and proofs are given. These constructions are then applied to parallel mechanisms consisting of 3 RPS legs and 3UPU legs. Some details of the rigid-body motions that the platform of these mechanisms can execute are found. This is facilitated by the observations that rigid displacements permitted by an RPS leg are the displacements which constrain a point to a fixed plane, while the displacements of a UPU leg constrain a line to be coplanar to a fixed line.

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“…According to [25], this is one possible characterization of line-symmetric motions. In general, the curve s is a regular conic section, but it can also happen that it consists of one or two straight lines, implying Schönflies self-motions.…”

Section: Generalized Dietmaier Self-motionsmentioning

confidence: 99%

“…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. [25]). In this context, it should finally be noted that most of the known hexapodal self-motions (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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Half-turns and line symmetric motions

Cited by 32 publications

References 14 publications

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

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

Some Mobile Overconstrained Parallel Mechanisms

On the Self-Mobility of Point-Symmetric Hexapods

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