Mobile icosapods

Gallet, Matteo; Nawratil, Georg; Schicho, Josef; Selig, J. M.

doi:10.1016/j.aam.2016.12.002

Cited by 6 publications

(16 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, Theorem 1 also holds for point-symmetric motions, if "plane-reflection" is substituted by "point-reflection". A similar result holds for line-symmetric motions; one only has to replace "plane-reflection" by "line-reflection" and "indirectly congruent" by "directly congruent" (see e.g., [9]).…”

mentioning

confidence: 68%

“…We want to follow the second approach by assuming that the self-motions are symmetric rollings. Therefore, this paper closes a gap as line-symmetric self-motions and point-symmetric (Point-symmetric motions are obtained by reflecting the fixed system in a 1-parametric continuous set of points and according to [7] (Section 8), these motions are pure translations) self-motions are already well-studied [9,28]. In addition, this motion-type seems to be a good candidate for self-motions, due to the following property implied by the symmetry of the motion: Theorem 1.…”

mentioning

confidence: 95%

“…Assumptions on the self-motion; e.g., (a) line-symmetric self-motion [9], (b) type II Darboux-Mannheim self-motion [26], (c) Schoenflies self-motion [27], (d) translational self-motion [28], (e) self-motion of maximal degree [29], or more generally characterizations like linear relations between direction cosines [30][31][32][33].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Hexapods with Plane-Symmetric Self-Motions

Nawratil

2018

Robotics

View full text Add to dashboard Cite

A hexapod is a parallel manipulator where the platform is linked with the base by six legs, which are anchored via spherical joints. In general, such a mechanical device is rigid for fixed leg lengths, but, under particular conditions, it can perform a so-called self-motion. In this paper, we determine all hexapods possessing self-motions of a special type. The motions under consideration are so-called plane-symmetric ones, which are the straight forward spatial counterpart of planar/spherical symmetric rollings. The full classification of hexapods with plane-symmetric self-motions is achieved by formulating the problem in terms of algebraic geometry by means of Study parameters. It turns out that besides the planar/spherical symmetric rollings with circular paths and two trivial cases (butterfly self-motion and two-dimensional spherical self-motion), only one further solution exists, which is the so-called Duporcq hexapod. This manipulator, which is studied in detail in the last part of the paper, may be of interest for the design of deployable structures due to its kinematotropic behavior and total flat branching singularities.

show abstract

mentioning

confidence: 68%

mentioning

confidence: 95%

See 1 more Smart Citation

Hexapods with Plane-Symmetric Self-Motions

Nawratil

2018

Robotics

View full text Add to dashboard Cite

show abstract

“…A line-symmetric mobile pod is a parallel manipulator for which all its configurations are given by involutions, namely, half-turns around lines, possibly composed with a fixed isometry. For more information about line-symmetric motions, one can see [Kra37,GNSS17,Naw18].…”

Section: Introductionmentioning

confidence: 99%

A new line-symmetric mobile infinity-pod

Gallet¹,

Schicho²

2021

Preprint

View full text Add to dashboard Cite

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.

show abstract

“…Nonetheless, this shows that the location of the points is not in general position with respect to the Segre embedding. Since the Geiss--Schreyer family is a special case of Borel's Fb1 family of icosapods [12], as shown in [18], we note that every 6 \times 6 submatrix generically has rank 6 on Fb1.…”

mentioning

confidence: 99%

Exceptional Stewart--Gough Platforms, Segre Embeddings, and the Special Euclidean Group

Hauenstein¹,

Sherman²,

Wampler³

2018

SIAM J. Appl. Algebra Geometry

View full text Add to dashboard Cite

Abstract. Stewart--Gough platforms are mechanisms which consist of two rigid objects, a base and a platform, connected by six legs via spherical joints. For fixed leg lengths, a generic Stewart--Gough platform is rigid with 40 assembly configurations (over the complex numbers), while exceptional Stewart--Gough platforms have infinitely many assembly configurations and thus have self-motion. We define a family of exceptional Stewart--Gough platforms called Segre-dependent Stewart--Gough platforms which arise from a linear dependency of point-pairs under the Segre embedding and compute an irreducible decomposition of this family. We also consider Stewart--Gough platforms which move with two degrees of freedom. Since the Segre embedding arises from a representation of the special Euclidean group in three dimensions which has degree 40, we consider the special Euclidean group in other dimensions and compute spatial Stewart--Gough platforms that move in 4-dimensional space.

show abstract

Mobile icosapods

Cited by 6 publications

References 30 publications

Hexapods with Plane-Symmetric Self-Motions

Hexapods with Plane-Symmetric Self-Motions

A new line-symmetric mobile infinity-pod

Exceptional Stewart--Gough Platforms, Segre Embeddings, and the Special Euclidean Group

Contact Info

Product

Resources

About