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A Kokotsakis mesh is a polyhedral structure consisting of an n-sided central polygon P 0 surrounded by a belt of polygons in the following way: Each side a i of P 0 is shared by an adjacent polygon P i , and the relative motion between cyclically consecutive neighbor polygons is a spherical coupler motion. Hence, each vertex of P 0 is the meeting point of… (More)

- Hellmuth Stachel
- 2000

In this paper the dependencies between the instantaneous invariants of a spatial motion and the local invariants of the axodes are studied in a way that includes all types of ruled surfaces. New proofs for mostly wellknown formulas are given which should meet the main target of this note, namely to demonstrate anew the elegance and effectiveness that E.… (More)

This is a geometric approach to spatial involute gearing which has recently been developed by Jack Phillips (2003). After recalling Phillips' fundamental theorems and other properties, some geometric questions around this interesting type of gearing are discussed. 1 PRELIMINARIES In the series of International Conferences on Geometry and Graphics there had… (More)

According to the planar version of Ivory's Theorem the family of confocal conics has the property that in each quadrangle formed by two pairs of conics the diagonals are of equal length. It turned out that this theorem is closely related to self-adjoint affine transformations. This point of view is capable of generalization to hyperbolic and other spaces.

- Hellmuth Stachel
- 1999

More than hundred years ago R. Bricard determined all continuously ex-ible octahedra. On the other hand, also the geometric characterization of rst-order exible octahedra has been well known for a long time. The objective of this paper is to analyze the cases between, i.e., octahedra which are innnitesimally exible of order n > 1 but not continuously… (More)

- Hellmuth Stachel
- 2007

It is shown that the examples presented 1998 by A. Walz are special cases of a more general class of exible cross-polytopes in E 4. The proof is given by means of 4D descriptive geometry. Further, a parameterization of the one-parameter self-motions of Walz's polytopes is presented.

- Hellmuth STACHEL
- 2009

Miura-ori is a Japanese folding technique named after Prof. Koryo Miura, The University of Tokyo. It is used for solar panels because it can be unfolded into its rectangular shape by pulling on one corner only. On the other hand it is used as kernel to stiffen sandwich structures. In this paper some insight will be given into the geometric structure of this… (More)

- Hellmuth Stachel
- 1999

Innnitesimally exible frameworks are well known in kinematics, in particular recently as singular postures in robotics. The objective of this paper is to analyze a bipartite planar framework in view of higher-order innnitesimal exibility. The characterization of rst-order exibility of such frameworks has been well known for a long time. Now explicit… (More)

- Hellmuth Stachel, Georg Nawratil, Antonios Kokotsakis
- 2010