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- Hellmuth Stachel
- Computer Aided Geometric Design
- 2010

A Kokotsakis mesh is a polyhedral structure consisting of an n-sided central polygon P0 surrounded by a belt of polygons in the following way: Each side ai of P0 is shared by an adjacent polygon Pi, and the relative motion between cyclically consecutive neighbor polygons is a spherical coupler motion. Hence, each vertex of P0 is the meeting point of four… (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.

- Wilhelm Fuhs, Hellmuth Stachel
- Computers & Graphics
- 1988

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.

This is a geometric approach to spatial involute gearing which has recently been developed by Jack Phillips [2]. New proofs of Phillips’ fundamental theorems are given. And it is pointed out that also a permanent straight line contact is possible for conjugate helical involutes. In addition, the gearing is illustrated in various ways.

- Hellmuth Stachel
- 2011

A polygonal mesh is a connected subset of a polyhedral surface. We address the problem whether the intrinsic metric of a mesh, i.e., its development, can determine the exterior metric. If this is the case then the mesh is rigid. Among the non-rigid cases even flexible versions are possible. We concentrate on quadrangular meshes and in particular on a mesh… (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)

- Gunther Windisch, Boris Odehnal, Reinhold Reimann, Friedrich Anderhuber, Hellmuth Stachel
- Journal of orthopaedic research : official…
- 2007

The contact areas between the articular surfaces of the talus and tibia are essential for understanding the mobility of the ankle joint. The purpose of our study was to reveal the contact area among the superior articular surface of the trochlea tali (target surface T) and the inferior articular surface of the tibia (query surface Q) under… (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
- 2007

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)