Hellmuth Stachel

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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)
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.
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)
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)