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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)
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)
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 (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)
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)
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)
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)
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.
The problems around rigidity and exibility of geometrical structures have a long history in mathematics. Recently obtained results like the proof of the \Bellows Conjecture" have brought them back into the center of mathematical interest. However, innnitesimal exibility | usually of order one | has also been studied in kinematics for a long time. In… (More)