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)
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)
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)
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.
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)
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)
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)
The geometry of multiple images has been a standard topic in Descriptive Geometry and Photogrammetry (Remote Sensing) for more than 100 years. During the last twenty years great progress has been made within the field of Computer Vision, a topic with the main goal to endow a computer with a sense of vision. The previously graphical or mechanical methods of… (More)