Journal for Geometry and Graphics, Vol. 3, No. 2, pp. 183-191 (1999)

Some Moebius-Geometric Theorems connected to Euclidean Kinematics

Gunter Weiss, Karla Nestler, Gert Meinl

Institute for Geometry, Dresden University of Technology
Zellescher Weg 12-14, D-01062 Dresden, Germany

Abstract: To four positions of an object in the Euclidean plane there exists an infinite set of four-bar linkages interpolating these given positions. The set contains an interpolating slider-crank as a special case. The design of such a mechanism is based on geometric reasoning and the use of elementary geometric theorems. Usually such theorems and geometric mappings are proved by kinematic arguments. But they are also interesting for their own, independently from the kinematic point of view. There occur e.g. configurations of circles and lines related to Miquel's configuration in a (real) Moebius plane. Beginning with their kinematic aspects, some `elementary' geometric theorems are discussed and generalized.

Keywords: Kinematics in the Euclidean plane, four-bar linkages, isogonal relation with respect to a triangle, Wallace's theorem, Moebius-geometry

Classification (MSC2000): 53A17; 51M04; 51B10

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