Differential Geometry and Geometric Structures
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Geometry of Mechanisms

We are interested in flexible and in infinitesimally flexible structures - in theory as well as in applications, like gearing or the design of mechanisms for real world problems.



Platform

Figure 1: Non-planar manipulator with cylindrical singularity surface.

Platform

Figure 2: Planar manipulator (type II) with cylindrical singularity surface.

G. Nawratil: Results on Planar Parallel Manipulators with Cylindrical Singularity Surface. Advances in Robot Kinematics - Analysis and Design (J. Lenarcic, P. Wenger eds.), pages 321-330, Springer, 2008, ISBN 978-1-4020-8599-4.


G. Nawratil: Main Theorem on Planar Parallel Manipulators with Cylindrical Singularity Surface. In Proc. of 33rd South German Colloquium on Differential Geometry, TU Vienna, to appear.


G. Nawratil: All Planar Parallel Manipulators with Cylindrical Singularity Surface. Technical Report No. 191, Geometry Preprint Series, Vienna Univ. of Technology, August 2008.


There are only two types of non-architecturally singular parallel manipulators (of Stewart Gough type) with planar base and platform, whose singularity set for any orientation of the platform is a cylindrical surface with rulings parallel to a given fixed direction p in the space of translations.

These manipulators have the advantage that their singularity set can easily be visualised as conic section by choosing p as projection direction. Moreover the computation of singularity free zones reduces to a 5-dimensional task.

Furthermore, we conjecture that there exists only one such design (see Figure 1) for the non-planar case, namely the generalisation of type I of the planar case.

An example for type II of the planar case is illustrated in Figure 2.


Contact areas

Contact areas of the facies articulatio trochlea talii superior and the facies articulatio tibiae inferior.

B. Odehnal and H. Stachel. The upper talocalcanean join. Technical Report 127, Geometry Preprint Series, Vienna Univ. of Technology, October 2004.


We reconstruct special surfaces like rotational and helical ones from 3D data with line geometry methods. This technique is applied to the surface of the talocalcanean join in order to understand in what sense the geometry of the surface influences the motion of body parts.


Publications

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Georg Nawratil
Boris Odehnal
Hellmuth Stachel
Flexible Structures
Line Geometry
Stewart Gough Platforms with Self-Motions
Analyse ebener Getriebe
(in German)

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Last modified on December 11th, 2013.