Institute of Geometry

Research in this area deals with the geometry and kinematics of mechanisms with a focus on applications on the one hand, and theoretical kinematicson the other hand. Applications are diverse and range from car side windows to x-ray spectrometry.
A major topic are overconstrained linkages, i.e., mechanisms which move despite the fact that a simplistic count of degrees of freedom yields rigidity.

• A. Gfrerrer and J. Lang. Fully variable valve control: A geometric approach. J. Geometry Graphics 22/1 (2018), 99-114.
• J. Kraxner, M. Schäfer, O. Röschel, G. Kothleitner, G. Haberfehlner, M. Paller, and W. Grogger. Quantitative EDXS: In fluence of geometry on a four detector system. Ultramicroscopy 172 (2017), 30-39. [doi].
• A. Gfrerrer and J. Lang. Geometry and kinematics of a convertible's rear side window. J. Geom. Graph. 20/1 (2016), 101-114. [MR].
• O. Röschel. Overconstrained mechanisms based on special planar chains. In Proc. 16th Int. Conf. Geometry and Graphics, pages 903-911. 2014. Innsbruck, August 4--6.
• O. Röschel. Overconstrained mechanisms based on planar four-bar-mechanisms. Computer Aided Geometric Design 31 (2014), 595-601. [doi].
• P. Fazekas, O. Röschel, and B. Servatius. The kinematics of a framework presented by H. Harborth and M. Möller. Beitr. Algebra Geometrie 54/1 (2013), 201-209. [doi].
• M. Barton, L. Shi, M. Kilian, J. Wallner, and H. Pottmann. Circular arc snakes and kinematic surface generation. Computer Graphics Forum 32/2 (2013), 1-10, Proc. Eurographics. [doi].
• O. Karpenkov, J. Schepers, and B. Servatius. On stratifications for planar tensegrities with a small number of vertices. Ars Math. Contemp. 6 (2013), 305-322. [arxiv: 1201.3557].
• O. Röschel. A Fulleroid-like mechanism based on the cube. J. Geometry and Graphics 16 (2012), 19-27.
• O. Röschel. Overconstrained mechanisms based on trapezohedra. In Proceedings of the 15th International Conference on Geometry and Graphics (ICGG 2012), pages 629-637. 2012.
• A. Gfrerrer. Motion of a line segment whose endpoint paths have equal arc length. In G. Weiss, editor, Int. Workshop on Line Geometry an Kinematics 2011, pages 21-26. Dresden University of Technology, 2011, ISBN 978-3-86780-244-4.
• O. Röschel. An overconstrained chain of 16 regular triangles. In G. Weiss, editor, Proceedings of the 1st International Workshop on Line Geometry and Kinematics, pages 87-93. Dresden University of Technology, 2011, ISBN 978-3-86780-244-4.
• A. Gfrerrer, J. Lang, A. Harrich, M. Hirz, and J. Mayr. Car side window kinematics. Computer-Aided Design 43 (2011), 410-416. [doi].
• P. Zsombor-Murray and A. Gfrerrer. Mapping similarity between parallel and serial architecture kinematics. Meccanica 46/1 (2011), 183-194. [doi].
• A. Harrich, J. Mayr, M. Hirz, P. Rossbacher, J. Lang, A. Gfrerrer, and A. Haselwanter. CAD-based synthesis of a window lifter mechanism. SAE Technical Paper 2010-01-0009, 2010. Proc. SAE World Congress, Detroit. [doi].
• O. Röschel. The self-motions of a fulleroid-like mechanism. In Proc. 14th Int. Conf. Geometry and Graphics, pages 1-7. 2010. Kyoto, August 5--9.
• P. J. Zsombor-Murray and A. Gfrerrer. A unified approach to direct kinematics of some reduced motion parallel manipulators. J. Mechanisms Robotics 2 (2010), #,021006. [doi].
• F. Doray, O. Karpenkov, and J. Schepers. Geometry of configuration spaces of tensegrities. Discrete Comput. Geom. 43/2 (2010), 436-466. [MR], [doi].
• O. N. Karpenkov. On the flexibility of Kokotsakis meshes. Geom. Dedicata 147 (2010), 15-28. [MR], [doi].
• A. Gfrerrer and P. J. Zsombor-Murray. 3R-wrist positioning - a classical problem and its geometric background. In A. Kecskemethy and A. Müller, editors, Proceedings of the 5th International Workshop on Computational Kinematics, pages 175-182. Springer, 2009, ISBN 978-3-642-01946-3. [doi].
• A. Gfrerrer. Geometry and kinematics of the Mecanum wheel. Comput. Aided Geom. Des. 25 (2008), 784-791. [MR].
• A. Gfrerrer. Axial equiform Bricard motions. Grazer math. Berichte 352 (2008), 17 - 40.
• A. Hofmeister, W. Sextro, and O. Röschel. Error-workspace analysis of plane mechanisms. In Proc. EUCOMES, pages 1-12. 2006.
• S. Mick and O. Röschel. Frameworks generated by the octahedral group. KoG 9 (2005), 3-10.
• H. Wresnik. Bewegungen mit ebenen Bahnen im einfach isotropen Raum. Teil I. Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 15 (2005), 23-47.
• H. Wresnik. Bewegungen mit ebenen Bahnen im einfach isotropen Raum. Teil II. Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 15 (2005), 49-71.
• A. Gfrerrer and P. J. Zsombor-Murray. Robotrac mobile 6R closed chain. In Proc. CSME Forum, pages 21-24. 2002, ISBN 0-9730900-1-4. CD.
• O. Röschel. New models of moveable polyhedra. In V. Mykhailenko, editor, Proc. 10th Int. Conf. on Geometry and Graphics, volume 1, pages 127-131. 2002.
• J. Lang, S. Mick, and O. Röschel. The rigidity rate of positions of Stewart-Gough platforms. J. Geom. Graph. 5/2 (2001), 121-132. [MR].
• O. Röschel. Zwangläufig bewegliche Polyedermodelle. III. Math. Pannon. 12/1 (2001), 55-68. [MR].
• A. Gfrerrer and P. J. Zsombor-Murray. Kinematics of a two-legged manipulator with actuated spherical joints. In Proc. 2nd Workshop Computational Kinematics. 2001. held May 19-22 2001, Seoul.
• A. Gfrerrer. Study's kinematic mapping - a tool for motion design. In J. Lenarcic and M. M. Stanisic, editors, Recent Advances in Robot Kinematics, pages 7-16. 2000.
• O. Röschel. Möbius mechanisms. In J. Lenarcic and M. M. Stanisic, editors, Advances in Robot Kinematics, pages 375-382. Kluwer, 2000.
• A. Gfrerrer. On the construction of rational curves on hyperquadrics. Grazer Math. Berichte 340 (1999), 1-69. [MR].