<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The analysis of simpler preliminary design gives useful input for more complicated three-dimensional building frame structure. A zonohedron, as a preliminary structure of design, is a convex polyhedron for which each face possesses central symmetry. We considered zonohedron as a special framework with the special assumption that the polygonal faces can be deformed in such a way that faces remain planar and centrally symmetric, moreover the length of all edges remains unchanged. Introducing some diagonal braces we got a new mechanism. This paper deals with the flexibility of this kind of mechanisms, and investigates the rigidity of the braced framework. The flexibility of the framework can be characterized by some vectors, which represent equivalence classes of the edges. A necessary and sufficient condition for the rigidity of the braced rhombic face zonohedra is posed. A real mechanical construction, based on two simple elements, provides a CAD prototype of these new mechanisms.</p></abstract>

The analysis of simpler preliminary design gives useful input for more complicated three-dimensional building frame structure. A zonohedron, as a preliminary structure of design, is a convex polyhedron for which each face possesses central symmetry. We considered zonohedron as a special framework with the special assumption that the polygonal faces can be deformed in such a way that faces remain planar and centrally symmetric, moreover the length of all edges remains unchanged. Introducing some diagonal braces we got a new mechanism. This paper deals with the flexibility of this kind of mechanisms, and investigates the rigidity of the braced framework. The flexibility of the framework can be characterized by some vectors, which represent equivalence classes of the edges. A necessary and sufficient condition for the rigidity of the braced rhombic face zonohedra is posed. A real mechanical construction, based on two simple elements, provides a CAD prototype of these new mechanisms.

Bracing Zonohedra With Special Faces

Institute of Civil Engineering, Szent István University, Budapest, Hungary

YBL Journal of Built Environment

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Bracing Zonohedra With Special Faces"}

The analysis of simpler preliminary design gives useful input for more complicated three-dimensional building frame structure. A zonohedron, as a preliminary...

Bracing Zonohedra With Special Faces

Published Online: Jan 29, 2016

Page range: 88 - 95

DOI: https://doi.org/10.1515/jbe-2015-0009

Keywords
rigidity, bar any joint framework, zonohedra, bracing, optimization

© 2015 Gyula Nagy, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Bracing Zonohedra With Special Faces

Published Online: Jan 29, 2016

Page range: 88 - 95

DOI: https://doi.org/10.1515/jbe-2015-0009

Keywordsrigidity, bar any joint framework, zonohedra, bracing, optimization

© 2015 Gyula Nagy, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
rigidity, bar any joint framework, zonohedra, bracing, optimization