A kinematic approach to Kokotsakis meshes
A kinematic approach to Kokotsakis meshes
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DOI：
10.1016/j.cagd.2010.05.002
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发表时间：
2010-08-01
影响因子：
1.5
通讯作者：
Stachel, Hellmuth
中科院分区：
文献类型：
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作者：
Stachel, Hellmuth
Kokotsakis网格是一种多面体结构，由一个n边的中心多边形P-0组成，由一个四边形或三角形组成的带以下列方式包围：P-0的每个边a（i）由相邻的多边形P-i共享，并且循环连续的相邻多边形之间的相对运动是球面耦合器运动。因此，P-0的每个顶点都是四个面的交点。在n = 3的情况下，网格是八面体的一部分。这些具有刚性面和可变二面角的结构最早是在上个世纪的三十年代被研究的。然而，在过去的几年里，有一个复兴：在何种条件下，这种网格是无限或连续灵活的问题在离散微分几何中获得了很高的现实性。本文的目标是重新访问著名的连续柔性的例子（Bricard，格拉夫，绍尔，Kokotsakis）从运动学的角度来看，并扩展他们的名单由一个新的家庭。(C)2010 Elsevier BV保留所有权利。
A Kokotsakis mesh is a polyhedral structure consisting of an n-sided central polygon P-0 surrounded by a belt of quadrangles or triangles 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 four faces. In the case n = 3 the mesh is part of an octahedron.These structures with rigid faces and variable dihedral angles were first studied in the thirties of the last century. However, in the last years there was a renaissance: The question under which conditions such meshes are infinitesimally or continuously flexible gained high actuality in discrete differential geometry. The goal of this paper is to revisit the well-known continuously flexible examples (Bricard, Graf, Sauer, Kokotsakis) from the kinematic point of view and to extend their list by a new family. (C) 2010 Elsevier B.V. All rights reserved.