Kinematics of Expansive Planar Periodic Mechanisms
Kinematics of Expansive Planar Periodic Mechanisms
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DOI：
10.1007/978-3-319-06698-1_41
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发表时间：
2014-01-01
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影响因子：
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通讯作者：
Streinu, Ileana
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文献类型：
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作者：
Borcea, Ciprian S.;Streinu, Ileana
如果一个柔性杆件-关节框架的任意两个关节之间的距离增加或保持不变，则该框架被称为膨胀运动。有限二维框架的膨胀运动已被充分表征。在这里，我们调查他们的周期性对应物。理解它们的关键是一族单自由度机构，称为周期性尖伪三角剖分。多自由度机构的膨胀无穷小运动形成一个多面体圆锥，其极值射线从框架的不同完成伪三角剖分获得。我们说明其结构上的框架相关联的一个星形瓷砖的飞机。
A flexible bar-and-joint framework is said to be moving expansively if the distance between any two of its joints either increases or stays the same. Expansive motions of finite 2D frameworks have been fully characterized. Here, we investigate their periodic counterparts. The key to their understanding is a family of one-degree-of-freedom mechanisms called periodic pointed pseudo-triangulations. Expansive infinitesimal motions for mechanisms with several degrees of freedom form a polyhedral cone whose extremal rays are obtained from different completions of the framework to pseudo-triangulations. We illustrate its structure on a framework associated to a stellated tiling of the plane.