论文标题
携带平面曲线的异位变形锥和气缸
Isometrically deformable cones and cylinders carrying planar curves
论文作者
论文摘要
我们研究具有至少两条平面曲线的1参数等距变形的锥和圆柱体，它们在这种连续的屈曲期间保持平面，并位于非平行平面。我们在平滑和离散设置中研究了这个几何/运动学问题，因为它是通用构造所谓的T-Hedral拉链管的基础。与可以轻松求解的圆柱状情况相反，圆锥形的情况更棘手，但是我们成功地为离散情况提供了封闭的形式解决方案，该解决方案用于证明这些锥体对应于平面对称类型的Bricard Octahedra的帽子。对于平滑的情况，我们能够通过符号计算将问题减少到普通的微分方程，但其解决方案仍然是一个开放的问题。
We study cones and cylinders with a 1-parametric isometric deformation carrying at least two planar curves, which remain planar during this continuous flexion and are located in non-parallel planes. We investigate this geometric/kinematic problem in the smooth and the discrete setting, as it is the base for a generalized construction of so-called T-hedral zipper tubes. In contrast to the cylindrical case, which can be solved easily, the conical one is more tricky, but we succeed to give a closed form solution for the discrete case, which is used to prove that these cones correspond to caps of Bricard octahedra of the plane-symmetric type. For the smooth case we are able to reduce the problem by means of symbolic computation to an ordinary differential equation, but its solution remains an open problem.
