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.

翻译：我们研究圆锥体和圆柱体,用一个1参数等离子体变形,至少有两个平面曲线,在这种连续的伸展期间仍为平面,位于非平行平面上;我们调查平滑和离散环境中的几何/皮肤问题,因为这是普遍建造所谓的T-面拉链管的基础;与可以轻易解决的圆柱体情况相反,圆锥体是一个比较棘手的问题,但我们成功地为离散情况提供了封闭形式的解决办法,用来证明这些锥体与平面对称型的Bricard enthedra的上限相对应;对于光滑的情况,我们可以通过象征性的计算来将问题减少到普通的差别方程式,但解决办法仍然是尚未解决的问题。</s>