铰链结构的奇异性
Singularities of Hinge Structures
摘要：
受蛋白质链和其他分子构象中存在的铰链结构的启发，我们研究了与体铰链和面板铰链链相关的某些映射的奇异性。这些是顺序铰接系统，其中两个连续的刚性件通过铰链连接，即余维两轴。奇点，或称临界点，对应于轴的线性跨度中的维度下降，被视为格拉斯曼簇在其普吕克嵌入中的点。这些结果在任意维数下都是有效的。三维的情况也与机器人有关。
英文摘要：
Motivated by the hinge structure present in protein chains and other molecular conformations, we study the singularities of certain maps associated to body-and-hinge and panel-and-hinge chains. These are sequentially articulated systems where two consecutive rigid pieces are connected by a hinge, that is, a codimension two axis. The singularities, or critical points, correspond to a dimensional drop in the linear span of the axes, regarded as points on a Grassmann variety in its Plücker embedding. These results are valid in arbitrary dimension. The three dimensional case is also relevant in robotics.
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