论文标题
空间运动学和射击二元组的射击差异几何形状
Space Kinematics and Projective Differential Geometry Over the Ring of Dual Numbers
论文作者
论文摘要
我们研究了刚体位移组与双重季度组之间的同构，这是双数数乘法组从二重数字在双重数字上的差异几何学的角度来看。在这个空间中，一些看似奇怪的现象具有清晰的运动学解释。一个例子是存在具有连续的切线的非紧张曲线，这些曲线与具有垂直darboux运动的圆柱体组中的运动相对应。我们还建议在该射影空间中选择曲线的圆锥形的几何有意义的方法，并说明其相应的动作。此外，我们研究了这些特殊动议的因素化，并将获得的结果用于构建过度链接。
We study an isomorphism between the group of rigid body displacements and the group of dual quaternions modulo the dual number multiplicative group from the viewpoint of differential geometry in a projective space over the dual numbers. Some seemingly weird phenomena in this space have lucid kinematic interpretations. An example is the existence of non-straight curves with a continuum of osculating tangents which correspond to motions in a cylinder group with osculating vertical Darboux motions. We also suggest geometrically meaningful ways to select osculating conics of a curve in this projective space and illustrate their corresponding motions. Furthermore, we investigate factorizability of these special motions and use the obtained results for the construction of overconstrained linkages.
