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Keywords:
kinematics; characteristics; enveloped surfaces
kinematics; characteristics; enveloped surfaces
Summary:
Double Points on Characteristics. A fixed surface $\Phi $ of a moving space $\Sigma $ will envelope a surface of the fixed space $\Sigma ^{\prime }$, if we move $\Sigma $ with respect to $\Sigma ^{\prime }$. In the general case at each moment of the one-parameter motion there exists a curve $c$ on $\Phi $, along which the position of $\Phi $ and the enveloped surface are in contact. In the paper we study the interesting special case, where $c$ has some double point $P\in \Phi $. This depends on relations between differential geometric properties in the neighbourhood of $P$ of the moved surface and the instantaneous motion of the one-parameter motion. These properties are characterized in this paper. Then some further kinematic results for the characterized motions are shown.
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