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Keywords:
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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