Kinematic surfaces with congruent generatrix curves

Abstract

Kinematic surfaces of general type are considered to include rotational, spiroidal and translation surfaces. The author indicates that a class of kinematic surfaces under consideration also comprises instances of eleven other classes. A classification of general kinematic surfaces with congruent formations is compiled, with the most well-known specific kinematic surfaces indicated in addition to classes and groups containing surfaces formed by a rigid curve as it moves in space. The classification is based on the methods of forming the kinematic surfaces: (1) a stationary and mobile axoid with a generatrix curve rigidly connected to it; (2) a stationary directrix curve and a mobile rigid generatrix curve sliding along the directrix curve with the curves not necessarily having a common point; (3) the translation surfaces of one plane curve along another, with the curves sharing a common sliding point. The suggestion of organising a class of kinematic surfaces of general type does not imply their exception from the other classes of surfaces. The term “kinematic surfaces of general type” is used when it is necessary to show the wider group of surfaces but not to enumerate all classes with examined surfaces. The application of kinematic surfaces in construction, mechanical engineering is described, the explanation of some natural phenomena and processes in electrodynamics, fluid dynamics and astrophysics for the simulation of spiral objects is given.

Keywords

• rotative surface
• spiroidal surface
• translation surface
• surface of congruent sections