The pendulum type surfaces with congruential cross sections

Abstract

The article discusses new kinematic surfaces that can be attributed to the class of surfaces of congruent cross sections. The surfaces of congruent cross sections were first identified in a separate class by Professor I.I. Kotov. Circular, elliptical and parabolic cylinders are taken as the guiding surfaces, and circles and parabolas are taken as generating plane curves, which can be located in the plane of the generating curve of the guiding cylinder or in a plane parallel to its longitudinal axis. The introduction of a new independent parameter helped to solve the set geometric problems. The analytical formulas are presented in generalized form, so the shape of the flat generatrix curve can be arbitrary. Two types of surfaces are considered: 1) when the local axes of the generating curves remain parallel during their movement; 2) when these axes rotate. The resulting surfaces can be of interest to architects, or can find application in machine-building thin-walled structures or in the study of the trajectories of bodies during their oscillatory-translational motion.