Zakharova T. Constructing of flat and spatial curves in the function of natural parameter

Dissertation for the conferment of graduate degree of candidate of technical sciences of the specialty 05.01.01 - Applied geometry, engineering graphics. - Kyiv National University of Construction and Architecture, Kyiv, Ukraine, 2014. Dissertation is devoted to the development of methods of constructing flat and spatial curves in the function of the natural parameter. Methods of constructing of such curves among their special classes: algebraic, spirals, spherical, surfaces of rotation and so on are obtained in the dissertation. Application of such curves in the different tasks of the applied mechanic is considered. The motion of material particle on the cylindrical surface with horizontal generators perpendicular to the generators with constant speed and force of the pressure of particle to the curve is developed in the dissertation. The problem of kinematics incompressibility flexible tape which is pushed by the given direction on an inclined plane is developed in the dissertation. Projecting edge of a blade cutting elements of shears is provided and it's stable power cutting branches along the entire length of the blade. Conic curve in the function of the natural parameter for the bycilinder-conic drum of mine hoisting plant is founded, which provides the ability to control the density of winding turns of rope on the drum and the calculation of the length of rope and torque in any position of the drum position.