ANALYTICAL DESCRIPTION OF CYCLIC CURVES FOR PARAMETRICAL MODELLING IN THE CAD SYSTEMS

Abstract

Nowadays, the cyclic curves have a wide application in technical branches mainly in mechanics. They are very important for component design and testing simulation for different conditions. Cyclic curves profiles is possible to find in a lot of machine equipments with rotary parts. It is begin in different gears (clock machines), rotary parts of engine, piston pump, accelerometers etc. We can find in the Wankel´s engine but also in the water or wind turbines and other equipments. Cycloid profiles are able to keep a high loads because of they are used in the building industry (bridges, tunnels). The cyclic curves are created trajectory of circle point which moves without slip on a given curve. The paper deals with research of circle moving based on only geometrical basic independently of the time when was realised. For the moving is not important moving speed. The result is a mathematical description of cyclic curves (cycloids, epicycloids, hypocycloids and involutes) which is applied to design module of modern CAD systems which use parametrical modelling by equations.