N. Artem’eva, O.O. Mugin, O.G. Mugin MECHANICAL REDUCTION AND SPEED-INCREASING DRIVERS BASED ON AN EPICYCLOID AND A HYPOCYCLOID The study deals with mechanical drives wich are fundamentally different from traditional toothed gears. <...> It is possible to construct the new mechanical drives (reduction and speed-increasing drives) that are smaller in size, have a lower noise level and a high gear ratio (up to 500) at one stage, using the qualities of the plane curves of epycycloid and hypocycloid. <...> Keywords: epicycloids, hypocycloid, reduction and speed-increasing drives, input eccentric shaft, output shaft, roller, toothed gear, rolling contact bearings. <...> Long before the Common Era the mathematicians and the astronomers of Ancient Greece were interested in the amazing qualities of cycloidal curves of the epicycloid and hypocycloid. <...> In the Russian school of Machine and Mechanism Theory they are known as Class IV Pairs. <...> The progressive f ield is the study of the geometry of the Novikov’s Gear’s teeth. <...> In 1931 a German engineer Lorenz Braren patented the first drive of this kind. <...> Compared to the involute toothing the cycloidal toothing in reduction and speed-increasing drives has a number of advantages. <...> Due to a more frequent toothing these drives are long-lasting, smaller in size, volume and weight, and have a better carrying capacity. <...> The central idea of the design of these drives is that rolling bodies (or rollers) roll against specially profiled surfaces of two other bodies. <...> The interaction of the bodies that transfer motion from the input to the output shaft is caused due to a rolling contact bearing. <...> They are used in the robotics, the machine tool, the chemical machine building, the hoisting machinery, chain conveyors, radars, excavators and drilling equipment. <...> A very important characteristic of the drive is a low level of noise and vibration. <...> Although the term “bolt tooth reduction toothing”[5] is close in a way to the term “toothing”, in our opinion, the geometry of the this gears is fundamentally different. <...> Let us take a look at one step of this drive basing on an equation of cycloidal curves represented as parameters [6]. <...> The epicycloid equation: [(R+r) Cosφ-λr Cos((R/r)+1) φ]e1 +[(R+r) Sinφ -λr Sin((R/r)+1) φ]e2 The hypocycloid equation: [(R-r) Cos <...>