Lisnjak A. Geometrical modelling of actions of me-chanical devices on the basis of properties of triangle Reuleaux.

Object - the phenomenon формообразова-ния complex curves under the form by geometrical modelling versions rolling triangle Reuleaux; the purpose - development of a way of the description of figures of constant width by the equation polynomial type, and by the example of triangle Reuleaux to construction of images of his results rolling on one of trochoidal laws, or under the law of rotating carry which model actions of mechanical devices of the certain class; methods - elements of the theory of R-functions, geometrical modelling of moving of tri-angle Reuleaux on planes, use computer schedules in Maple environment; theoretical and practical re-sults - the differential equation for definition of func-tions which are included into the description of curves of constant width is made, and the way of his decision is developed, descriptions of triangle Reuleaux by the equations in parametrical and im-plicitly - polynomial a kind are found, is developed circuits of synchronous rotation of multipair trianglesReuleaux with constant dot paired contact between them; scientific novelty - for the first time the curve of constant width is described by the differential equation, and his decision as lines Fourier with un-paired composed is resulted, the description of trian-gle Reuleaux in implicit - polynomial kind with use of bases Grobner for the first time is received, the analogue of triangle Reuleaux as bypass families epitrochoids for the first time is received and value of the managing parameter on which his form will co-incide with the form of classical triangle Reuleaux is designed, circuits of the synchronous manipulation of multipair triangles Reuleaux with constant paired dot contact between them for the first time are de-veloped; a degree of introduction - it is introduced on Kharkov NPP " Plodder "; sphere of use - geometri-cal modelling and designing of versions rolling on the basis of modern mathematical processors.