Dual rotation hodographs in mechanisms
In this paper it is found that just as the result of composition of two uniform rectilinear motions is uniform rectilinear motion, the result of composition of two uniform one-way rotational motions is also uniform rotational motion. Basically generalization of Galileo relativity principle is presented on non-accelerated rotational motion. In this connection seven theorems having five corollaries have been proven. A hodograph in case of composition of two uniform oppositely directed rotational motions proves to be an ellipse. In particular case the ellipse can degenerate into a straight line segment. Characteristics of elliptical hodograph are determined, including large and small semi-axes, roots of characteristic equation, eccentricity, foci, the angle of the axes. The reverse problem is solved - determination of rotation speed by type of hodograph, including elliptical and circular. In composition of two asynchronous (multiple) rotations hodographs can be by type of a limacon, resembling Pascal’s limacon. The condition of occurrence of a limacon hodograph loop is found out. The practical aspect of the theme is determined by the fact that in milling cutter drives in machines for cleaning of large diameter pipes and many mechanisms (multi inert oscillator, planetary gear) summation of rotational motions is realized, and a hodograph shape is useful information while development of similar devices.