A Method of Determining the Shape of the Gear Teeth with Pitch Curve Containing Transition Curves

The article presents the method of determining profiles of teeth in the toothed gear transmission with a special shape of the rolling line of an internally toothed closed curve rack. The shape of the rack allows a pinion to run around it, which enables the propulsion of moving elements of a mechanism with reciprocating (to and fro) motion. The aim of using the clothoid as the fragments of the pitch curve of the rack is to reduce the dynamic loads associated with the change of direction of motion of the pinion axis. The article describes the method of determining the teeth profiles based on the clothoid pitch curve. A mathematical description of curves defining the profiles of these teeth is given. The validity of the method was verified with a computer model of the transmission and then virtual kinematic simulation of its operation.