A transmission device for installation on a driveshaft, having a base body which encloses the driveshaft, a pinion which in the mounted state is arranged in the base body and on the driveshaft, and a rack which interacts with the pinion and runs through the base body. The transmission device is distinguished by the fact that the base body is open on one side in such a way that it can be fitted onto a driveshaft in the radial direction, and in that the pinion is in multiple parts such that it is possible to perform a mounting process on the driveshaft during which the parts of the pinion can be joined together by a radial movement with respect to the driveshaft.