A grinding machine including an electric drive with a drive wheel, wherein the electric drive is arranged on a base unit of the grinding machine, a grinding spindle unit constructed as a grinding arm arranged removable on the base unit and which includes a grinding tool and a gear element which transmits the rotational movement of the drive wheel to the grinding tool. To facilitate the change of the grinding arm, the gear element includes: a driver which is supported on the grinding spindle unit and which is directly or indirectly in rotary union with the grinding tool, two guide wheels which are supported on the grinding spindle unit and a belt which is guided around the driver and the guide wheels, wherein in the mounted state of the grinding spindle unit at the base unit the drive wheel contacts the belt between the two guide wheels and hereby drives the same.