The very first Servi-Cycles did not use any transmission. To stop, you shut off the motor. In 1940, the shifter models came out. These used a foot shift, that moved the transmission pulley in or out to change the gear ratio.
In 1953, Simplex introduced the Automatic, which, as the name implies, was completely Automatic. The transmission pulley used weights to move the sheaves in and out to adjust the ratio of the drive.They work exactly like a Torque Convertor on a modern go kart.