A harmonic drive is a mechanism that reduces the speed of the input shaft by a specified ratio.

　　A cycloidal drive, or cycloidal reducer, is a mechanism that reduces the speed of the input shaft according to a specified ratio. Cycloidal reducers are compact, feature minimal backlash, and offer relatively high transmission ratios.

　　The input shaft drives an eccentric bearing, which in turn causes the cycloidal disk to perform an eccentric cycloidal motion. The periphery of this disk meshes with a fixed ring gear, and its surface is equipped with a series of output shaft pins or rollers. As the cycloidal disk rotates, these output shaft pins directly drive the output shaft. Radial motion of the disk is not transmitted to the output shaft.

　　 Advantages

　　Unlike involute gearboxes, cycloidal drives feature zero backlash and high torque capacity while maintaining a compact footprint. They are particularly well suited for applications requiring low speed and high torque. Cycloidal drives can be engineered to provide a larger contact area than any gear‑based transmission—such as planetary gearsets. By engaging multiple teeth simultaneously, they deliver exceptionally high torque relative to their size, though this comes at the cost of sliding contact.

　　 Working principle

　　 Parts of a harmonic drive mechanism

　　The input shaft is eccentrically mounted on a rolling bearing—typically a cylindrical roller bearing—causing the cycloidal disk to oscillate in a circular path.[2] As the cycloidal disk is pushed toward the ring gear, it rotates independently about the bearing. This mechanism is analogous to a planetary gear set. The rotational direction of the disk and the output are opposite to that of the input shaft.

　　The number of pins on the ring gear exceeds that on the cycloidal disk. This causes the cycloidal disk to rotate about the bearing at a speed greater than that of the input shaft, thereby generating an overall rotation in the opposite direction to the input shaft’s rotation.

　　The cycloidal gear has holes whose diameters are larger than the diameter of the output needle rollers housed within them—specifically, their size equals the eccentricity of the input shaft. The output needle rollers move inside these holes and, driven by the oscillatory motion of the cycloidal gear, ensure the stable rotation of the output shaft.

　　The reduction ratio of a cycloidal pinwheel drive is given by the following formula, where P denotes the number of pins on the ring gear and L denotes the number of lobes on the cycloidal wheel.

　　Epicyclic gears typically employ a shortened cycloidal profile to minimize the eccentricity of the gear disc and the resulting unbalanced forces at high speeds. Consequently, two epicyclic gears are usually mounted with a 180° phase shift.

　　Many modern precision actuators generate eccentric motion through multiple shafts that also transmit the output force; typically, two to five shafts are arranged in a circular pattern identical to that of the simplest‑design output roller. The shafts are driven by a central input shaft via planetary gears. Because these shafts remain aligned with the input gear at all times, the output can be transmitted through roller bearings rather than relying on intermittent surface contact. Thanks to the planetary input, this configuration effectively constitutes a two‑stage drive and can be designed for direct actuation by a high‑speed brushless motor. This type is commonly used in robotic actuators.