1. Working principle of harmonic reducer ‌gearbox
The working principle of harmonic reducer gearbox‌ is based on elastic mechanics and gear meshing theory. The wave generator is usually elliptical or hyperbolic, and the change of its shape will cause the flexible gear to produce periodic elastic deformation, and then mesh and disengage with the rigid gear, thereby transmitting power. When the wave generator rotates inside the flexible gear, the change of its shape will cause the flexible gear to produce periodic deformation, so that the meshing state of the flexible wheel and the rigid wheel will change continuously, thereby achieving the deceleration effect ‌.

2. Structure of harmonic reducer ‌ gearbox
‌1. Rigid wheel ‌: The rigid wheel is a rigid internal gear, usually made of high-strength materials such as steel. Its tooth shape is triangular or involute, and the number of teeth is slightly more than the flexible wheel (usually two more teeth). The rigid wheel is usually used as a fixed component in the harmonic reducer, meshing with the flexible wheel to transmit motion and power.
‌2. Flexible wheel ‌: The flexible wheel is a thin-walled cylindrical external gear with a large elastic deformation capacity. Its inner hole diameter is slightly smaller than the long axis of the wave generator, and its tooth shape is the same as that of the rigid wheel, but the number of teeth is less. Under the action of the wave generator, the flexible wheel produces periodic elastic deformation, meshing and disengaging with the rigid wheel, thereby transmitting power.
‌3. Wave generator‌: The wave generator is the active part of the harmonic reducer, usually composed of an elliptical disk and a flexible ball bearing or a rotating arm with rollers at both ends. When the wave generator is installed in the inner hole of the flexible wheel, because its length is slightly larger than the diameter of the inner hole of the flexible wheel, the flexible wheel is forced to support into an elliptical shape, thereby realizing the meshing transmission with the rigid wheel. The rotation of the wave generator drives the flexible wheel to produce continuous deformation, forming a simple harmonic waveform motion, and realizing the deceleration function.

3. Design features of harmonic reducer gearbox
1. Large transmission speed ratio‌: The transmission speed ratio of a single-stage harmonic gear is in the range of 70~320, which can reach 1000 in some devices, and the multi-stage transmission speed ratio can reach more than 30000. It can be used not only for deceleration, but also for speed increase. ‌ 
‌2. High load-bearing capacity‌: There are many teeth meshing at the same time in the harmonic gear transmission, and the number of teeth meshing at the same time in the double-wave transmission can reach more than 30% of the total number of teeth. In addition, the flexible wheel is made of high-strength material, and the teeth are in surface contact, so the load-bearing capacity is high‌.
3‌. High transmission accuracy‌: Due to the multi-tooth meshing, the error is averaged, and the transmission error is only about 1/4 of the ordinary cylindrical gear transmission. By slightly changing the radius of the wave generator, the tooth gap can be very small, or even meshing without side clearance, and the transmission idle stroke is small, which is suitable for reverse rotation‌.
‌4. High transmission efficiency and smooth movement‌: Since the flexible wheel teeth move uniformly in the radial direction during the transmission process, even if the input speed is very high, the relative slip speed of the teeth is still extremely low, the tooth wear is small, and the efficiency is high (up to 69%~96%). When meshing in and out, both sides of the gear participate in the work, there is no impact phenomenon, and the movement is smooth‌.
5. Simple structure, small size and light weight: The harmonic reducer has only three basic components (wave generator, flexible gear and rigid gear), and the input and output shafts are coaxial, with a simple structure and easy installation. Compared with general reducers, the volume of the harmonic gear reducer can be reduced by 2/3 and the weight can be reduced by 1/2 when the output torque is the same.
6. It can transmit motion to a confined space: By utilizing the flexibility of the flexible wheel, this advantage is unmatched by other existing transmissions.

4. Application significance of harmonic reducer gearboxes
1. Industrial robots: Harmonic reducer gearboxes are widely used in industrial robots, and can provide high reduction ratios and high torque density to meet the precise positioning requirements of robot joints. Its low noise and vibration characteristics help to improve the comfort of the working environment.
2. Aerospace: In the field of aerospace, harmonic reducer gearboxes are favored for their high reliability, precise control and lightweight design. It can work stably in extreme environments to ensure the precise control of spacecraft.
‌3. Medical devices‌: Surgical robots and diagnostic equipment require high-precision and high-stability transmission systems. Harmonic reducers can provide precise speed and position control, while their sealed design helps maintain the sterility of the surgical environment. ‌
4. Automation equipment‌: In automation equipment, the high efficiency and compact design of harmonic reducers help improve production efficiency and reduce energy consumption. Its standardized interface and modular design facilitate integration. ‌
5. Precision instruments‌: Harmonic reducer gearboxes are used in precision instruments to achieve high-precision motion control and meet the needs of various high-precision tasks.

Source:https://blog.udn.com/stepperrelation/182117918