# Vibration Suppression of Collaborative Robot Servo with Dual Encoders
## 2 Vibration Causes of Cooperative Robot  
There are various reasons for the vibration of collaborative robots, such as issues in motor manufacturing, the gear clearance of the reducer, mismatched control parameters, non-smooth control commands, insufficient rigidity of the robot body, and the presence of elastic factors. This paper focuses on studying how to suppress vibrations caused by the elastic factors of robot joints [8].  
In the structure of collaborative robots, the motor is connected to the end load through a reducer and link. When the motor rotates, the speed is transmitted to the load end through the reducer and connecting link. As shown in Figure 1, \(\omega 1\) represents the rotational speed on the motor side, while \(\omega 2\) represents the speed on the reducer side, which is also the speed on the load side. Sometimes, the motor speed control on the motor side is very stable, but on the reducer side, the speed is not as stable, and there is vibration. This is because the transmission device is not an ideal rigid body; there are elastic factors, and there is clearance in the reducer. Our feedback element is the motor encoder, so there is a lack of effective methods to address the vibrations caused by the connecting device. If the reducer were ideally rigid and without gaps, the relationship between the motor side speed \(\omega 1\) and the reducer side speed \(\omega 2\) would be: \(\omega 1\) = ratio \(\times\)\(\omega 2\); however, in reality, due to elastic deformation and gaps, \(\omega 1\
eq\) ratio \(\times\)\(\omega 2\). If the motor side speed \(\omega 1\) is used as feedback, when \(\omega 1\) is stable, \(\omega 2\) will exhibit fluctuations. Consequently, vibration phenomena will occur in the actuator or load side. By sampling the speed \(\omega 2\) at the reducer side, incorporating it into the feedback loop, and adding it to the control system, good vibration suppression effects can be achieved.  
The type of reducer is a harmonic reducer. The motor shaft should be connected to the harmonic reducer's waveform generator. The waveform generator has an elliptical structure and is equipped with thin-walled ball flexible bearings. The flexible wheel should be installed into the waveform generator. The outer side of the flexible wheel has external teeth. When the motor rotates, the elliptical waveform generator rotates together with the flexible wheel. The rotation of the waveform generator generates a propulsion waveform  
Figure 1: A schematic diagram for a robot joint.  
for the flexible wheel, and after assembly with the rigid wheel, the outer teeth of the flexible wheel mesh with the inner teeth of the rigid wheel. At least 30% of the gears are in a meshing state. Coordinated meshing motion is achieved through the rotating flexible and rigid wheels of the wave generator. The inner circumference of the rigid wheel should be traversed. This is because the flexible wheel has two fewer teeth than the steel wheel. The rotation of the wave generator generates misalignment between the flexible and rigid wheels, thereby driving the movement of the steel wheel. The steel wheel is connected to the link. The flexible wheel has 218 teeth, while the steel wheel has 220 teeth, resulting in a reduction ratio of 109. After the flexible wheel has completed one full rotation, its gears have advanced by 218 teeth, and the steel wheel only rotates two teeth. The harmonic reducer consists of a waveform generator, flexible wheels, and steel wheels, so there is a certain degree of flexibility involved.