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If N is even, the backlash error cancels each other out in the transmission, and there is no error between the output position and the target position; if N is an odd number, then the driven wheel continues to rotate the gear backlash δ to reach the target position. The reason can be clearly seen from the vector point of view: both 12 and 34 characterize the gear backlash, but in opposite directions, thereby canceling each other out. Therefore, it can be judged that even if the gear pair is not only 0 points during the movement, the above conclusion is still established.
The basic idea of ​​eliminating the backlash of the gear to eliminate the backlash of the gear is to compensate for the angular displacement of the driven wheel due to the change of the output. Based on the knowledge of Section 1, this angular displacement compensation is only one time in the entire motion. Input: target position, gear backlash δ.
Output: Reach the target position. initialization. The purpose of the initialization is to make the driven wheel and the driving wheel closely mesh. For the sake of simplicity, it may be desirable to initialize the output to the initialization position counterclockwise. Therefore, the subsequent first output change is the clockwise rotation of the output. The output moves to the target position and confirms the last direction of rotation. Determine if error compensation is required. If the last rotation direction is counterclockwise, it means that the output end is 2n (n=0, 1, 2, 3,...) times to reach the position, which is the target position. If the last rotation direction is clockwise, it means that the output end is rotated by (2n 1) times to reach the position, which is exactly the same as the target position by a rotation angle δ. Compensate for situations that require compensation. The output continues to rotate δ° in the clockwise direction. Otherwise, go directly to the next step.
Application Examples The study in this paper is applied to a multi-joint robotic arm as shown. All encoders are mounted on the motor end, ignoring the error of the motor and the encoder is considered to be at the input of the gear reducer. Here, the waist joint (a positive and negative rotating disc) is taken as an example to describe in detail how the compensation method is applied in teaching. The reducer used for the lumbar joint is Maxion's GP32C type with a rotation accuracy of 1°. Figure 4 Multi-joint robot arm 3.1 capture target position value initialization. The output moves to limit 1 first, then clockwise to limit 2, then counterclockwise to the initialization position 0. As shown. Figure 5 initializes the motion to the target position and arrives. Make sure the last direction of rotation is clockwise (or counterclockwise). The encoder is installed at the input of the reducer, assuming that the encoder rotates to the input with a rotation angle of A and the output to B=A/i (i is the reduction ratio). Determine if (or not) error compensation is required. Confirm the target position value as: -(B-δ)=-B δ (or B).
The other position moves to the target position and the output is arbitrarily rotated within the movable range. The output moves to the target position and confirms the last direction of rotation. Determine if error compensation is required. Compensate for situations that require compensation. The output continues to rotate δ° in the clockwise direction. Otherwise, go directly to the next step.
Through the above method, the error of the arm in the circumferential direction is 2 mm at a distance of 800 mm, and the angle error is 2/800×180/π=0.14°. It can be seen that through such a compensation operation, the gear backlash can be significantly improved.
Conclusion Through the example, we can see the effective application of this compensation method in the actual engineering. This research provides a basis for more rational selection of gear-type equipment, especially to overcome the blind pursuit of gear rotation accuracy design ideas.