Abstract:Motion interpolation methods functioning as a key technology in motion control directly impact the trajectory accuracy and operational efficiency of motional objects. The current circular interpolation method of variable synchronization ratio does not consider the establishment of synchronous transition process, leading to the large interpolation errors in the circular interpolation and low sensitivity of interpolation accuracy to the speed. Thus this study proposes a circular interpolation method with the variable synchronization ratio based on the optimization of synchronization establishment timing. Based on the acceleration and deceleration control strategy, the establishment of synchronous transition process time is calculated in each interpolation cycle, which is required for each synchronous slave axis to reach the new synchronization state after acceleration or deceleration. Then, the angle increment of each synchronous slave axis during the establishment of synchronous transition process time is obtained, thus the precise position of the synchronous master axis corresponding to the changed synchronization ratios of the slave axes is calculated, which facilitates the determination of optimal timing for such changes. By changing the synchronization ratio of the master axis in advance to optimize the synchronization establishment timing, the slave axes reach the new synchronization state with the master axis when it moves to the circular arc, thereby effectively reducing the trajectory deviation caused by synchronization lag. The circular interpolation is achieved by continuously changing the synchronization ratio. The experimental results of variable synchronization ratio circular interpolation on a two-dimensional motion platform show that the proposed method achieves a significant improvement in interpolation accuracy compared to the reported variable synchronization ratio circular interpolation method. When completing the full-circle interpolation with radii of 20 mm and 100 mm, the average offset distances of the interpolation trajectory center at a speed of 10 mm/s and an interpolation step length of 1 mm are reduced by approximately 84.7% and 85.6%, respectively, and the average mean squared error (MSE) values are decreased by about 58.7% and 68.1%, respectively. Moreover, the change of average MSE value is relatively small when the interpolation speed changes. This further enhances the circular interpolation accuracy and effectively reduces the sensitivity of interpolation accuracy to speed.