【摘要】 时间最优速度规划是提高五轴混联机构加工效率和加工精度的有效方式之一，以电机速度、加速度以及加加速度为约束条件进行时间最优速度规划，可以提高五轴混联机构的加工效率。求解该速度规划模型，需要进行复杂繁琐的末端速度、加速度、加加速度以及速度雅可比矩阵及其一、二、三阶导数的求解。针对这个问题，提出一种基于差分的五轴混联机构微分运动学的求解方法，可简化速度规划模型的建立过程。同时，考虑速度规划存在长路径大量离散点的情况，使得全局速度规划方法效率较低。针对这个问题，提出一种并行速度规划方法。该方法首先利用三次B样条函数和伪加加速度将速度规划模型转换为线性规划模型，然后选取并行窗口区域中点建立连接区域，并将重叠区域内进给速率的最大值作为连接区域的进给速率，最后使用自适应辛普森积分方法将弧长域转换为时间域。理论分析与实验结果表明，所提方法极大地简化了五轴混联机构速度规划模型、进一步提高了五轴混联机构速度规划的效率。更多还原

【Abstract】 Time-optimal speed planning is one of the effective ways to improve the machining efficiency and accuracy of five-axis hybrid mechanisms. Time-optimal speed planning with motor speed, acceleration, and jerk as constraints can improve the machining efficiency of five-axis hybrid mechanisms. To solve this speed planning model, it is necessary to solve the complex and tedious problems of end-point speed, acceleration, jerk, and speed Jacobian matrix and its first, second, and third derivatives. To address this issue, a differential kinematics solving method based on a five-axis hybrid mechanism is proposed, which can simplify the process of establishing a velocity planning model. At the same time, considering the situation where there are a large number of discrete points on long paths in the speed planning, the efficiency of the global speed planning method is low. To address this issue, a parallel speed planning method is proposed. The method first converts the velocity planning model into a linear planning model using cubic B-spline functions and pseudo-acceleration. Then, it selects the midpoint of the parallel window region to establish a connection region, and uses the maximum feed rate in the overlapping region as the feed rate for the connection region. Finally, it uses the adaptive Simpson integration method to convert the arc length domain into a time domain. Theoretical analysis and experimental results show that the proposed method greatly simplifies the velocity planning model of five-axis hybrid mechanisms and further improves the efficiency of velocity planning for five-axis hybrid mechanisms.更多还原