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以经典牛顿法为基础 ,针对 3 - RRR球面并联机构的机构学特点及控制中的特殊要求 ,提出了面向控制的高效迭代算法。利用机构运动连续性条件划分不同的控制阶段 ,当机构处于连续运动状态时 ,迭代结构中使用固定雅可比矩阵进行运算 ,缩短了单步迭代时间 ;当机构处于非连续运动状态时 ,使用变步长策略 ,引入调整量系数 ,抑制了大偏置初值带来的求解振荡。给出的算例证明 ,应用上述策略的正运动学求解算法兼顾了较大范围的收敛性与局部求解的快速性 ,运算速度满足控制过程的实时性要求。该方法同样适用于其它少自由度并联机构的正运动学求解。
Based on classical Newton ’s method, aiming at the mechanical characteristics of 3 - RRR spherical parallel mechanism and its special requirements in control, an efficient control algorithm is proposed. In the condition of continuous motion, the fixed Jacobian matrix is used in the iterative structure to reduce the single-step iteration time. When the mechanism is in discontinuous motion, Long strategy, the introduction of adjustment coefficient, inhibit the initial bias caused by large solution to the oscillation. The given examples prove that the positive kinematic solution algorithm applying the above strategy has both the convergence of a large area and the rapidity of local solution, and the computing speed meets the real-time requirements of the control process. This method is also applicable to the positive kinematics of other less-degree-of-freedom parallel mechanisms.