为了提高3-RRRU空间刚柔耦合并联机构的轨迹跟踪精度, 提出了一种基于瞬态刚体校正法的逆动力学模型求解方法来构建该机构的非线性控制策略。首先, 利用自然坐标法和绝对节点坐标法建立该机构的非线性逆动力学模型, 它考虑了各支链柔性空间梁单元的剪切效应, 并能描述柔性梁的大范围非线性弹性变形。然后, 通过分析刚柔耦合动力学模型在求解过程中出现的相容性问题, 结合自然坐标法与理想运动学模型, 提出了瞬态刚体校正法并求出逆动力学模型的稳定数值因果解。最后, 基于该数值解构建并联机构的非线性控制策略, 通过仿真与实验验证了该方法的可行性与有效性。仿真与实验结果表明: 逆动力学方程组的求解精度为10-6, 约束方程的相容误差为10-8; 与刚性并联机构的控制方法相比, 该方法在圆形轨迹下的最大跟踪误差降低了0.465 mm, 圆度误差降低了0.416 mm。结果表明: 该求解方法解决了闭链机构多体动力学方程的违约问题, 有效地改善了系统的综合收敛性能, 所构建的控制策略提高了并联机构的轨迹跟踪精度。

To improve the trajectory tracking performance of a spatial rigid-flexible 3-RRRU parallel manipulator, a nonlinear control strategy based on a multibody inverse dynamic solution by means of a transient kinematic correction method was proposed. First, the nonlinear inverse dynamics of a spatial 3-RRRU parallel robot with flexible links was developed according to both the Natural Coordinate Formulation (NCF) and the Absolute Nodal Coordinate Formulation (ANCF). The derived models consider the shear deformation and can describe the large deformation for each beam. By analyzing the compatibility problem during the solution process of the rigid-flexible dynamics of the close-chain mechanism, we were able to develop the transient kinematic correction method and the derived stable causal solutions according to the NCF and the ideal kinematic model. Finally, the control strategy for the manipulator is presented, which was based on the solutions and simulations, and experiments were performed to verify the feasibility and effectiveness of the method. The results showed that the solution precision of the inverse dynamics was 10-6 and that the compatibility error of the constraints was 10-8. Compared with those based on the control strategy of the rigid parallel mechanism, the maximum tracking error and the roundness error of a prescribed circular trajectory based on the provided control strategy can decrease by 0.465 mm and 0.416 mm, respectively. The presented method can solve the compatibility problem of multibody dynamics with constraints, thus effectively improving the overall convergent performance of a dynamic system. The control strategy can provide better tracking performance for the parallel mechanism.