ABSTRACT

Machining errors in parallel kinematic machines primarily depend on their extent of kinematic nonlinearity. In this paper, a computer integrated model of the kinematic nonlinearity and trajectory interpolation method for a 4DOF parallel milling machine is developed. The nonlinear errors prompted during various trajectory modes are analyzed. It is proved that in order to avoid significant non-linearity, the actuator and the end-effector space must possess identical order of trajectory. The effects of tool path length, its spatial location, and the Jacobian matrix properties on the kinematic nonlinearity error, are studied. Results showed that the path length is the governing factor for the nonlinear behavior of the mechanism. Moreover, the kinematic error is illustrated to have a reverse relationship with maximum singular values of the inverse Jacobian matrix. Experiments are conducted using digital dial indicators. Experimental results verified the accuracy of the proposed mathematical approach and confirmed its applicability in actual machining processes. Moreover, the proposed interpolation algorithm successfully limits the kinematic error under the machining tolerance by minimal segmentation. Finally, it is demonstrated that the proposed method is superior in terms of accuracy, to the median osculating circle (MOC) method.

摘要

并联运动机器的加工误差主要取决于它们的运动非线性程度。本文建立了四自由度平行铣床运动学非线性与轨迹插值方法的计算机集成模型。分析了在各种轨迹模式下提示的非线性误差。证明了为了避免显着的非线性，执行器和末端执行器空间必须具有相同的轨迹顺序。研究了刀具路径长度、其空间位置和雅可比矩阵特性对运动非线性误差的影响。结果表明，路径长度是机构非线性行为的控制因素。而且，运动误差被说明为与逆雅可比矩阵的最大奇异值具有反向关系。使用数字百分表进行实验。实验结果验证了所提出的数学方法的准确性，并证实了其在实际加工过程中的适用性。此外，所提出的插值算法通过最小分割成功地限制了加工公差下的运动误差。最后，证明了所提出的方法在准确性方面优于中密切圆（MOC）方法。所提出的插值算法通过最小分割成功地限制了加工公差下的运动误差。最后，证明了所提出的方法在准确性方面优于中密切圆（MOC）方法。所提出的插值算法通过最小分割成功地限制了加工公差下的运动误差。最后，证明了所提出的方法在准确性方面优于中密切圆（MOC）方法。