This paper presents an approach for the trajectory planning of a hybrid machine tool based on vibration error, which aims at determining the optimal location and machining time of a given machining path. Firstly, an elastodynamic model of the hybrid robot is proposed by taking compliance of joints and limbs into account. Then, in order to evaluate vibration error in a typical machining path, two indices, i.e., the mean value and fluctuation of vibration error throughout the whole trajectory are proposed. Based on the Isight platform, sensitivity analysis is conducted. In addition, optimal trajectories are derived when adopting 3–4–5 polynomial and B-splines, respectively. Results show that the machining time and machining angle have important impacts on the mean value and fluctuation of vibration error. Especially, effects of the machining angle on the vibration error cannot be neglected. Comparison shows that adopting B-splines is conductive to decreasing the required torque and power. This paper provides a method on determining optimal machining location quickly for a given path throughout the whole workspace. The proposed method can be applied to trajectory planning of other hybrid robots or parallel kinematic machines.

本文提出了一种基于振动误差的混合动力机床轨迹规划方法，旨在确定给定加工路径的最佳位置和加工时间。首先，通过考虑关节和四肢的柔顺性，提出了混合机器人的弹性动力学模型。然后，为了评估典型加工路径中的振动误差，提出了两个指标，即整个轨迹上的振动误差的平均值和波动。基于Isight平台，进行了敏感性分析。另外，当分别采用3–4–5多项式和B样条时，可以得出最佳轨迹。结果表明，加工时间和加工角度对平均值和振动误差波动有重要影响。特别，加工角度对振动误差的影响不可忽略。比较表明，采用B样条曲线有助于降低所需的扭矩和功率。本文提供了一种快速确定整个工作空间中给定路径的最佳加工位置的方法。所提出的方法可以应用于其他混合机器人或并联运动机器的轨迹规划。