## 1 Introduction  
Compared to a machining center, an industrial robot has a lower stiffness value. In addition, the stiffness distribution is nonlinear within the range of the workspace. [PERSON] et al. investigated the static stiffness of different robot pose configurations in a machining plane, and their results indicated that the values change in the range from \(5\times 10^{-7}\) m/N to \(14\times 10^{-7}\) m/N [1]. The stiffness value includes both the static stiffness and the dynamic stiffness. To improve machining accuracy, most studies have focused on the static stiffness of industrial robots. Through establishing stiffness models for industrial robots, the deformations resulting from the machining force can be compensated. [PERSON] et al. used two approaches to obtain the cartesian stiffness of an articulated industrial robot. The first approach established a stiffness model based on virtual joint modeling (VJM). Each joint stiffness value was identified through experiments, and the Cartesian stiffness was calculated with the stiffness model. Another approach measured the Cartesian stiffness directly in the workspace. The results indicated that the calculated stiffness based on the stiffness model was nearly twice as high as the experimental stiffness. Milling tests were conducted with Aluminum AW-2017A. The calculated displacement of the robot end effector based on the experimental stiffness is almost equal to the measured displacement [2]. [PERSON] et al. adopted the same approach to get the static stiffness model by measuring the stiffness of an industrial robot in the workspace. This stiffness model was used for real-time deformation compensation in robotic machining. End milling was conducted with an aluminum block. With the compensation, the mean error of the deformation in the milling process can be reduced from 0.4 mm to 0.1 mm [3]. [PERSON] et al. introduced a static stiffness model with 36 degrees of freedom to improve the accuracy of the stiffness modeling. The stiffness model was integrated into the robot controller for the compliance compensation. Circular paths were milled on the aluminum material. The distance from the nominal contour was calculated through compensated and uncompensated control strategies. The results indicated that the absolute average error of the compensated circular path can be reduced by nearly 50% [4]. Static stiffness is a major problem in robotic machining. In addition, low-frequency oscillations, which affect the surface quality, can appear during the milling process [5]. As the dynamic stiffness is more directly related to the vibration, obvious tool marks can appear on the workpiece surface if the robot has low dynamic stiffness. Therefore, the dynamic stiffness has an influence on the surface quality during the machining process. A few authors have discussed ways to obtain the dynamic stiffness of an industrial robot. An experimental modal analysis has been adopted to analyze the stiffness of industrial robots. Different robot position configurations were selected, and modal impact tests were implemented on the robot end effector to obtain the frequency spectrum. Based on a comparison of the amplitudes in the frequency spectrum, the stiffness variation has been discussed [6]. [PERSON] et al. investigated the dynamic stiffness distribution of an industrial robot at the first natural frequency in different poses. Through analyzing the variability of the dynamic stiffness, the machining direction can be determined [7]. [PERSON] and [PERSON] compared the dynamic characteristics of two lightweight robots (KUKA KR5 sixx and KUKA LBR) by analyzing their dynamic compliance [8]. A single-axis accelerometer was attached to the end effector of the manipulator. Modal tests with impact hammers were performed to obtain the frequency response function (FRF) across the 0-100 Hz frequency range.