# New Indices for Evaluating Vibration Characteristics of Flexible-Joint Robots
###### Abstract  
Structural vibration is a significant consideration for robotic applications such as machining where the robot is subject to large dynamic loading. Aiming at providing an efficient means to evaluating the vibration characteristics of industrial robots for these applications, this work proposes two new indices to quantify the elastic displacement of the tool mounted on the robot caused by the vibrations induced by external process loading for flexible-joint robots. For this purpose, a structural dynamic model is first developed to derive the frequency responses of the tool displacement. Then, the displacement-force and displacement-torque frequency response ratios are defined, which represent the mapping from the amplitudes of an external harmonic force and torque to the amplitude of tool displacement respectively. The upper bounds of the two ratios are used as evaluation indices for the vibration characteristics of the robot, which represent the worst situation of the tool displacement due to harmonic excitation with amplitude of unit force and unit torque respectively. With these indices, an efficient method is provided to predict whether the tool misalignment caused by periodic loading is acceptable for process quality requirement. Numerical simulation demonstrates the effectiveness of the proposed method for a robotic riveeting system being developed for aerospace assembly. vibration characteristics; structural dynamic model; performance evaluation; industrial robots; robotic machining +
Footnote †: journal: Applied  
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than conventional robotic tasks like welding and material handling where only static or low contact forces act on the robot. Since the natural frequencies of an industrial robot strongly depend on its configuration [15] and its stiffness varies significantly in different directions [16; 17], the vibration characteristics depend on the robot configuration and the direction of external force. It has been found that structural vibrations of the robot can cause tool misalignment [18], damage the surface quality [19], and reduce the fatigue lives of the tool and the robot [20; 21]. Furthermore, the system can become instable due to the interaction between the robot vibrations and the process forces [22; 23] and the stability condition can be affected by some process parameters such as feed rate and spindle speed [24; 25]. All these have indicated the complexity of vibration characteristics of robots under dynamic loading and the possible serious effect on process quality. A first question for developing an automation system for such processes is whether to use and how to select a robot so that the forced vibrations excited by the process are acceptable for quality requirement. This brings the need for an efficient means to evaluating the vibration characteristics of robots, which, however, is usually not provided by robot manufacturers. A variety of indices can be found in literature to evaluate robot performance [26]. For instance, the condition number of Jacobian matrix has been proposed to measure the robot dexterity [27], and the manipulating force ellipsoid can quantify the static torque-force transmission from robot joints to its end-effector [28]. The dynamic manipulability ellipsoid and the radius of acceleration have been derived for evaluating robots' acceleration performance respectively. The former represents the achievable end-effector accelerations in a configuration for given joint torque limits [29], and the latter is a global performance measure of the achievable acceleration from any joint position and velocity in the operating region [30].