The parasitic dynamics of shaking force balanced mechanisms; a frequency domain analysis

High-speed robots cause oscillating reaction forces and moments at the base frame, inducing disruptive ground vibrations and a loss of accuracy at the end-effector. Under the common assumption of rigid links, dynamic balance may eliminate these shaking forces and moments by adding masses throughout the mechanism. In practice, robot links have a finite stiffness, such that the addition of mass may lead to parasitic dynamics, undesired vibrations and a degradation of controller performance and robot accuracy. This paper shows that this rigid body assumption is insufficient and investigates the influence of the link flexibility on the balance quality and compares it to a common passive vibration isolation solution. For practical illustration and validation, the analysis is conducted on a simplified planar delta robot. Both models and experiments indicate that force balancing results in a 40 dB/dec attenuation of exported vibrations. This effect, however, is limited to a frequency range below the first parasitic eigenfrequency of the mechanism. Performance deteriorates close to and beyond this frequency. Furthermore, introducing mass into the system lowers the eigenfrequencies, thereby compromising the robot’s controller bandwidth and dynamic performance. Alternatively, it is demonstrated that a partial balancing solution accomplishes an 80 % shaking force reduction without the loss of controller bandwidth, paving the way for high-speed robots that do not disrupt adjacent high-precision machinery.