The influence of flexibility on the force balance quality: a frequency domain approach

High accelerations of fast moving robots induce high fluctuating reaction forces and moments, resulting in undesirable vibrations and loss of accuracy. These fluctuations can be reduced or even eliminated by dynamic balancing techniques, e.g. by addition of counter-masses. However, these techniques typically disregard the flexibility of the mechanism. This flexibility potentially leads to undesirable eigenfrequencies and unbalance of an otherwise perfectly balanced mechanism. In this paper, the effect of link flexibility on the force balance quality is investigated in the frequency domain. This is done for a 2-DOF parallel manipulator with realistic stiffnesses. With the use of flexible multi-body software, the frequency transfer functions for the shaking forces are obtained for an unbalanced, a force balanced and a partially balanced case. The results show that, firstly, force balance results in a strong attenuation of the shaking forces’ frequency content up to the first eigenfrequency. Secondly, the addition of balance mass results in a reduction of the first parasitic eigenfrequency of the system leading to a worsened performance around the first eigenfrequency and a reduction in controller bandwidth. Identification of these effects leads to an optimal, intermediate solution, which mitigates the negative effects of dynamic balance, resulting in low-frequency shaking force attenuation of 30 dB without loss of controller bandwidth.