Industrial robots are commonly used in various industries due to their flexibility. However, their adoption for machining tasks is minimal because of the low dynamic stiffness characteristic of serial kinematic chains. To overcome this problem, we propose coupling two industrial robots at the flanges to form a parallel kinematic machining system. Although parallel kinematic chains are inherently stiffer, one possible disadvantage of the proposed system is that it is heavily overactuated. We perform a modal analysis to show that this may be an advantage, as the redundant degrees of freedom can be used to shift the natural frequencies by applying tension to the coupling module. To demonstrate the validity of our approach, we perform a milling experiment using our coupled system. An external measurement system is used to show that tensioning the coupling module causes a deformation of the system. We further show that this deformation is static over the tool path and can be compensated for.