THE IDEAL LOCATIONS FOR THE CONTRA-ROTATING SHAFTS OF GENERALIZED LANCHESTER BALANCERS

The inertia Of the moving parts of high-speed planar mechanisms create s a shaking force that is variable in magnitude, direction and line of action throughout a cycle. Alternatively, the instantaneous shaking f orce vector can be represented by an equal parallel force acting throu gh an arbitrarily chosen origin, together with a moment about that ori gin. The two components of the force and the moment can be computed by kinetostatic analysis at discrete intervals of a cycle to create thre e arrays. The discrete Fourier transform converts these arrays from th e time to the frequency domain. The lowest frequency term of order k = 1 is of cycle frequency. Terms of higher order k > 1 have frequencies that are k times cycle frequency. The shaking force frequency term of order k can be represented by two contra-rotating-force vectors of co nstant, but generally unequal, magnitude rotating at k times cycle fre quency. The forces can be eliminated by equal and opposite forces exer ted by counterweights mounted on contra-rotating shafts rotating at th e same speed. However, if the locations of these shafts are both arbit rarily chosen, a shaking couple of order k will generally remain unbal anced. Fast Fourier transform (FFT) analysis of the array of moments a s well as the force components enables suitable shaft locations to be determined in such a way that this couple vanishes. The couple vanishe s if the balancing shafts are coaxial with a centre at an invariant lo cation in the plane. The couple can also be eliminated even though the location of either shaft, but not both, is chosen arbitrarily. The lo cation of the second shaft is then determinate and two procedures are explained to determine that location.