THE IDEAL SHAFT LOCATIONS OF 3-ROTATING-MASS BALANCERS FOR SPATIAL MECHANISMS

The k(th) frequency term of the shaking force of high speed spatial me chanisms can be represented by three rotating force vectors of constan t, but generally unequal, magnitude rotating on three mutually perpend icular planes at k times cycle frequency. The forces can be eliminated by equal and opposite forces exerted by counterweights mounted on the shafts rotating at the same speed. However, if the locations of these shafts are all arbitrarily chosen, the k(th) frequency term of the sh aking couple will generally remain unbalanced. The equivalent system o f the moment as well as the force components enables suitable shaft lo cations to be determined in such a way that this couple vanishes. The couple can be eliminated even though the location of one shaft among t hree is chosen arbitrarily, the locations of the other two shafts are then determined. An example of a 7 link 7-R spatial linkage is given t o demonstrate the theory and the balancing effects of the three-rotati ng-mass balancers.