Abstract
The k th frequency term of the shaking force of high speed spatial mechanisms can be represented by three rotating force vectors of constant, but generally unequal, magnitude rotating on three mutually perpendicular 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 shaking couple will generally remain unbalanced. The equivalent system of the moment as well as the force components enables suitable shaft locations to be determined in such a way that this couple vanishes. The couple can be eliminated even though the location of one shaft among three 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 to demonstrate the theory and the balancing effects of the three-rotating-mass balancers.
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