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On the balancers of any frequency term of the shaking moment of spatial mechanisms

Abstract It is proved in this paper that the hodograph of a frequency term (for example the kth frequency term) of the shaking moment of spatial mechanisms is an ellipse. Furthermore, expressions are provided for the lengths and attitudes of the semi-axes of this ellipse in terms of Fourier coefficients of the shaking moment. Accordingly, two equivalent systems of the kth frequency term of the shaking moment can be found; consequently two types of their balancers are proposed. A 7-R linkage is used as a numerical example for demonstrating the effects of the balancers. Additionally, it is also shown that the result of a previous work by other researchers, concerning the optimum balancing of a frequency term of pitching and yawing components of the shaking moment of high-speed machinery, is a special case of this study; furthermore, additional to the balancer they proposed, another is provided.