ON THE BALANCERS OF ANY FREQUENCY TERM OF THE SHAKING MOMENT OF SPATIAL MECHANISMS

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 mech anisms is an ellipse. Furthermore, expressions are provided for the le ngths and attitudes of the semi-axes of this ellipse in terms of Fouri er coefficients of the shaking moment. Accordingly, two equivalent sys tems of the kth frequency term of the shaking moment can be found; con sequently two types of their balancers are proposed. A 7-R linkage is used as a numerical example for demonstrating the effects of the balan cers. Additionally, it is also shown that the result of a previous wor k by other researchers, concerning the optimum balancing of a frequenc y term of pitching and yawing components of the shaking moment of high -speed machinery, is a special case of this study; furthermore, additi onal to the balancer they proposed, another is provided.