The Hodograph and the Balancer of any Frequency Term of the Shaking Force 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 force 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 force. Accordingly, a pair of counterweights, contra-rotating at k times of cycle frequency with their axes parallel to the unit normal vector of the hodograph plane, can be installed for eliminating the frequency term of the shaking force of spatial mechanisms. An example of a seven-link 7-R spatial linkage is included.