ESDU 90007 gives methods for partially balancing single-degree-of-freedom multi-bar linkages by adding counterweights rotating at constant speed. The methods are (a) Lanchester Balancer using two equal counter rotating weights sized and aligned to eliminate a single frequency term of the frame shaking force@ (b) a single weight sized and aligned to minimise the average shaking force@ (c) Generalised Lanchester Balancer using two unequal counter rotating weights sized and aligned to eliminate a single frequency term of both the frame shaking force and moment@ and (d) a moment balancer using two equal weights rotating in the same direction and sized and aligned to eliminate only the first-order frequency of the frame shaking moment. The mass-moment and orientation of each counterweight are determined by a step-by-step procedure that@ in the case of the Generalised Lanchester Balancer@ also provides the location for the axis for the second counterweight. Worked examples show the practical use of the procedures in the design of a crank-rocker linkage and in retrofitting a slider-crank mechanism. A Fortran program of the method is provided on disc in the software volume (ESDUpac A9007) both uncompiled and compiled within ESDUview@ a user-friendly interface that prompts on-screen for input data and runs under MS DOS.