An RGGR spatial mechanism with constant input speed and arbitrary link dimensions is considered. The coupler is a thin straight rod. The masses of the moving links are distributed so that the centre of their total mass is stat-ionary throughout the mechanism cycle to insure that the resultant shaking force transmitted to ground due to the inertia effects on the moving links vanishes. This is achieved by fixing two balancing weights to the input and output links. The balancing weight attached to the ouput link is a solid cylinder with the greatest feasible length, and with the axis of rotation of the output link coinciding with one of the generators of its cylinderical surface. The parallel plane sides of this balancing weight are, in general, inclined to its axis. Both balancing weights are so designed that the Root-ivlean-Square shaking moment arising from the force-balanced mechanism is minimum. Anumerical example is presented.