Abstract: As is now well-known, in literature no general method has yet been worked out for shaking force balancing of spatial linkages because of their complexities. In the present paper, a novel approach is introduced B y which the position vector of mass center of a certain moving link in a N-link spatial linkage can be appropriately resolved according to linkage structure characteristics. With the aid of direction cosine matrices and matrix loop equations, the position vector of mass center of such a link as R-R, R-P and P-S in linkages can be fully expressed in terms of the motion parameters of other links. Then the shaking force of the entire linkage may be fully balanced without attaching any counterweights to these links. For other kind of links, such as R-C, R-E, S-R, S-C and S-S, some components of the position vector of link mass center are expressed by motion parameters of other links as much as possible. As a consequence, it is possible to attach smaller counterweights to these links according to supplementary balancing conditions. The equations for the full shaking force balancing of single-loop spatial linkages such as RRRSR, RRCS, RRRCRR, RRERR RRSS',RSCR, RSS'R and RRPSR are derived as examples. In addition, a numerical example is given for full shaking force balancing of Bnnett's linkage.