Synthesis of mechanisms with their center of mass (CoM) at an invariant point on one of the elements is useful for the design of statically balanced and shaking-force balanced mechanisms and manipulators. For this purpose, a kinematic architecture based on a general 4R four-bar linkage is found by applying the method of principal vectors as a linkage together with a similar four-bar linkage. The balance conditions are obtained for an arbitrary mass distribution of each of the elements and a balanced grasper mechanism and a balanced two-degree-of-freedom manipulator are derived as practical examples.