This paper proposes a design method of a static balancing mechanism using unit gravity compensators (e.g., 1-dof gravity compensator). In the design of a multi-dofs static balancing mechanism it is necessary to determine how many springs (or unit gravity compensators) are required and where they should be placed. This problem can be overcome by computing the mapping matrix between the joint space and gravity compensator space. The mapping matrix is obtained by analyses of the potential energy function. The number of rows of the mapping matrix indicates the amount of unit gravity compensators and linear joint constraints representing locations of unit gravity compensators. Example studies are presented to verify the effectiveness of the proposed method. Simulations are performed in that static balancing mechanisms designed by the proposed method can counterbalance the gravitational torques completely.