We propose a design method for a gravity compensator using unit spring balancers for multi-degree-of-freedom (DOF) and multilink manipulators. Existing spring balancers can be applied to a new design of a gravity compensator. When applying spring balancers to a new gravity compensator, it is necessary to determine how many spring balancers are required and where they should be placed. Our proposed design method can determine the number of spring balancers and their locations. In this study, the design of a spring balancer for multi-DOF and multilink manipulators is considered as a mapping between two spaces (i.e., the joint space for gravitational torques and the spring balancer space to compensate torques). The mapping matrix is obtained through eigenvalue analyses of the potential energy function. The number of rows of the mapping matrix represents the number of unit gravity compensators. The row vector of the mapping matrix also indicates the locations of the unit gravity compensators. Examples are presented to validate the effectiveness of the proposed method.