This paper presents the static balancing design of a special reconfigurable linkage that can switch between two one-degree-of-freedom (DoF) working configurations. We will show that the studied dual-mode linkage only requires one mechanical spring or one counterweight for completely balancing its gravitational effect in theory at both modes. First, the theoretical models of the spring-based and the counterweight-based designs are derived. The proposed design concepts were then demonstrated by a numerical example and validated by software simulation. Experimental tests on both designs were also performed. The result of this study shows that a reconfigurable mechanism with N working configurations can be completely statically balanced by using less than N passive energy elements.