Counterbalancing mechanisms considerably reduce the size of actuators in serial robots. However, by limiting the joints' angles, imposing dead-point configurations, adding extra links, and attaching heavy/bulky balancing springs/counterweights, they sacrifice the dexterity of serial robots. Such limitations prevent serial robots from being implemented in significant robotic applications including biomedical robotic tasks. This paper proposes a novel cable-driven mechanism which addresses all of these limitations and simultaneously moves all actuators to the base. Via a kinematic and potential energy analysis, effectiveness of the proposed mechanism is proven. In order to experimentally evaluate the proposed approach, a fully-balanced four-link serial arm is fabricated and tested which shows 81.7% reduction in the average torque of the actuators. In order to provide maximum dexterity level with the minimum number of components in the proposed mechanism, an optimal design approach is proposed and studied. In this approach, the number of links to reach a desired target along a border-collision-free motion is minimized. Via different experimental and simulation examples, effectiveness of the proposed approach is demonstrated.