A gravity equilibrator is a statically balanced system which is designed to counterbalance a mass such that any preferred position is eliminated and thereby the required operating effort to move the mass is greatly reduced. Current spring-to-mass gravity equilibrators are limited in their range of motion as a result of constructional limitations. An increment of the range of motion is desired to expand the field of applications. The goal of this paper is to present a compact one degree-of-freedom mechanical gravity equilibrator that can statically balance a rotating pendulum over an unlimited range of motion. Static balance over an unlimited range of motion is achieved by a coaxial gear train that uses noncircular gears. These gears convert the continuous rotation of the pendulum into a reciprocating rotation of the torsion bars. The pitch curves of the noncircular gears are specifically designed to balance a rotating pendulum. The gear train design and the method to calculate the parameters and the pitch curves of the noncircular gears are presented. A prototype is designed and built to validate that the presented method can balance a pendulum over an unlimited range of motion. Experimental results show a work reduction of 87% compared to an unbalanced pendulum and the hysteresis in the mechanism is 36%.