This paper presents the analysis of a gravity compensated four-bar linkage mechanism with zero-free-length linear spring suspension. The objective of the study is to seek the possibility of employing the four-bar linkage or similar mechanisms for assisting vertical planar motion of a load mass in a gravitational field. The analysis is based on the system potential energy framework. Firstly, an arrangement of springs for gravity compensation in a four-bar linkage mechanism is proposed. It is then shown that for a four-bar linkage with symmetric geometric and mass properties the potential energy of the system has interesting and useful characteristics near the configuration at which the middle link is horizontal: an ideal operating configuration. The study also covers more practical cases where there is asymmetry in the mass distribution. The potential use of the mechanism in these cases is validated through a study of the sensitivity of the system potential energy function around the equilibrium point. Finally, based on the results obtained a novel mechanism is proposed for achieving gravity compensated vertical plane motion of a load mass. The proposed mechanism can have a wide range of travel and has significant potential for use not only in low-speed mechanical systems but also in high-speed heavy automated systems, where operating accelerations are of the order of 1g or less.