We present a new mechanical oscillator architecture that can be made insensitive to linear and angular accelerations while keeping constant oscillation frequency. The oscillator has the kinematics of a Watt linkage, so we call it a Watt oscillator. In order to predict its behaviour when it is subjected to external forces, we propose an analytical model using simplifying hypotheses. The solutions given by the analytical model were tested using an FEM model in order to obtain a dynamically balanced mechanism with frequency insensitive to external forces. A satisfactory correspondence between theory and FEM was found.