Computational and analytical works have shown that certain coupling schemes can lead to significant enhancements in sensitivity, accuracy, and lower costs for a wide range of sensor devices whose output and performance depends directly on the ability of individual units to generate stable limit cycle oscillations. Vibratory gyroscopes are very good candidates for this new paradigm as their accuracy and sensitivity are directly dependent on the ability of a driving signal to produce and maintain oscillations with stable amplitude, phase, and frequency. To achieve higher accuracy, we show proof of concept of a novel scheme: a drive-free coupled gyroscope system in which the coupling alone can lead to self-regulated limit cycle oscillations in the drive- and sense-axes with stable constant amplitude and phase-locking.