In this paper, the projective function synchro-nization of chaos between two gyroscope systems with dis-tinct behaviors is investigated under sinusoidal constraints.The objective of the research is to adjust a current gyroscopesystem to the idealized behaviors in design through synchro-nization. From the theory of discontinuous dynamical sys-tems, the mechanism of function synchronization of chaoticmotionsisstudied.Theanalyticalconditionsforthefunctionsynchronizationareachieved,andtheinvariantdomainofthefunctionsynchronizationisobtained.Numericalillustrationsfor partial and full, projective function synchronization oftwo gyroscopes with different dynamical behaviors are car-riedout.Thescalingfactorsinsuchfunctionsynchronizationare satisfied through numerical results.