  Universal sensing the motion of mechanical resonators with high precision and
low back-action is of paramount importance in ultra-weak signal detection which
plays a fundamental role in modern physics. Here we present a universal scheme
that transfer mechanically the motion of the resonator not directly measurable
to the one can be precisely measured using mechanical frequency conversion.
Demonstration of the scheme at room temperature shows that both the motion
imprecision and the back-action force are below the intrinsic level of the
objective resonator, which agree well with our theoretical prediction. The
scheme developed here provides an effective interface between an arbitrary
mechanical resonator and a high quantum efficient displacement sensor, and is
expected to find extensive applications in high-demanding mechanical-based
force measurements.
