  The Newtonian constant of gravitation $G$ historically has the largest
relative uncertainty over all other fundamental constants with some
discrepancies in values between different measurements. We propose a new scheme
to measure $G$ by detecting the position of a test mass in a precision
displacement sensor induced by a force modulation from periodically rotating
source masses. To seek different kinds of experimental setups, laser
interferometers for the gravitational wave detection and optically-levitated
microspheres are analyzed. The high sensitivity of the gravitational wave
detectors to the displacement is advantageous to have a high signal-to-noise
ratio of $10^{-6}$ with a few hours of the measurement time, whereas the
tunability of parameters in optically-levitated microspheres can enable
competitive measurements with a smaller scale setup dedicated to the $G$
measurement. To achieve an accuracy of $G$ better than currently available
measurements, developments in force calibration is essential. These
measurements can provide an alternative method to measure $G$ precisely,
potentially leading to the improvement in the accuracy of $G$, as well as a
better search for non-Newtonian gravity at a length scale of $\sim1$ m.
