Sphere mass center determination by velocity modulation

This paper presents a new technique, called velocity modulation, for measuring the mass center location of a sphere, improving upon the accuracy of previous methods by at least a factor of 4. The sphere is rolled down a set of parallel rails. The offset of the sphere’s mass center with respect to its geometric center modulates the sphere’s velocity at the rolling frequency, which is detected by a series of differential optical shadow sensors. The measured times that the sphere crosses the sensors is compared with a simplified mechanics model in order to recover the sphere’s mass center location. The precision of the technique is demonstrated by the repeatability of independent measurements in one plane of a 50.8 mm (2 in.) stainless steel gage sphere. The best standard deviation achieved is 145 nm (95% confidence interval = 227 nm).