Research on verticality of mass center measuring rotary table and concept and application of vector equalizing effect

Maintaining the verticality (parallel to the gravity axis) of a centroid measurement turntable's rotation axis with high precision is challenging. Traditional methods for adjusting verticality are often complex and difficult to sustain over time. Current adjustment methods are not always accurate or sustainable, necessitating a more effective solution. In this study, we seek to derive the variations in the angle between the rotation axis and the plumb line of the turntable. In doing so, we intend to develop a practical method to eliminate linear errors caused by non-vertical axes. We derive a specific equation based on the relationship between the rotation axis and the plumb line and validate it through experiments. We introduce the concept of "vector balancing effect" and establish a method to eliminate linear errors caused by non-vertical axes. As an application example, we propose a measurement technique for determining the lateral centroid by evenly distributing three weights along the circumference. This method aims to eliminate system errors related to non-vertical axes in centroid measurements based on the gravity axis. In our tests, we successfully reduced the lateral centroid error from approximately 0.16 mm to about 0.03 mm, which is very close to the non-verticality of 0.12 mm. This method provides valuable insights for achieving precise vertical axes in traditional experimental turntables.