An improved pendulum method for the determination of the center of gravity and inertia tensor for irregular-shaped bodies

Abstract

An improved Trifilar Torsional Pendulum (TTP) for the experimental determination of the Center of Gravity (C.G.) and inertia tensor (the three moments of inertia and the three products of inertia) for an irregular-shaped body is proposed and developed. In the improved apparatus, a universal joint is adopted to facilitate the adjustments of the C.G. of the body in line with the pendulum axis. To enhance the precision of the measurement, a tri-coordinate measuring machine is employed to measure the coordinates of the predefined points and vectors of axes, which are then used for calculating the C.G. and inertia tensor for an irregular-shaped body. The theoretical fundaments of an improved TTP, the experimental setup, data processing procedures, and error estimation for measuring C.G. and inertia tensor are presented. With the proposed TTP and data processing procedure, the relative error in the determination of the moments of inertia can be estimated within 1%, and the deviation of the measured C.G. to the theoretical C.G. is within 1.5 mm. An example is given to demonstrate the effectiveness of the new approaches.