817. Angle of Inclination From One Measuring System


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J T McGee: 817. Angle of Inclination From One Measuring System. 1970.



If the location of a body’s principal axes can be determined from data taken from one measuring system instead of two or three measuring systems, there is the possibility of increased accuracy and the reduction in required equipment investment and operation time required to obtain data. This paper presents the theory, develops the controlling equations of the measurement system, and gives experimental results from measurements of known incremental mass property changes to a test body. Three well-established principles are the basis of the measuring system’s theory of operation and controlling equations.
1. A body that is free to turn about any axis will try to align itself so that it spins about the axis of its maximum moment of inertia.
a. Similarly, if a body is gimbaled about an axis that is perpendicular to and intersects the axis of rotation, the body will try to align itself so that it spins about the axis of maximum moment in the plane that contains the axis of rotation and is perpendicular to the gimbal axis.
2. The product of inertia of a body varies as the sine of twice the angle the body’s principal axes form with the measuring system’s reference frame.
3. The moment of a couple is independent of the position or orientation of any moment axis.
The curve which describes the relationship between the product of inertia of the test body and the angle its datum axes form with the measuring system’s reference frame is determined from the results of experimental data input to the system’s controlling equations. A curve for two orthogonal planes must be determined to provide the body’s principal axes location by orthogonal projection. The measuring system used to obtain data for evaluation in this paper was an experimental model. Refinements could certainly be made to most of the system’s measurement elements. However, the purpose of this evaluation is to establish the analytical soundness and give an indication of the potential of measuring systems utilizing the principles above.


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