Discovering Razi acceleration in multiple rotating coordinate frames system

This paper outlines the procedure of calculating inertial acceleration in a kinematic system involving more than two relatively rotating coordinate frames. The equation of relative motion between two frames - one inertial and one rotating - exhibits inertial acceleration terms like centripetal, Coriolis and tangential accelerations. It is shown that by introducing a third relatively-rotating frame, the Razi acceleration term appears in the equation, complementing the three aforementioned inertial acceleration terms. This is demonstrated by extending the application of Euler derivative transformation formula to include multiple coordinate frames. To show the appearance of the Razi acceleration, an experimental investigation is conducted using a multiple-axis robotic arm to simulate an "enclosed rotation" motion. A sensor is attached to the end-effector of the robotic arm to measure its acceleration. A comparison of the result with the equation produced by the derivative transformation formula is presented to show the effect of the Razi acceleration on a rigid body undergoing rotation about multiple axes