Abstract
The finite displacement transformation formulae are presented for the most general case of rigid body translation and rotation, which is consistent with Chasle's theorem. Then, a conversion is made from the scaler presentation on the x, y, and z axes to the vector presentation. The results are then presented considering the following: (1) the case where the rotation axis passes through the origin and the translation part of the total displacements does not exist, which leads to the finite rotation transformation matrix; and (2) the case of small rotations, which simplifies the results.
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