Abstract
This work treats the kinematics of rigid bodies in general spatial motion using vector algebra. New results as well as other known properties are derived and expressed in simple form with geometrical reasoning and explanation. A special emphasis goes to the second-order motion properties. A simple definition and a geometrical approach for the investigation of the existence of the acceleration center is considered. The existence of a unique acceleration center or a single infinity of acceleration centers forming a line of acceleration centers is investigated in detail. The concept of the acceleration center is used to simply determine the acceleration of any point in the moving body in matrix form. Furthermore the distribution of the acceleration field corresponding to the acceleration center is studied in a systematic and easy way. It is believed that this is the first time this subject has been tackled from a general perspective, considering completely general the spatial motion of rigid bodies, in a simple and straightforward approach. Planar and spherical kinematics are stemmed as special cases of the kinematics of bodies in spatial motion. This study is intended to clear away the subject of second-order motion properties and lead to a general understanding.
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