Basics of Kinematics

This chapter deals with the fundamentals of kinematics of spatial rigid body motions. The position, velocity, and acceleration of a rigid body in space are described vectorially. The time derivative of vectorial motion quantities with respect to different moving reference systems is defined. This leads to the relationships for the composition of two motions to one resulting motion, which have a significant relevance in the kinematics of multibody systems. Rigid body rotations are geometrically described by the axis-angle pair and the rotation tensor derived from it. It is shown how multiple rotations and the angular velocity of a rigid body can be interpreted geometrically. The Cardan and Euler angles, as well as the Euler and Rodrigues parameters derived from the axis-angle pair, are introduced as parameterizations of rotations and demonstrated with examples.