ABSTRACT
This chapter begins by presenting a pair of motivational examples and then presents a formal set of definitions. It presents a more modern treatment of the theory of screws based on linear algebra and matrix groups. The chapter provides a description of rigid body motion using the tools of linear algebra and screw theory. It describes the orientation of the body by giving the relative orientation between a coordinate frame attached to the body and a fixed or inertial coordinate frame. The chapter emphasizes the connection of other other representations with the exponential coordinates presented above; more classical treatments of other representations can be found in standard kinematics texts. It represents rigid motions by using rigid body transformations to describe the instantaneous position and orientation of a body coordinate frame relative to an inertial frame. The chapter refers to all transformations between coordinate frames as rigid body transformations, whether or not a rigid body is explicitly present.
