Projective Geometry in Kinematics

Abstract: In this thesis, we study projective geometry and show a connection to kinematics. We show how the group of rigid body motions in three-dimensional space can be parameterized on a hyperbolic quadric in a seven-dimensional projective space. We also show that this quadric is a geometry with triality, and we discuss triality from a kinematic viewpoint. Finally, we discuss topics for further research based on this theory.