Application of Line geometry to theoretical kinematics and the kinematic analysis of mechanical systems

The theory of screws as developed by R. S. Ball, is concerned principally with rigid-body motions in three-dimensional Euclidean space. A number of scattered references, notably F. Klein [18], have mentioned algebraic approaches to the subject. In this paper which is essentially tutorial, we have used concepts of line geometry in order to present such a self-contained algebraic formulation. Other approaches to the subject, which are not considered here, are possible and useful: for example, motor algebra (F. M. Dimentberg) and surface geometry (K. H. Hunt, K. J. Waldron). The algebraic treatment is both general and well-adapted to kinematic analysis and numerical methods. These applications have been described. © 1970.