On the line geometry of rigid-body inertia

© 2014, Springer-Verlag Wien. In this work, several classical ideas concerning the geometry of the inertia of a rigid body are revisited. This is done using a modern approach to screw theory. A screw, or more precisely a twist, is viewed as an element of the Lie algebra to the group of proper rigid-body displacements. Various moments of inertia, about lines, planes and points are considered as geometrical objects resulting from least-squares problems. This allows relations between the various inertias to be found quite simply. A brief review of classical line geometry is given; this includes an outline of the theory of the linear line complex and a brief introduction to quadratic line complexes. These are related to the geometry of the inertia of an arbitrary rigid body. Several classical problems concerning the mechanics of rigid bodies subject to impulsive wrenches are reviewed. We are able to correct a small error in Ball’s seminal treatise. The notion of spatial percussion axes is introduced, and these are used to solve a problem concerning the diagonalisation of the mass matrix of a two-joint robot.