The material addresses subjects sufficiently fundamental to be within the desirable competence of any mechanical roboticist, and in each area advanced screw-theory based methods have been used to great advantage.

Basic vector-space properties of twists and wrenches: physical interpretation of the linear operations; linear dependence and independence, subspaces; bases and coordinates.

Scalar products, dual spaces, reciprocity. Constraint and freedom in mechanisms. Constraint analysis. Type synthesis of single-loop mechanisms and parallel manipulators.

Velocity and singularity analysis of parallel and interconnected-chain mechanisms. Derivation of input-output velocity equations and singularity conditions.

Mappings between screw spaces, stiffness, and inertia. Structure of robot compliance. Eigenvalue problems and eigenscrews. Synthesis with springs.

6D formulation of the dynamics of individual rigid bodies and rigid-body systems. Equations of motion. Dynamics algorithms.

Basic Lie group theory, matrix representations of the group of rigid-body displacements. Lie algebras as related to screw theory. The exponential map and its applications in modern robotics.