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

Geometry of screw systems. Classification of two- and three-systems of screws. Persistent screw systems: definition, conditions and examples

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 mechanisms. Derivation of input-output velocity equations and singularity conditions

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