Discrete kinematic systems: Basic relations of combinatorial kinematics

The study examines the properties of rigid body systems and generally discrete kinematic systems with group and network theory methods. It formulates the loop law – the constraint equation of closed cyclic subsystems – for discretionary motion groups, and deduces therefrom a logically complete collection of formulas for structure, degree of freedom and degree of constraint. The name combinatorial kinematics is proposed for this chapter of kinematics, based on correlations and involved in structural analysis and synthesis, without limiting its scope to specific system types.