Kinematics ofKinematicsrigid-body systems constrained systems of rigid bodies is analyzed. First, an unconstrained rigid body is considered in its rest (reference) position, undergoing a geometrical transformation which leads it into a new (current) position. Six generalized displacements describing the transformation are defined, and a General Formula, giving the displacements of all points as a function of the former quantities, is derived. Attention is focused on infinitesimal displacements for which all the kinematic relationships are linearized. A system of rigid bodies is then considered, whose current configuration is described by the set of the generalized displacements of all bodies. Constraints are successively introduced, of internal and external type, and their multiplicity is discussed. The kinematic problem is formulated: it consists of determining the current configuration assumed by a system of rigid bodies under prescribed displacement at constraints and/or distortions. Depending on the number and on the geometry of the constraints versus the number of the degrees-of-freedom of the system deprived of constraints, a classification is performed, based on the Rouché-Capelli Theorem. Four classes are recognized: kinematically determined, under-determined, over-determined and degenerate systems, for each of which the solutions to the kinematic problem (if any, and possibly not unique) are found. Graphic methods, giving insight into the mechanical behavior of planar kinematically determined systems, are also illustrated.