We propose a kinematic model of a system moving in an (m + 1)-dimensional euclidean space and consisting of n rigid bars attached successively to each other and subject to the nonholonomic constraints that the instantaneous velocity of the source point of each bar is parallel to that bar. We prove that the associated control system is controllable and feedback equivalent to the m-chained form around any regular configuration. As a consequence, we deduce that the n-bar system is flat and show that the Cartesian position of the source point of the last (from the top) bar is a flat output. The n-bar system is a natural generalisation of the n-trailer system and we provide a comparison of flatness properties of both systems.