Chaplygins nonholonomic systems[1, 2] are familiar mechanical systems subject to unintegrable linear constraints, whose equations of motion are derived from the Lagrange-dAlembert principle together with an assumption of ideal constraints and Chetaevs condition, and the constraints and Lagrangian admit as many number of ignorable or cyclic coordinates as that of the constraints the systems are subject to.Of course, the equations of motion can also be derived from the Hamiltonian principle embedded variation identity[3].Such a characteristic of Chaplygins systems makes their second-order equations of motion decouple with the first-order nonholonomic constraints, which leads to a reduction of the systems into conditional holonomic nonconservative systems.It is proved that the reduced configuration manifold as a submanifold of the total configuration of Chaplygins systems is a Riemann-Cartan manifold, whose torsion is determined by the nonintegrability of the linear constraints.