Abstract: The dynamic problem of constrained multibody systems in Riemannian configuration space is researched. The orthonormal bases of normal subspace and tangent subspace of the system manifold are constructed adopting the singular value decomposition of the constraint matrix and a modified Gram-Schmidt process. The dynamic equations of the system are projected along the dual bases, and new formulas of the system dynamic response are obtained. A numerical analysis method is also given. A numerical example is prese...