<p>The reduced multibody system transfer matrix method is a multibody system dynamics method adopting tree topology description and utilizing joint coordinates as the generalized coordinates of the system. For a multibody system containing closed loops, it is necessary to “cut” a joint in each inner loop, which will be replaced by geometric constraint equations confined on the generalized coordinates of the spanning tree system, as well as a pair of internal forces in equilibrium implied on the two connected body elements. The reduced multibody system transfer matrix method employs relatively lower order coefficient matrices that are independent of the degrees of freedom of the system, resulting in faster computational speed compared to those methods that establish and solve the global dynamics equations of the system characterized by the global inertial matrix, whose dimension is no less than the degrees of freedom of the system, no matter utilizing joint coordinates or not. However, in the process of multibody system dynamics modeling, the redundancy in constraints, which causes rank deficiency of the constraint equations’ Jacobian matrix, is an unavoidable problem. In this paper, an algorithm based on the singular value decomposition is proposed to resolve the singularity problem in the context of reduced multibody system transfer matrix method when handling redundant constraints. The singular value decomposition is utilized to compute the Moore-Penrose generalized inverse, resulting in the minimum norm solution for the constraint forces at the cut-off joints within closed-loop constraints. The proposed method is validated by two numerical examples.</p>