The recursive projection schemes used in most existing recursive methods for solid deformable structure dynamic problems in precision manufacturing systems lead to dense coefficient matrices in the acceleration equations and consequently there is a strong dynamic coupling between the joint and elastic coordinates. When the number of elastic degrees of freedom in engineering materials increases, the size of the coefficient matrix in the acceleration equations becomes large and consequently the use of these recursive methods for solving the joint and elastic accelerations becomes less efficient. This paper discusses the problems associated with the recursive projection schemes used in the existing recursive methods, and it is shown that decoupling the joint and elastic accelerations using the nonlinear recursive method requires the factorization of nonlinear matrices whose dimensions are independent of the number of elastic degrees of freedom of the multibody system. An amalgamated formulation that can be used to decouple the elastic and joint accelerations for different multibody manufacturing systems is then proposed. The use of the nonlinear recursive method developed in this paper is demonstrated using the open-loop and closedloop chains in precision manufacturing systems.