There are two principal methods to derivate motion of equation of robot manipulator, which are Newton-Euler (NE) method and Lagrange method. The NE method enables to make a dynamical model of robots and it is possible to calculate internal force and torque not generating real motion of robot manipulator, seemed to be an advantage of the NE method that Lagrange method does not have. This merit can be applicable for propagations of constraint and impact force/torque when discussing humanoids walking based on strict dynamical models. So far, the NE method has been applied to a robot of open-loop serial-linkage structure. However, the NE method has been limited to a motion without contacting with environment. Although robot task to the hand contact with environment, for example assembly task, grinding task is important, it has not been formulated in the way of the NE method. So, this paper proposes iterative calculation method for representing constraint dynamical motion of robot manipulator utilizing inverse dynamic calculation the NE method, leading and enabling the forward dynamics calculation of constraint motions to be dealt recursively through proposed the extended NE method for constraint motions, with no use of explicit representation of equation of motions. We applied this method to 2-linkage and 3-linkage manipulators and evaluated its validity by numerical simulations.