Aiming at the contact impact problem caused by the manipulator in the course of operating, a method of determining the state of the system after contact collision is proposed based on the impulse principle and Gauss’ principle of least constraint. First of all, the dynamic model of the manipulator system is proposed based on Lagrange equation, besides the solution model of the external impulse of collision of the system under the collision is derived according to the classical collision theory and the equation involving coefficient of restitution; the velocity of collision point is decoupled from the impulse of collision, which is beneficial to the calculation. Secondly, based on the Gauss’ principle of least constraint and the state variables of the system before the contact collision, the instantaneous velocity solution equation of the manipulator system after collision is established according to the method of solving the extreme value of a multivariable function; according to the speed after the impact, it can be determined whether the angular velocity of the manipulator is fit for the permited working range. Finally, taking a planar three link manipulator as an example for collision dynamics modeling and simulation result, the size of the external impulse of collision and the change regularity of the manipulators’ angular velocities and each joint angle before and after the collision of the system are studied and analyzed，the driving moment required of each joint is given according to the change regularity of each joint angle before and after the collision. The research shows that the joint will have a rigid impact and each rod will shake at the collision instantaneous; the impulse of collision will be changed in the form of diminishing by the way of the distal joint to the proximal joint. The obtained conclusion in this paper may provide a theoretical basis for the motion control of the manipulator under the external impact.