It is a common movement type in industrial production for the end-effector of industrial manipulator executing tasks according to desired track. The high nonlinearity and coupling are shown from the dynamics characteristic of industrial manipulator because of the constrained relationship brought by desired task.Therefore,it is difficult to establish dynamical equation with traditional Lagrange equation. Aiming at the dynamics modeling of industrial manipulator subject to constraint,the additional torque and dynamical equation of industrial manipulator subject to some desired trajectory is acquired based on the famous Udwadia-Kalaba equation in analytical mechanics field. The disadvantage of obtaining dynamical equation from traditional Lagrange equation by Lagrange multiplier is overcome by the new approach. The stimulation results of the varying law of the joint angles and the motion path of the end-effector prove that the dynamical equation established by this method conforms to the matter of fact.