The Manipulatordynamicsdynamic model of a robot plays an important role for the analysis of manipulator structures, simulation of motion, and the design of control algorithms. The analysis of the dynamic model can be helpful in the mechanical design of prototype robots. Simulating robot motion allows motion planning techniques and control strategies to be tested without the need of a physically available system. Computation of the forces and torques required for the execution of typical motions provides useful information for sizing actuators and transmissions. The chapter starts by defining the problems of direct dynamics and inverse dynamics and discussing their relevance. Two methods are presented for deriving the equations of motion of a robot in configuration space. The first method uses an Euler–Lagrange formulation, which is based on the computation of kinetic and potential energy of the mechanical system, with additional specific features in the case of manipulators. This systematic approach leads to closed-form symbolic equations, highlighting the general properties of the dynamic model. In particular, the linearity property of the model in terms of a set of dynamic coefficients is used to address the problem of dynamic identification of the model. The analytical derivation of the dynamic model of simple manipulator structures is presented. The second method is based on a Newton–Euler formulation and proceeds from the inertial balance of forces and torques acting on the individual robot bodies. Using the kinematic structure of robot manipulators, this method yields a model in a recursive numerical form that is computationally efficient for simulation and real-time control. In addition, a technique for dynamic scaling of trajectories is introduced, which adapts the timing law to the dynamic characteristics of the robot. The chapter ends by deriving the robot dynamic model in task space and by considering the modifications of the dynamics in the presence of geometric constraints.