An efficient and accurate evaluation of the robots dynamics efforts plays an important role in both the analysis of its behavior and the synthesis of appropriate controllers.This paper proposes an efficient methodology which is based on Lie group,for the evaluation of the manipulators high-order kinematics and dynamics.In particular,the proposed method derives the generalized velocities,accelerations and jerks so as to evaluate the first derivative of the generalized forces.The main advantage of this approach is that evaluated formulations are shown to be more concise,computationally effective and easily differentiated with the exponential operation.The simple closed-form set of equations of kinematics,dynamics and corresponding derivatives that are particularly useful for applications in robot design and online applications.