In this paper, based on the concept of natural orthogonal complement, an algorithm is devised to analyze the inverse and forward dynamics and dynamic sensitivity of n-linkage planar serial robots. The first goal is to derive the governing dynamic equations of a planar serial robot systematically, more precisely, number of the linkages, mass, moment of inertia and the length of the linkages are the inputs of the algorithm and the output will be the dynamics equations of the robot. As a comparison study, a planar serial mechanism, namely, dynamic modeling of 6R serial revolute manipulator is investigated and the results of the proposed algorithm are compared with other methods, i.e, Adams software and MatODE. In the next step, in order to develop a dynamic sensitivity analysis scheme, Sobol and EFAST methods are employed. By the use of the dynamic equations of the robots, the sensitivity of the actuating torques to the design parameters such as mass and length of the linkages is analyzed. Dynamic sensitivity of three planar serial robots namely, 2R-PSM, 3R-PSM and 6R-PSM is studied in two different configurations such as singular and isotropic. At the end, the effects of various angular velocities on the sensitivity of actuated torques to the design parameters are investigated. The obtained results reveal that the tolerance of uncertainty in the design parameters of robot affects the actuating torques significantly and also the Sobol’s method predict the sensitivity of the robot more precisely.