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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.

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In this study, a modified method has been introduced for forward dynamic analysis of fast parallel robots. For this purpose, inspired by the Lagrange-Virtual Spring (LVS) method, the Decoupled Natural Orthogonal Complement (DeNOC) method is modified which is a Newtonian based method. So far, virtual springs have been already used in energy based methods. However using the virtual springs in DeNOC method is a novel approach which is proposed in current study. In order to clarify the advantages of Modified Decoupled Natural Orthogonal Complement (MDeNOC) method, a planar 3RRR mechanism is chosen as case study. According to the results, the process of deriving the equations of motion is much less costly while the accuracy of MDeNOC is similar to the LVS and unlike the energy methods, the modified method is also able to calculate the constraint reactions, as well. On the other hand, the calculation time of MDeNOC is much more than the DeNOC and hence, is not suitable for real time calculations. Also, in closed loop systems, constraints must be defined in such a way that express the virtual springs’ longitudinal changes; otherwise, MDeNOC will not give proper results.