The software, implementing mathematical models of 2D and 3D active exoskeletons with electric drives, has been developed in the environment of universal computer mathematical system "Wolfram Mathematica". Each model has the same structure and includes five mobile links. Generalization of these models for the case of arbitrary finite number of n links is made. The angles, calculated between the links of the models, are used in the software described in the article, which differ these models from the existing ones. Cylindrical hinges are used for the articulated interconnection of the links in the 2D model. As for the 3D model, the spherical hinges perfectly implement all mobility degrees available in the human musculoskeletal system. This fact also differ the proposed 3D model from the existing ones, which have limited mobility and use not only spherical, but also cylindrical hinges to join some links in order to reduce dimension of the system of differential equations of motion. The comparative analysis of the obtained mathematical models for the two mechanisms in the form of Lagrange equations of the second kind is made. The system of electromechanical equations for the model using asynchronous AC motor is listed. The solution of direct and inverse dynamics problems is given for 2D model. As for the 3D model, no numerical solution of the Cauchy problem has been obtained due to large dimension of the system of differential equations of motion and limited computing power. Therefore, the idea about exoskeleton motion control model based on artificial intelligence that needs to be developed is suggested.