Nowadays, the displacement of nanoparticles by means of the atomic force microscope nanorobot is widely used in nanomanufacturing process. Because of not being able to simultaneously observe the manipulation process, the dynamic models for motion modes are of great use. For precise displacement of cylindrical nanoparticles, it is essential to know the moment the particle dislodges from the substrate and the maximum magnitude of force exerted on the particle during the operation. However, the focus of existing models is mainly on manipulation of spherical particles and fails to address the manipulation of cylindrical particles which needs a more comprehensive approach. In this paper, a comprehensive algorithm by which the critical time and force can be determined is developed. By using the proposed algorithm, the maximum angle of spinning is specified. The paper also examines the effects of environmental, operational, and geometrical parameters on the critical force and time. In order to validate the results, simulations have been compared with existing experimental findings. Also by gradually reducing the effect of the comprehensive model, this model has been compared with the existing model for manipulation of spherical particles. By applying the presented algorithm, it is possible to precisely displace cylindrical nanoparticles and use them to build nanostructures.