Modeling and simulation of critical force and time in 3D manipulations using rectangular, V-shaped and dagger-shaped cantilevers

• A comprehensive algorithm for different cantilever geometries has been proposed.
• Dynamic cantilever force has been introduced.
• The critical time-force for pushing cylindrical nanoparticles has been obtained.
• All the effective parameters have been investigated.

The AFM-based nanorobots are extensively used nowadays for transferring and displacing various nano particles. Because of not being able to simultaneously perform and observe a manipulation operation, simulating the motion dynamics of nano particles in a manipulation operation has greatly attracted the attention of many researchers. This paper has focused on the 3D modeling of motion dynamics by using different cantilevers (rectangular, V-shaped and dagger-shaped) and has simulated the kinematics and dynamics of a manipulation operation. In order to validate the results, by gradually reducing the 3D parameters, the obtained results have been compared with the 2D manipulation results. The simulations have been extended to the rolling, sliding and spinning motion modes. Also, the first critical force and time for the sliding motion mode and the second critical force and time for the spinning motion mode have been simulated for all three types of cantilevers (rectangular, V-shaped and dagger-shaped). By employing the algorithm presented in this paper, it is possible to carry out precise manipulations of nano particles by means of the three mentioned cantilevers. At the end, all the effective geometrical and operational parameters have been investigated.