Nowadays, atomic force microscopy has widely attracted researchers’ attention in manufacturing of micro/nano equipment. For this purpose, the displacement and manipulation equations for micro/nano-particle are essential. Although surface forces such as friction and adhesion are ignorable in macro scale, increased surface to volume ratio in micro/nano scale makes them very important. Various friction models have been used for two-dimensional manipulation in previous works. In this paper, HK friction model has been used to model and simulate three dimensional manipulation dynamically in order to have closer results to real manipulation. For this purpose, the important friction models have been studied and developed to use in micro/nano scale. Then, three-dimensional manipulation equations have been obtained and stiffness coefficient matrix for beam is extracted and all these equations have been combined to calculate the critical force and time of manipulation. Finally, simulation of obtained equations was used to calculate the critical force and time values of the three-dimensional manipulation for gold particle using HK friction model. The results indicate that rolling starts around x-axis before y-axis, and sliding starts along y-axis before x-axis.

Keywords: HK friction model, Au nanoparticle, 3D-manipulation, Atomic force microscope

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