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This paper presents the investigation of general formulation and numerical solution of the dynamic load carrying capacity (DLCC) of flexible link manipulator. The proposed method is based on open loop optimal control problem. A two point boundary value problem (TPBVP) is provided, extracted from the Pontryagin's minimum principle. The indirect approach is employed to derive optimality conditions. The system’s dynamics equation of motion is obtained from Gibbs-Appell (G-A) formulation and assumed mode method (AMM). Elastic properties of the links are modeled according to the assumption of Timoshenko beam theory (TBT) and its associated mode shapes. As TBT is more accurate compared with the Euler-Bernoulli beam theory, it is exploited for mathematical modeling of flexible links. The main contribution of the paper is to calculate the maximum allowable load of a flexible link robot while an optimal trajectory is provided. Finally, the result of the simulation and experimental platform are compared for a two-link flexible arm to verify the introduced technique. The efficiency of the proposed method is illustrated by performing some simulation studies on the IUST flexible link manipulator. Simulation and experimental results confirm the validity of the claimed capability for controlling point-to-point motion of the proposed method and its application toward DLCC calculation.

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Nowadays, movement of micro/nano particles has been attracted considerable attention to manufacturing different devices in micro/nano scale and medical and biological applications. Atomic Force Microscope Probe is widely being used for precise small scale movements. During nano-manipulation, micro/nano particles can be moved to a desired destination with high accuracy using Atomic Force Microscope while in contact mode with precise probe control. In this article, by selecting a proper amount of torque applied to the probe tip, deviation from the center and movement of probe have been investigated to assure the contact between the probe and micro/nano particle. Different liquid environments (water, alcohol, and plasma) with different micro/nano particles including biological and non-biological have been used for this investigation. In addition, using sliding mode control, Atomic Force Microscope Probe was used in different environments such as water, alcohol, and plasma. Obtained results showed that the time needed to control different micro/nano particles in plasma was shorter than that of in water; also the time needed in water was shorter than that of in alcohol.