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In this paper, differential quadrature element method (DQEM) is used to analyze the free transverse vibration of multi-stepped rotors resting on multiple bearings. Timoshenko beam theory is used to show the gyroscopic effects; Also each bearing is replaced with four springs; two translational and two rotational acting on two perpendicular directions. Governing equations, compatibility conditions at the each step and each bearing and external boundary conditions are derived and formulated by the differential quadrature rules. First, convergence and versatility of the proposed method are tested by the presented exact solutions. Then, the Campbell diagram is derived for a desired case study and variation of natural frequencies is investigated versus angular velocity of spin. The most advantage of the proposed method is being less time-consuming in comparison with the other methods, especially for cases with high number of steps and bearings. Accuracy of the proposed method is confirmed by the presented exact solutions and effect of angular velocity of spin on natural frequencies (Campbell diagram) is investigated. Comparison of the proposed method with the exact solutions revealed the convergence and accuracy of the proposed method.

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The purpose of this study, control and monitoring of a rehabilitation robot with two degrees of freedom (2-DOF) for rehabilitation of the lower limbs of patients with loss of ability for movement due to injury, disease, stroke or surgical operations. After determining the movements, that is included flexion-extension movements of the knee and hip joints, the performance of the mechanism was investigated using dynamic analysis and simulation. Then, a programmable logic controller (PLC) was employed to control the robot performance. Finally, the accuracy of PLC program was guaranteed by monitoring the robot. Passive, assistive and resistive exercises were considered in programming the controller. In assistive exercises, the forces needed by the patient to perform the movements were actually set automatically by using the feedback data provided by the patient's forces. In addition, to perform the resistive exercises rather than using actual weights, negative loads were employed. The results obtained represent considerable accuracy to perform the movements and create safe conditions for the patient. Also, high flexibility in programming has provided the possibility to perform a wide range of rehabilitation exercises.