In this article, impedance control of a two link flexible link manipulators is addressed. The concept of impedance control of flexible link robots is rather new and is being addressed for the first time by the authors. Impedance Control provides a universal approach to the control of flexible robots, in both constrained and unconstrained maneuvers. The initial part of the paper concerns the use of Hamilton's principle to derive the mathematical equations governing the dynamics of joint angles, vibration of the flexible links and the constraining forces. The approximate elastic deformations are then derived by means of the Assumed-Mode-Method (AMM). Using the singular perturbation method, the dynamic of the manipulator is decomposed into fast and slow subsystems. The slow dynamic corresponds to the rigid manipulator and the fast dynamic is due to vibrations of flexible links. The sliding mode control (SMC) theory has been used as the means to achieve the 2nd order target impedance for the slow dynamics. A controller based on state feedback is also designed to stabilize the fast dynamics. The composite controller is constructed by using the slow and fast controllers. Simulation results for a 2-DOF robot in which only the 2nd link is flexible confirm that the controller performs remarkably well under various simulation conditions.
In this article, impedance control of a two link flexible link manipulators is addressed. The concept of impedance control of flexible link robots is rather new and is being addressed for the first time. Impedance Control provides a universal approach to the control of flexible robots — in both constrained and unconstrained maneuvers. The initial part of the paper concerns the use Hamilton’s principle to derive the mathematical equations governing the dynamics of joint angles, vibration of the flexible links and the constraining forces. The approximate elastic deformations are then derived by means of the Assumed-Mode-Method (AMM). Using the singular perturbation method, the dynamic of the manipulator is decomposed to the fast and the slow subsystems. The slow dynamic corresponds to the rigid manipulator and fast dynamic is due to vibrations of flexible links. The sliding mode control (SMC) theory has been used as the means to achieve the 2nd order target impedance for the slow dynamics. A controller based on state feedback is also designed to stabilize the fast dynamics. The composite controller is constructed by using the slow and fast controllers. Simulation results for a 2 DOF robot in which only the 2nd link is flexible confirm that the controller performs remarkably well under various simulation conditions.
KEYWORDSMicro-ring; Modi ed couple stress theory; Resonant frequency.Abstract. In this paper, based on the modi ed couple stress theory, the size-dependent dynamic behavior of circular rings on elastic foundation is investigated. The ring is modeled by Euler-Bernoulli and Timoshenko beam theories, and Hamilton's principle is utilized to derive the equations of motion and boundary conditions. The formulation derived is a general form of the equation of motion of circular rings and can be reduced to the classical form by eliminating the size-dependent terms. On this basis, the size-dependent natural frequencies of a circular ring are calculated based on the non-classical Euler-Bernoulli and Timoshenko beam theories. The ndings are compared with classical beam theories. Response of the micro-ring under application of static and dynamic loads is investigated and compared with the classical theories. Results show that when the thickness of the ring is in the order of the length scale of the ring material, the natural frequencies evaluated using the modi ed couple stress are considerably more than those predicted based on the classical beam theories, while the de ection and natural frequencies of the classical and non-classical beam theories approach one another for the rings with thickness much larger than the material length scale.
The size-dependent dynamic behavior and flexural vibration of rotating micro-rings are investigated in this paper. Using the modified couple stress theory and Hamilton’s principle, the governing equations of motion of the rotating micro-ring are derived. The natural frequencies for both extensional and inextensional micro-rings are obtained in closed form along with the forward and backward traveling waves derived. The results indicate that the natural frequencies of the rotating micro-ring are clearly size dependent, but the size dependency decreases as the speed of rotation of the ring increases, while it decreases when the radius-to-thickness ratio of the ring increases. A comparison between the natural frequencies of the extensional and inextensional micro-rings is performed. Moreover, the effect of the radius-to-thickness ratio of the ring on the behavior of the micro-ring is investigated. Good agreement is found between the natural frequencies obtained and the experimental results reported in the literature.
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