Nonlinear dynamics of flexible links in planar parallel robots using a new beam element

Abstract

In the present research, a previously presented beam element in planar static problems is extended to planar dynamic problems. As investigated in the previous work of the author, formulation of the presented Euler–Bernoulli beam element is simpler and the beam element more efficient than similar elements in large deflection problems. In the present element, the main idea is estimating the dimensions of the body in the deformed configuration, instead of estimating its absolute or relative positions. Therefore, two parameters, the length and slope angle of the beam centroid curve, are selected to be estimated by interpolating polynomials. To verify the efficiency of the element, obtained results for the flexible pendulum are compared with previous works. Because of the simple and efficient formulation of the element, it can be efficiently used for dynamic analysis of planar flexible linkages, and especially in flexible parallel robots, which are the main aims of the present research. Finally, the inverse dynamic of the flexible 3-RRR parallel robot is presented.

Controller Design for Three-Axis Stabilized Platform Using Adaptive Global Fast Terminal Sliding Mode Control with Non-Linear Differentiator

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Vibration control of coupled Duffing oscillators in flexible single-link manipulators

“…In the majority of the existing studies, the structural nonlinearities were ignored for simplicity and the flexible-link manipulators were considered as a linear model with infinite vibrational modes (Chen and Huang, 2017). Recently, the dynamic modeling of several types of flexible-link manipulators was developed from the nonlinear dynamics perspective (Altıner et al, 2019;Cao and Liu, 2020;Chen et al, 2019;Feliu-Talegon and Feliu-Batlle, 2019;Pratiher, 2019, 2020;Meng et al, 2018;Ni et al, 2020;Shafei and Shafei, 2018;Sharifnia, 2020;Tavallaeinejad et al, 2016;Vakil et al, 2012;Wang and Lou, 2019). The nonlinear model can exhibit relatively large-amplitude vibrations and complicated dynamics.…”