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In-Plane Vibration of a Beam Picking and Placing a Mass Along Arbitrary Curved Tracking

Shueei-Muh Lin 1

Mechanical Engineering Department, Kun Shan University, Tainan, Taiwan 710-03, Republic of China. E-Mail:

Computer Modeling in Engineering & Sciences 2011, 72(1), 17-36.


In this study, examine the in-plane vibration of a robot arm picking and placing a mass along arbitrary curved tracking. This mathematical model is established. It is a moving mass problem. Due to the effect of movement along arbitrary curved tracking, the corresponding differential equation is nonlinear with the time-dependent coefficients and non-homogenous boundary conditions. So far, a few literatures devoted to investigate this system due to its complexity. The solution method procedure for this system is presented. It integrates several methods as the transform of variable, the subsection method, the mode superposition method, and the Green function method. Meanwhile, the shift function for the transform of variable is derived. The orthogonality condition for the mode superposition method is proved. For suppressing vibration and overshoot the boundary control method is design. The method is verified to be very effective. The dynamic behavior of a robot arm placing a mass is investigated. It is found that the effect of placing a mass during the way of movement on the vibration is significant. Finally, the effects of several parameters on the overshoot and residual vibration are investigated.


Cite This Article

Lin, S. (2011). In-Plane Vibration of a Beam Picking and Placing a Mass Along Arbitrary Curved Tracking. CMES-Computer Modeling in Engineering & Sciences, 72(1), 17–36.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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