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Chaos in Inverted Flexible Pendulum With Tip Mass

[+] Author Affiliations
Prasanna Gandhi, Jaish Meena

Indian Institute of Technology Bombay, Mumbai, India

Paper No. IMECE2014-38500, pp. V04BT04A030; 6 pages
  • ASME 2014 International Mechanical Engineering Congress and Exposition
  • Volume 4B: Dynamics, Vibration, and Control
  • Montreal, Quebec, Canada, November 14–20, 2014
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4648-3
  • Copyright © 2014 by ASME


Flexible link systems are increasingly being used in the robotic and other applications. The dynamics of distributed parameter single flexible link system, especially in the vertical planes, is known to demonstrate chaotic behavior upon harmonic excitation. However, to the best of authors knowledge, chaotic dynamics of ultra-large deflection flexible systems with distributed and lumped parameters considered together has not been considered in the literature so far. Dynamics of a representative case, an inverted flexible pendulum with tip mass on cart system, is analysed in this paper. Experimental results on a custom built system consisting of link having 1. ultra large deformation (300 times thickness) as compared to thickness, 2. a tip mass, and 3. base fixed to a cart, under harmonic excitation under several frequencies were obtained. Poincaré maps with large set of data show successive progression with a small cluster of points to start with splitting into two clusters finally leading to butterfly figure of chaotic vibrations. Effect of variation of the excitation amplitude is also explored leading to interesting change in the patterns of Poincaré maps observed.

Copyright © 2014 by ASME
Topics: Chaos , Pendulums



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