Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T05:49:12.220Z Has data issue: false hasContentIssue false
  • English
  • Français

Modeling and Experimental Validation of the Chaotic Behavior of a Robot Whip

Published online by Cambridge University Press:  04 November 2019

Thomas M. Kwok Open the ORCID record for Thomas M. Kwok [Opens in a new window] ,
Zheng Li ,
Ruxu Du  and
Guanrong Chen
Thomas M. Kwok*
Affiliation:
Dept. of Mechanical and Automation Engineering Chinese University of Hong Kong Hong Kong SAR, China
Zheng Li
Affiliation:
Dept. of Surgery The Chinese University of Hong Kong Hong Kong SAR, China
Ruxu Du
Affiliation:
S. M. Wu School of Intelligent Engineering South China University of Technology Guangzhou, China
Guanrong Chen
Affiliation:
Dept. of Electronic Engineering City University of Hong Kong Hong Kong SAR, China
*
*Corresponding author (mfkwok@mae.cuhk.edu.hk)
Get access

Abstract

Although the whip is a common tool that has been used for thousands of years, there have been very few studies on its dynamic behavior. With the advance of modern technology, designing and building soft- body robot whips has become feasible. This paper presents a study on the modeling and experimental testing of a robot whip. The robot whip is modeled using a Pseudo-Rigid-Body Model (PRBM). The PRBM consists of a number of pseudo-rigid-links and pseudo-revolute-joints just like a multi-linkage pendulum. Because of its large number of degrees of freedom (DOF) and inherited underactuation, the robot whip exhibits prominent transient chaotic behavior. In particular, depending on the initial driving force, the chaos may start sooner or later, but will die down because of the gravity and air damping. The dynamic model is validated by experiments. It is interesting to note that with the same amount of force, the robot whip can generate a velocity more than 3 times and an acceleration up to 43 times faster than that of its rigid counterpart. This gives the robot whip some potential applications, such as whipping, wrapping and grabbing. This study also helps to develop other soft-body robots that involve nonlinear dynamics.

Keywords

Robot whipPseudo-rigid-body modelTransient chaosEscape rate
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 3 , June 2020 , pp. 373 - 394
Copyright
Copyright © 2019 The Society of Theoretical and Applied Mechanics

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Banerjee, H., Tse, Z. T. H and Ren, H. L., “Soft robotics with compliance and adaptation for biomedical applications and forthcoming challenges”, Int. J. of Robotics & Automation, 33, pp. 69–80 (2018).CrossRefGoogle Scholar
Zhong, Y., Li, Z. and Du, R. X., “A novel robot fish with wire-driven active body and compliant tail”, IEEE-ASME Trans. on Mechatronics, 22, pp. 1633–1643 (2017).CrossRefGoogle Scholar
Iida, F. and Laschi, C., “Soft robotics: Challenges and perspectives”, Procedia Computer Science, 7, pp. 99–102 (2011).CrossRefGoogle Scholar
Erfanian, V. and Kabganian, M., “Adaptive Trajectory Control and Dynamic Friction Compensation for a Flexible-Link Robot,” J. of Mechanics, 26, pp. 205–217 (2010).CrossRefGoogle Scholar
Lin, H. P., “Dynamic Responses of Beams with a Flexible Support Under a Constant Speed Moving Load,” J. of Mechanics, 24, pp. 195–204 (2008).CrossRefGoogle Scholar
Bisshopp, K. E. and Drucker, D. C., “Large deflection of cantilever beams”, Quarterly of Applied Mathematics, 3, pp. 272–275 (1945).CrossRefGoogle Scholar
Hofmeister, L. D., Freenbaum, G. A. and Evensens, D. A., “Large strain, elasto-plastic finite element analysis”, AIAA Journal, 9, pp. 1248–1254 (1971).CrossRefGoogle Scholar
Liu, L., Jiang, H., Dong, Y., Quan, L. and Tong, Y., “Study on Flexibility of Intracranial Vascular Stents Based on the Finite Element Method,” J. of Mechanics, pp. 1–10 (2018).Google Scholar
Banerjee, A., Bhattacharya, B. and Mallik, A. K., “Large deflection of cantilever beams with geometric non-linearity: Analytical and numerical approaches”, Int. J. of Non-Linear Mechanics, 43, pp. 366–376 (2008).CrossRefGoogle Scholar
Saggere, L. and Kota, S., “Synthesis of planar, compliant four-bar mechanisms for compliant- segment motion generation”, J. of Mechanical Design, 123, pp. 535–541 (2001).CrossRefGoogle Scholar
Howell, L. L., Compliant Mechanisms, John Wiley & Sons, Canada (2001).Google Scholar
Su, H. J., “A load independent pseudo-rigid-body 3R model for determining large deflection of beams in compliant mechanisms”, Proc. of the 2008 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 109–121 (2008).CrossRefGoogle Scholar
Howell, L. L. and Midha, A., “Parametric deflectiona aproximations for end-loaded, large-deflection beams in compliant mechanisms”, J. of Mechanical Design, 117, pp. 156–165 (1995).CrossRefGoogle Scholar
Yu, Y. Q., Feng, Z. L. and Xu, Q. P., “A pseudo-rigid- body 2R model of flexural beam in compliant mechanisms”, Mechanism and Machine Theory, 55, pp. 18–33 (2012).CrossRefGoogle Scholar
Yu, Y. Q. and Zhu, S. K., “5R pseudo-rigid-body model for inflection beams in compliant mechanisms”, Mechanism and Machine Theory, 116, pp. 501–512 (2017).CrossRefGoogle Scholar
Kwok, T. M., Zhong, Y. and Du, R., “Dynamic modeling and experimental validation of a robotic whip”, Proc. of the CAD Conference and Exhibition, pp. 47–53 (2018).CrossRefGoogle Scholar
François, B., “Topological chaos: what may this mean?” J. of Difference Equations and Applications, 15, pp. 23–46 (2009).Google Scholar
Li, T. Y. and Yorke, J. A., “Period three implies chaos”, The American Mathematical Monthly, 82, pp. 985–992 (1975).CrossRefGoogle Scholar
Devaney, R. L., An Introduction to Chaotic Dynamical Systems, Addison Wesley, New York (1989).Google Scholar
Liu, C., Liu, T., Liu, L. and Liu, K., “A new chaotic attractor”, Chaos, Solitons & Fractals, 22, pp. 1031–1038 (2004).CrossRefGoogle Scholar
Varney, P. and Green, I., “Nonlinear phenomena, bifurcations, and routes to chaos in an asymmetrically supported rotor–stator contact system”, J. of Sound and Vibration, 336, pp. 207–226 (2015).CrossRefGoogle Scholar
Wu, L., Marghitu, D. B. and Zhao, J., “Nonlinear dynamics response of a planar mechanism with two driving links and prismatic pair clearance”, Mathematical Problems in Engineering, 2017 (2017).CrossRefGoogle Scholar
Xu, Y., Mahmoud, G. M., Xu, W. and Lei, Y., “Suppressing chaos of a complex Duffing’s system using a random phase”, Chaos, Solitons & Fractals, 23, pp. 265–273 (2005).CrossRefGoogle Scholar
Jeng, J. D., Kang, Y. and Chang, Y. P., “Identification for Chaos and Subharmonic Responses in Coupled Forced Duffing’s Oscillators,” J. of Mechanics, 27, pp. 139–147 (2011).CrossRefGoogle Scholar
Rivas-Cambero, I. and Sausedo-Solorio, J. M., “Dynamics of the shift in resonance frequency in a triple pendulum”, Meccanica, 47 (2012).CrossRefGoogle Scholar
Marszal, M., Jankowski, K., Perlikowski, P. and Kapitaniak, T., “Bifurcations of oscillatory and rotational solutions of double pendulum with parametric vertical excitation”, Mathematical Problems in Engineering, 2014 (2014).CrossRefGoogle Scholar
Nakamura, Y., Suzuki, T. and Koinuma, M., “Nonlinear behavior and control of a nonholonomic free-joint manipulator”, IEEE Transactions on Robotics and Automation, 13, pp. 853–862 (1997).CrossRefGoogle Scholar
Jain, H., Ranjan, A. and Gupta, K., “Analysis of chaos in double pendulum”, Proc. of the 6th International Conference on Emerging Trends in Engineering and Technology, pp. 171–176 (2013).CrossRefGoogle Scholar
Siciliano, B., Robotics Modelling, Planning and Control, Springer, London (2009).Google Scholar
Shabana, A. A., Dynamics of Multibody Systems, Cambridge University Press, New York (2013).CrossRefGoogle Scholar
Tél, T., “The joy of transient chaos”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 25, pp.1–11 (2015).CrossRefGoogle ScholarPubMed
Moon, F. C., Chaotic Vibrations: An Introduction for Applied Scientists and Engineers John Wiley & Sons, New York (2005).CrossRefGoogle Scholar
Rosenstein, M. T., Collins, J. J. and Luca, C. J. D., “A practical method for calculating largest Lyapunov exponents from small data sets”, Physica D: Nonlinear Phenomena, 65, pp. 117–134 (1993).CrossRefGoogle Scholar
Moon, F. C., Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineers. Canada, John Wiley & Sons, Inc. (1992).CrossRefGoogle Scholar
Chen, G., “Chaos, Bifurcations, and Their Control,” Wiley Encyclopedia of Electrical and Electronics Engineering (2018).CrossRefGoogle Scholar
Ashby, M., Material property data for engineering materials. Granta Design Ltd., Cambridge (2016).Google Scholar