IJAT Vol.11 No.3 pp. 368-377
doi: 10.20965/ijat.2017.p0368


A Novel Geometric Formula for Predicting Contractile Force in McKibben Pneumatic Muscles

Guido Belforte, Terenziano Raparelli, and Silvia Alessandra Sirolli

Department of Mechanical and Aerospace Engineering, Politecnico di Torino
Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Corresponding author

November 25, 2016
March 2, 2017
Online released:
April 28, 2017
May 5, 2017
textile pneumatic muscle, analytical model for textile actuators, geometric model for braided muscles, nonlinear actuators
Several analytical models exist in the literature for predicting the behavior of braided pneumatic muscles (McKibben muscles). Such models take into consideration the various variables and parameters that are related to the muscle geometry, material properties, and the loads applied to the system, and propose various relationships between these variables. Owing to the complexity of the muscle structure, in several cases, instead of a physical model, empirical or experimental models are used, which generally have limited validity for specific muscle types, i.e., they are only valid for a restricted range of operating parameters. This study proposes a new analytical formula based on the geometry of a pneumatic muscle studied in the rest and work phases and a simple experimental method to obtain corrective factors useful to design muscles. A mathematical formula can thus be obtained that allows one to deduce the measurements of interest in the system as a function of the specific parameters and permits one to interpret in qualitative terms the behavior of the muscle at each moment for various values of pressure, contraction, and applied load and to identify any critical situations. This model can therefore be a very useful design tool because it allows one to adapt the muscle geometry based on the required forces and contractions for different applications that are compatible with the muscle structure on which the model is based. This paper also presents a method for evaluating the efficiency of the muscles, useful to better use them in different applications.
Cite this article as:
G. Belforte, T. Raparelli, and S. Sirolli, “A Novel Geometric Formula for Predicting Contractile Force in McKibben Pneumatic Muscles,” Int. J. Automation Technol., Vol.11 No.3, pp. 368-377, 2017.
Data files:
  1. [1] C. Ferraresi, W. Franco, and A. M. Bertetto, “Flexible Pneumatic Actuators: a Comparison Between the McKibben and Straight Fiber Muscles,” J. of Robotics and Mechatronics, Vol.13 No.1, pp. 56-63, 2001.
  2. [2] F. Daerden and D. Lefeber, “Pneumatic Artificial Muscles: actuators for robotics and automation,” European J. of Mechanical and Environmental Engineering, Vol.47, pp. 10-21, 2002.
  3. [3] G. Belforte, G. Quaglia, F. Testore, G. Eula, and S. Appendino, “Wearable Textiles for Rehabilitation of Disabled Patients using Pneumatic Systems,” Smart Textile for Medicine and Healthcare, Materials Systems and Applications, CRC Press, Chapter 12, pp. 221-252, 2007.
  4. [4] Y. Muramatsu, H. Kobayashi, Y. Sato, H. Jiaou, T. Hashimoto, and H. Kobayashi, “Quantitative Performance Analysis of Exoskeleton Augmenting Devices – Muscle Suit – for Manual Worker,” Int. J. Automation Technol., Vol.5 No.4, pp. 559-567, 2011.
  5. [5] S. Kousidou, N. Tsagarakis, D. G. Caldwell, and C. Smith, “Assistive Exoskeleton for Task Based Physiotherapy in 3-Dimensional Space,” Proc. of the IEEE BioRob 2006, 2006.
  6. [6] D. G. Caldwell, N. G. Tsagarakis, S. Kousidou, N. Costa, and I. Sarakoglou, ““Soft” Exoskeletons for Upper and Lower Body Rehabilitation — Design, Control And Testing,” Int. J. of Humanoid Robotics, Vol.4 No.3, pp. 1-24, 2007.
  7. [7] T. Deaconescu and A. Deaconescu, “Pneumatic Muscle Actuated Isokinetic Equipment for the Rehabilitation of Patients with Disabilities of the Bearing Joints,” Proc. of the Int. MultiConf. of Engineers and Computer Scientists, IMECS 2009, Vol.II, 2009.
  8. [8] T. Raparelli, P. B. Zobel, and F. Durante, “The Upper and Lower Assist System Developed at the University of L’Aquila,” Proc. of the 1st Int. Conf. on Complex Medical Engineering, pp. 488-493, 2005.
  9. [9] H. Tomori and T. Nakamura, “Theoretical Comparison of McKibben-Type Artificial Muscle and Novel Straight-Fiber-Type Artificial Muscle,” Int. J. Automation Technol., Vol.5, No.4, pp. 544-550, 2011.
  10. [10] K. Liu, T. Ma, B. Gu, Y. Wang, D. Zhao, and Y. Lu “A new method to predict contractile force for pneumatic muscle actuators,” Advanced Robotics, Vol.29, No.17, pp. 1127-1136, 2015.
  11. [11] T. J. Yeh, M. J. Wu, T. J. Lu, F. K. Wu, and C. R. Huang, “Control of McKibben pneumatic muscles for a power-assist, lower-limb orthosis,” Mechatronics, Vol.20, pp. 686-697, 2010.
  12. [12] B. Li, C. Zou, W. Wang, and Z. Yang, “Vibration control based on pneumatic muscle,” The 22nd Int. Congress on Sound and Vibration ICSV22, 2015.
  13. [13] T. Nakamura and H. Shinohara, “Position and Force Control Based on Mathematical Models of Pneumatic Artificial Muscles Reinforced by Straight Glass Fibers,” 2007 IEEE Int. Conf. on Robotics and Automation, 2007.
  14. [14] R. H. Gaylord, “Fluid Actuated Motor System and Stoking Device,” U.S. Patent No.2844126, 1958.
  15. [15] H. F. Schulte, “The characteristics of the McKibben Artificial Muscle,” The Application of External Power in Prosthetics and Orthotics, Publication 874, National Academy of Sciences–National Research Council, Washington DC, USA, Appendix H, pp. 94-115, 1961.
  16. [16] C. P. Chou and B. Hannaford, “Static and Dynamic Characteristics of Mckibben Pneumatic Artificial Muscles,” Proc. of the IEEE Int. Conf. on Robotics and Automation, Vol.1, pp. 281-286, 1994.
  17. [17] C. P. Chou and B. Hannaford, “Measurement and Modeling of McKibben Pneumatic Artificial Muscles,” Proc. of the IEEE Trans. on Robotics and Automation, Vol.12, No.1, pp. 90-102, 1996.
  18. [18] G. K. Klute and B. Hannaford, “Accounting for Elastic Energy Storage in McKibben Artificial Muscle Actuators,” Proc. of the ASME J. of Dynamic Systems, Measurement and Control, Vol.122 No.2, pp. 386-388, 2000.
  19. [19] L. R. G. Treloar, “The Physics of Rubber Elasticity,” Oxford University Press, 1958.
  20. [20] B. Tondu and P. Lopez, “Theory of an Artificial Pneumatic Muscle and Application to the Modelling of Mckibben Artificial Muscle,” C.R. Académie des Sciences Paris, t. 320, Série IIb, pp. 105-114, 1995.
  21. [21] B. Tondu and P. Lopez, “Modeling and Control of Mckibben Artificial Muscle Robot Actuators,” Proc. of the IEEE Control Systems Magazine, Vol.20, No.2, pp. 15-38, 2000.
  22. [22] N. Tsagarakis and D. G. Caldwell, “Improved Modelling and Assessment of Pneumatic Muscle Actuators,” Proc. of the 2000 IEEE Int. Conf. on Robotics & Automation, 2000.
  23. [23] S. Davis, N. Tsagarakis, J. Canderle, and D. G. Caldwell, “Enhanced Modelling and Performance in Braided Pneumatic Muscle Actuators,” The Int. J. of Robotics Research, Vol.22 No.3-4, pp. 213-227, 2003.
  24. [24] C. Ferraresi, W. Franco, and A. M. Bertetto, “Modelisation and Characterisation of a Pneumatic Muscle Actuator for No Conventional Robotics,” Proc. of the 7th Int. Workshop on Robotics in Alpe-Adria-Danube Region RAAD, 1998.
  25. [25] C. Ferraresi, W. Franco, and A. M. Bertetto, “Flexible Pneumatic Actuators: a Comparison Between the McKibben and the Straight Fibres Muscles,” J. of Robotics and Mechatronics, Vol.13 No.1, 2001.
  26. [26] C. S. Kothera, M. Jangid, J. Sirohi, and N. M. Wereley, “Experimental Characterization and Static Modeling of McKibben Actuators,” J. of Mechanical Design, Vol.131, 2009.
  27. [27] G. Belforte, G. Eula, I. Ivanov, and S. Sirolli, “Soft Pneumatic Actuators for Rehabilitation,” Actuators, Vol.3, pp. 84-106, 2014.
  28. [28] S. A. Sirolli, “Studio di Muscoli Pneumatici Innovativi e Loro Integrazione in Vestiti Attivi a Scopo Riabilitativo,” PhD Thesys, Politecnico di Torino, pp. 223, 2015.
  29. [29] J. M. Yarlott, “Fluid Actuator,” US Patent No.3645173, 1972.
  30. [30] G. Immega and M. Kukolj, “Axially Contractable Actuator,” US Patent No. 4939982, 1990.
  31. [31] J. R. Erickson, “Artificial Muscle Actuator Assembly,” US Patent No. 6067892, 2000.
  32. [32] F. Daerden, “Conception and Realization of Pleated Pneumatic Artificial Muscles and Their Use as Compliant Actuation Elements,” Ph.D. Thesis, Vrije Universiteit Brussel, 1999.
  33. [33] D. Villegas, M. van Damme, B. Vanderborght, P. Beyl, and D. Lefeber, “Third-Generation Pleated Pneumatic Artificial Muscles for Robotic Applications: Development and Comparison with McKibben Muscle,” Advanced Robotics, Vol.26, No.11-12, pp. 1205-1227, 2012.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Jun. 19, 2024