Bond Graph Modeling of Muscle-Tendon Actuation of a Phalange

  • Sandeep Kumar Uppal Dr. B. R. Ambedkar National Institute of Technology Jalandhar
  • Anand Vaz Dr. B. R. Ambedkar National Institute of Technology Jalandhar


In musculoskeletal actuation systems, it is essential to understand and analyze the extension and force patterns generated in the muscle-tendon units (MTUs) responsible for the motion of a phalange. This work proposes a systematically developed bond graph model for the muscle-tendon actuation system for the desired motion of the phalange of the hand. The phalange is represented by a cylindrical rigid body, actuated by four MTUs attached to it symmetrically. The MTU is based on Hill’s muscle model. The role of the central nervous system (CNS) that commands desired motions to the phalange is emulated through a virtual domain in the model. The virtual domain decides the activation pattern of MTUs. Accordingly, the MTUs apply forces on the phalange to achieve the desired motion. Simulation results for important motions such as flexion-extension, adductionabduction, and circumduction show that the model effectively captures the dynamics of the musculoskeletal actuation system.


musculoskeletal actuation, bond graph, muscle-tendon units, central nervous system, simulation,


1. J.N. Ingram, K.P. Körding, I.S. Howard, D.M. Wolpert, The statistics of natural hand movements, Experimental Brain Research, 188(2): 223–236, 2008, doi: 10.1007/s00221-008-1355-3.
2. A. Freivalds, Biomechanics of the Upper Limbs: Mechanics, Modeling and Musculoskeletal Injuries, CRC Press, Boca Raton, 2011.
3. J.H.C. Wang, Q. Guo, B. Li, Tendon biomechanics and mechanobiology – A minireview of basic concepts and recent advancements, Journal of Hand Therapy, 25(2): 133–141, 2012, doi: 10.1016/j.jht.2011.07.004.
4. T.J. Roberts, A.M. Gabaldón, Interpreting muscle function from EMG: Lessons learned from direct measurements of muscle force, Integrative and Comparative Biology, 48(2): 312–320, 2008, doi: 10.1093/icb/icn056.
5. K.N. An, E.Y. Chao, W.P. Cooney, R.L. Linscheid, Forces in the normal and abnormal hand, Journal of Orthopaedic Research, 3(2): 202–211, 1985, doi: 10.1002/jor.1100030210.
6. M.E. Johanson, F.J. Valero-Cuevas, V.R. Hentz, Activation patterns of the thumb muscles during stable and unstable pinch tasks, Journal of Hand Surgery, 26(4): 698–705, 2001, doi: 10.1053/jhsu.2001.26188.
7. J.L. Sancho-Bru, A. Pérez-González, M. Vergara-Monedero, D. Giurintano, A 3-D dynamic model of human finger for studying free movements, Journal of Biomechanics, 34(11): 1491–1500, 2001, doi: 10.1016/S0021-9290(01)00106-3.
8. L.A. Wojcik, Modeling of musculoskeletal structure and function using a modular bond graph approach, Journal of Franklin Institute, 340(1): 63–76, 2003, doi: 10.1016/S0016-0032(03)00011-5.
9. F. Chen Chen, S. Appendino, A. Battezzato, A. Favetto, M. Mousavi, F. Pescarmona, Constraint study for a hand exoskeleton: Human hand kinematics and dynamics, Journal of Robotics, 2013: 910961, 2013, doi: 10.1155/2013/910961.
10. A. Vaz, K. Singh, G. Dauphin-Tanguy, A Bond graph model for the actuation mechanism of musculo-skeletal joints, [in:] Volume 2: Automotive Systems; Bioengineering and Biomedical Technology; Computational Mechanics; Controls; Dynamical Systems, pp. 69–75, 2008, doi: 10.1115/ESDA2008-59301.
11. A. Vaz, K. Singh, G. Dauphin-Tanguy, Bond graph model of extensor mechanism of finger based on hook-string mechanism, Mechanism and Machine Theory, 91: 187–208, 2015, doi: 10.1016/j.mechmachtheory.2015.03.011.
12. N. Mishra, A. Vaz, Bond graph modeling of a 3-joint string-tube actuated finger prosthesis, Mechanism and Machine Theory, 117: 1–20, 2017, doi: 10.1016/j.mechmachtheory.2017.06.018.
13. M. Santello, G. Baud-Bovy, H. Jörntell, Neural bases of hand synergies, Frontiers in Computational Neuroscience, 7(23): 1–15, 2013, doi: 10.3389/fncom.2013.00023.
14. N. Mishra, A. Vaz, Development of trajectory and force controllers for 3-joint stringtube actuated finger prosthesis based on bond graph modeling, Mechanism and Machine Theory, 146: 103719, 24 pages, 2020, doi: 10.1016/j.mechmachtheory.2019.103719.
15. R. Drake, A. Vogl, A. Mitchell, Gray’s Anatomy for Students, 3rd Ed., Churchill Livingstone Elsevier, Canada, 2015.
16. Y.C. Fung, Mechanical Properties of Living Tissues, 2nd Ed., Springer, New York, 1993.
17. D. Karnopp, D. Margolis, R. Rosenberg, System Dynamics, 5th Ed., John Wiley & Sons, New Jersy, 2012.
18. B. Alexander, V. Kotiuk, Proportions of hand segments, International Journal of Morphology, 28(3): 755–758, 2010.
19. H.E. Ash, A. Unsworth, Design of a surface replacement prosthesis for the proximal inter-phalangeal joint, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 214(2): 151–163, 2000, doi: 10.1243/0954411001535327.
20. C.E. Garrido Varas, T.J.U. Thompson, Metric dimensions of the proximal phalanges of the human hand and their relationship to side, position, and asymmetry, HOMO – Journal of Comparative Human Biology, 62(2): 126–143, 2011, doi: 10.1016/j.jchb.2010.07.005.
21. I.V. Grinyagin, E.V. Biryukova, M.A. Maier, Kinematic and dynamic synergies of human precision-grip movements, Journal of Neurophysiology, 94(4): 2284–2294, 2005, doi: 10.1152/jn.01310.2004.
22. R. Arshad, Modelling inhomogeneities within the human intervertebral disc, Master Thesis, no. 04, Institute of Mechanics, Chair II, University of Stuttgart, 2004.
23. J. Yang, R. Chiou, A. Ruprecht, J. Vicario, L.A. Macphail, T.E. Rams, A new device for measuring density of jaw bones, Dentomaxillofacial Radiology, 31: 313–316, 2002, doi: 10.1038/sj.dmfr.4600715.
24. J.H.C. Wang, Mechanobiology of tendon, Journal of Biomechanics, 39(9): 1563–1582, 2006, doi: 10.1016/j.jbiomech.2005.05.011.
25. E.L. Secco, A. Visioli, G. Magenes, Minimum jerk motion planning for a prosthetic finger, Journal of Robotic Systems, 21(7): 361–368, 2004, doi: 10.1002/rob.20018.
Aug 17, 2022
How to Cite
UPPAL, Sandeep Kumar; VAZ, Anand. Bond Graph Modeling of Muscle-Tendon Actuation of a Phalange. Computer Assisted Methods in Engineering and Science, [S.l.], v. 29, n. 3, p. 197–227, aug. 2022. ISSN 2956-5839. Available at: <>. Date accessed: 17 apr. 2024. doi: