The construction of artificial muscles is one of the most challenging developments in today’s biomedical science. The application of artificial muscles is focused both on the construction of orthotics and prosthetics for rehabilitation and prevention purposes and on building humanoid walking machines for robotics research. Research in biomechanics tries to explain the functioning and design of real biological muscles and therefore lays the fundament for the development of functional artificial muscles. Recently, the hyperbolic Hill-type force-velocity relation was derived from simple mechanical components. In this contribution, this theoretical yet biomechanical model is transferred to a numerical model and applied for presenting a proof-of-concept of a functional artificial muscle. Additionally, this validated theoretical model is used to determine force-velocity relations of different animal species that are based on the literature data from biological experiments. Moreover, it is shown that an antagonistic muscle actuator can help in stabilising a single inverted pendulum model in favour of a control approach using a linear torque generator. 1. Introduction Research in muscle biomechanics, a vital and broad field for over 80 years now (A.V. Hill 1922: Nobel prize in physiology and medicine for his discovery relating to the production of heat in the muscle), explains the function and design of real biological muscles and therefore lays the fundament for the development of functional artificial muscles. Nevertheless, structure and functioning of biological muscles are not (yet) fully understood. In biology, microscopic muscle models are able to predict muscle characteristics and functioning of biological muscles quite well [1–9]. Unfortunately and as a tradeoff, they require a large number of parameters. In a bionics approach it is an enormous challenge to realise all these properties of biological muscle in one artificial muscle at once [10]. Macroscopic muscle models are commonly based on phenomenology. Macroscopic muscle models are indeed of (limited) predictive character but do not incorporate any structural knowledge. Recently, the nonlinear (hyperbolic-like) Hill-type force-velocity relation was derived from simple mechanical components [11]. It was shown that a contractile element (CE) consisting of a mechanical energy source (active element AE), a parallel damper element (PDE), and a serial element (SE) exhibits operating points with nonlinear (hyperbola-like) force-velocity dependency. In this concept, the force-velocity relation is no longer
References
[1]
A. F. Huxley, “Muscle structure and theories of contraction,” Progress in Biophysics and Biophysical Chemistry, vol. 7, pp. 255–318, 1957.
[2]
A. F. Huxley, “Mechanics and models of the myosin motor,” Philosophical Transactions of the Royal Society B, vol. 355, no. 1396, pp. 433–440, 2000.
[3]
H. E. Huxley, “Fifty years of muscle and the sliding filament hypothesis,” European Journal of Biochemistry, vol. 271, no. 8, pp. 1403–1415, 2004.
[4]
V. Lombardi, G. Piazzesi, M. A. Ferenczi, H. Thirlwell, I. Dobbie, and M. Irving, “Elastic distortion of myosin heads and repriming of the working stroke in muscle,” Nature, vol. 374, no. 6522, pp. 553–555, 1995.
[5]
V. Lombardi, G. Piazzesi, M. Reconditi et al., “X-ray diffraction studies of the contractile mechanism in single muscle fibres,” Philosophical Transactions of the Royal Society B, vol. 359, no. 1452, pp. 1883–1893, 2004.
[6]
G. Piazzesi and V. Lombardi, “A cross-bridge model that is able to explain mechanical and energetic properties of shortening muscle,” Biophysical Journal, vol. 68, no. 5, pp. 1966–1979, 1995.
[7]
M. Reconditi, M. Linari, L. Lucii et al., “The myosin motor in muscle generates a smaller and slower working stroke at higher load,” Nature, vol. 428, no. 6982, pp. 578–581, 2004.
[8]
I. A. Telley, J. Denoth, and K. W. Ranatunga, “Inter-sarcomere dynamics in muscle fibres: a neglected subject?” Advances in Experimental Medicine and Biology, vol. 538, pp. 481–500, 2004.
[9]
L. Tskhovrebova and J. Trinick, “Role of titin in vertebrate striated muscle,” Philosophical Transactions of the Royal Society B, vol. 357, no. 1418, pp. 199–206, 2002.
[10]
R. H. Baughman, “Materials science. Playing nature's game with artificial muscles,” Science, vol. 308, no. 5718, pp. 63–65, 2005.
[11]
M. Günther and S. Schmitt, “A macroscopic ansatz to deduce the Hill relation,” Journal of Theoretical Biology, vol. 263, no. 4, pp. 407–418, 2010.
[12]
D. F. B. H?ufle, M. Günther, R. Blickhan, and S. Schmitt, “Proof of concept of an artificial muscle: theoretical model, numerical model, and hardware experiment,” in Proceedings of International Conference of Rehabilitation Robotics (ICORR '11), pp. 1–6, July 2011.
[13]
D. F. H?ufle, M. Günther, R. Blickhan, and S. Schmitt, “Can quick release experiments reveal the muscle structure? A bionic approach,” Journal of Bionic Engineering, vol. 9, no. 2, pp. 211–223, 2012.
[14]
D. F. H?ufle, M. Günther, R. Blickhan, and S. Schmitt, “Proof of concept: model based bionic muscle with hyperbolic force-velocity relation,” Applied Bionics and Biomechanics, pp. 1–7, 2012.
[15]
S. Schmitt, D. F. H?ufle, R. Blickhan, and M. Günther, “Nature as an engineer: one simple concept of a bio-inspired functional artificial muscle,” Bioinspiration & Biomimetics, vol. 7, Article ID 036022, 2012.
[16]
A. V. Hill, “The heat of shortening and the dynamic constants of muscle,” Proceedings of the Royal Society of London. Series B, vol. 126, pp. 136–195, 1938.
[17]
M. Günther, S. Schmitt, and V. Wank, “High-frequency oscillations as a consequence of neglected serial damping in Hill-type muscle models,” Biological Cybernetics, vol. 97, no. 1, pp. 63–79, 2007.
[18]
G. K. Cole, T. van den Bogert, W. Herzog, and K. Gerritsen, “Modelling of force production in skeletal muscle undergoing stretch,” Journal of Biomechanics, vol. 29, pp. 1091–1104, 1996.
[19]
G. K. Klute, J. M. Czerniecki, and B. Hannaford, “Artificial muscles: actuators for biorobotic systems,” International Journal of Robotics Research, vol. 21, no. 4, pp. 295–309, 2002.
[20]
J. P. van Zandwijk, M. F. Bobbert, G. C. Baan, and P. A. Huijing, “From twitch to tetanus: performance of excitation dynamics optimized for a twitch in predicting tetanic muscle forces,” Biological Cybernetics, vol. 75, no. 5, pp. 409–417, 1996.
[21]
M. Günther and H. Ruder, “Synthesis of two-dimensional human walking: a test of the λ-model,” Biological Cybernetics, vol. 89, no. 2, pp. 89–106, 2003.
[22]
J. D. Madden, “Mobile robots: motor challenges and materials solutions,” Science, vol. 318, no. 5853, pp. 1094–1097, 2007.
[23]
E. Garcia, J. C. Arevalo, G. Muoz, and P. Gonzalez-De-Santos, “Combining series elastic actuation and magneto-rheological damping for the control of agile locomotion,” Robotics and Autonomous Systems, vol. 59, no. 10, pp. 827–839, 2011.
[24]
A. F. Huxley, “A note suggesting that the cross bridge attachment during muscle contraction may take place in two stages,” Proceedings of the Royal Society of London. Series B, vol. 183, no. 1070, pp. 83–86, 1973.
[25]
E. Bizzi, N. Hogan, F. A. Mussa-Ivaldi, and S. Giszter, “Does the nervous sytem use equilibriumpoint control to guide single and multiple joint movements?” Behavioral and Brain Sciences, vol. 15, pp. 603–613, 1992.
[26]
A. G. Fel'dman, “Functional tuning of the nervous system with control of movement or maintenance of a steady posture-II. Controllable parameters of the muscles,” Biophysics, vol. 11, no. 3, pp. 565–578, 1966.
[27]
J. Pratt, C.-M. Chew, A. Torres, P. Dilworth, and G. Pratt, “Virtual model control: an intuitive approach for bipedal locomotion,” International Journal of Robotics Research, vol. 20, no. 2, pp. 129–143, 2001.
[28]
M. F. Eilenberg, H. Geyer, and H. Herr, “Control of a powered ankle-foot prosthesis based on a neuromuscular model,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 18, no. 2, pp. 164–173, 2010.
[29]
A. S. Ghafari, A. Meghdari, and G. Vossoughi, “Feedback control of the neuromusculoskeletal system in a forward dynamics simulation of stair locomotion,” Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, vol. 223, no. 6, pp. 663–675, 2009.
[30]
D. A. Kistemaker, A. J. Van Soest, and M. F. Bobbert, “A model of open-loop control of equilibrium position and stiffness of the human elbow joint,” Biological Cybernetics, vol. 96, no. 3, pp. 341–350, 2007.