# Chapter 7

# Chapter 7: Feasible Neural Commands and Feasible Mechanical Outputs (*under construction*)

*Last updated Dec. 26 2015 by Francisco Valero-Cuevas*

**Abstract:**

Having understood the basic concepts related to the structure and function of tendon-driven limbs, we can now revisit and appreciate the question: ‘How does the nervous system control a tendon-driven limb?’ Chap. 5 shows why it is reasonable to consider optimization as a means to resolve the muscle redundancy that exists for the control of joint torques. But Chap. 6 paints an alternative picture when we see that orchestrating tendon excursions among muscles is severely overdetermined— which is the opposite of redundancy. In this chapter I begin to explore in detail the working hypothesis that having numerous muscles does not make them as redundant as proposed by the classical notion of muscle redundancy. I do this by introducing you to the concepts of how feasible muscle activations produce feasible mechanical outputs. This perspective grows out of the fusion of linear algebra, geometry, mechanics, and anatomy. It shows how the anatomical structure of the limb together with the constraints that define a mechanical task naturally specify a set of feasible neural commands. The fact that this set of feasible neural commands has a well- defined structure compels and allows us to revise and extend the classical notion of muscle redundancy, and propose a more general approach to neuromuscular control that emphasizes compatibility with evolutionary biology and clinical reality.

**Forum and commentary:**

*Coming soon!*

**Exercises:**

*Coming soon!*

**Additional references and suggested reading:**

*Coming soon!*

**References in book:**

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- F.J. Valero-Cuevas, A mathematical approach to the mechanical capabilities of limbs and fingers. Adv. Exp. Med. Biol. 629, 619–633 (2009)
- E.Y. Chao, K.N. An, Graphical interpretation of the solution to the redundant problem in biomechanics. J. Biomech. Eng. 100, 159–167 (1978)
- C.W. Spoor, Balancing a force on the fingertip of a two-dimensional finger model without intrinsic muscles. J. Biomech. 16(7), 497–504 (1983)
- P.W. Brand, A. Hollister, Clinical Mechanics of the Hand (Mosby Year Book, St.Louis, 1993)
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- R.M. Murray, Z. Li, S.S. Sastry, A Mathematical Introduction to Robotic Manipulation (CRC, Boca Raton, 1994)
- G. Strang, Introduction to Linear Algebra (Wellesley Cambridge Press, Wellesley, 2003)
- Wikipedia contributors, Polytope. Wikipedia, The Free Encyclopedia. http://en.wikipedia.org/wiki/Polytope. Accessed 2 June 2015
- Wikipedia contributors, Cartesian coordinate system. Wikipedia, The FreeEncyclopedia. http://en.wikipedia.org/wiki/Minkowski_addition. Accessed 12 Feb 2015
- Wikipedia contributors, Cartesian coordinate system. Wikipedia, The Free Encyclopedia. http://en.wikipedia.org/wiki/Zonohedron. Accessed 12 Feb 2015
- D. Eppstein, Zonohedra and zonotopes. Math. Edu. Res. 5, 15–21 (1996)
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- F.J. Valero-Cuevas, An integrative approach to the biomechanical function and neuromuscular control of the fingers. J. Biomech. 38, 673–684 (2005)
- J. Dattorro, Convex Optimization and Euclidean Distance Geometry (Meboo Publishing, Palo Alto, 2005)
- F.J. Valero-Cuevas, Predictive modulation of muscle coordination pattern magnitude scalesfingertip force magnitude over the voluntary range. J. Neurophysiol. 83, 1469–1479 (2000)
- F.J.Valero-Cuevas,J.D.Towles,V.R.Hentz, Quantification of fingertip force reduction in the forefinger following simulated paralysis of extensor and intrinsic muscles. J. Biomech. 33, 1601–1609 (2000)
- F.J. Valero-Cuevas, M.E. Johanson, J.D. Towles, Towards a realistic biomechanical model of the thumb: the choice of kinematic description may be more critical than the solution method or the variability/uncertainty of musculoskeletal parameters. J. Biomech. 36, 1019–1030 (2003)
- J.M. Inouye, F.J. Valero-Cuevas, Anthropomorphic tendon-driven robotic hands can exceed human grasping capabilities following optimization. Int. J. Robot. Res. 33, 694–705 (2013)
- J.M. Inouye, J.J. Kutch, F.J. Valero-Cuevas, A novel synthesis of computational approaches enables optimization of grasp quality of tendon-driven hands. IEEE Trans. Robot. 28(4), 958– 966 (2012)
- E. Moberg, Surgical treatment for absent single-hand grip and elbow extension in quadriplegia. Am. J. Bone Joint Surg. 57, 196–206 (1975)
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**Code:**

ncube.m: Download

**Note:** *This .m file is only required for matlab users since python has a more clever way of creating generator vectors.*

zonotope_multi_N_2D.m: Download

zonotope_multi_N_2D.py: Download

© Francisco Valero-Cuevas 2015