A Mathematical Approach to the Mechanical Capabilities of Limbs and Fingers

  • Francisco J. Valero-Cuevas
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 629)


Neuromuscular function is the interaction between the nervous system and the physical world. Limbs and fingers are, therefore, the ultimate mechanical filters between the motor commands that the nervous system issues and the physical actions that result. In this chapter we present a mathematical approach to understanding how their anatomy (i.e., physical structure) defines their mechanical capabilities. We call them “mechanical filters” because they attenuate, amplify, and transform neural signals into mechanical output. We explicitly distinguish between limbs and fingers because their subtle anatomical differences have profound effects on their mechanical properties. Our main message is that many aspects of neuromuscular function such as co-contraction, posture selection, muscle redundancy, optimality of motor command, are fundamentally affected (if not defined) by the physical structure of limbs and fingers. We attempt to present the fundamental filtering properties of limbs and fingers in a unified manner to allow for a direct and useful application of powerful mathematical concepts to the study of neuromuscular function. Every researcher of motor control is well advised to consider these filtering properties to properly understand the co-evolution and synergistic interactions between brain and body. At the end of the day, every inquiry in neuromuscular function can be reduced to the fundamental question whether and how the nervous system can perform the necessary sensorimotor functions to exploit and reach the mechanical capabilities of limbs and fingers.


Basis Vector Muscle Force Joint Torque Mechanical Output Flexion Torque 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Avis D, Fukuda K (1992) A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra. Discrete and Computational Geometry:295–313.Google Scholar
  2. Bobbert MF, van Ingen Schenau GJ (1988) Coordination in vertical jumping. J Biomech 21:249–262.PubMedCrossRefGoogle Scholar
  3. Brand P, Hollister A (1999) Clinical mechanics of the hand, 3rd Edition. St. Louis: Mosby-Year Book, Inc.Google Scholar
  4. Chvátal V (1983) Linear programming. New York: W.H. Freeman and Company.Google Scholar
  5. d'Avella A, Bizzi E (2005) Shared and specific muscle synergies in natural motor behaviors. Proc Natl Acad Sci U S A 102:3076–3081.PubMedCrossRefGoogle Scholar
  6. Dewald JP, Pope PS, Given JD, Buchanan TS, Rymer WZ (1995) Abnormal muscle coactivation patterns during isometric torque generation at the elbow and shoulder in hemiparetic subjects. Brain 118 (Pt 2):495–510.PubMedCrossRefGoogle Scholar
  7. Hogan N (1985) The mechanics of multi-joint posture and movement control. Biol Cybern 52:315–331.PubMedCrossRefGoogle Scholar
  8. Kuo AD, Zajac FE (1993) A biomechanical analysis of muscle strength as a limiting factor in standing posture. J Biomech 26(Suppl 1):137–150.PubMedCrossRefGoogle Scholar
  9. Kuxhaus L, Roach SS, Valero-Cuevas FJ (2005) Quantifying deficits in the 3D force capabilities of a digit caused by selective paralysis: application to the thumb with simulated low ulnar nerve palsy. J Biomech 38:725–736.PubMedCrossRefGoogle Scholar
  10. Leijnse JN (1996) A graphic analysis of the biomechanics of the massless bi-articular chain. application to the proximal bi-articular chain of the human finger. J Biomech 29:355–366.PubMedCrossRefGoogle Scholar
  11. Loeb GE (2000) Overcomplete musculature or underspecified tasks? Motor Control 4:81–83; discussion 97–116.PubMedGoogle Scholar
  12. Mayston MJ (2001) People with cerebral palsy: effects of and perspectives for therapy. Neural Plast 8:51–69.PubMedCrossRefGoogle Scholar
  13. Obholzer A (1954) Chain-synergies in neuromuscular re-education; in the infantile cerebral flaccid-spastic syndrome. S Afr Med J 28:105–110.PubMedGoogle Scholar
  14. Pearlman JL, Roach SS, Valero-Cuevas FJ (2004) The fundamental thumb-tip force vectors produced by the muscles of the thumb. J Orthop Res 22:306–312.PubMedCrossRefGoogle Scholar
  15. Spoor CW (1983) Balancing a force on the fingertip of a two dimensional finger model without intrinsic muscles. J Biomech 16:497–504.PubMedCrossRefGoogle Scholar
  16. Tresch MC, Cheung VC, d'Avella A (2006) Matrix factorization algorithms for the identification of muscle synergies: evaluation on simulated and experimental data sets. J Neurophysiol 95(4):2199–2212.Google Scholar
  17. Valero-Cuevas FJ (2000) Predictive modulation of muscle coordination pattern magnitude scales fingertip force magnitude over the voluntary range. J Neurophysiol 83:1469–1479.PubMedGoogle Scholar
  18. Valero-Cuevas FJ (2005) An integrative approach to the biomechanical function and neuromuscular control of the fingers. J Biomech 38:673–684.PubMedCrossRefGoogle Scholar
  19. Valero-Cuevas FJ, Hentz VR (2002) Releasing the A3 pulley and leaving flexor superficialis intact increase palmar force following the Zancolli lasso procedures to prevent claw deformity in the intrinsic minus hand. J Orthop Res 20:902–909.PubMedCrossRefGoogle Scholar
  20. Valero-Cuevas FJ, Zajac FE, Burgar CG (1998) Large index-fingertip forces are produced by subject-independent patterns of muscle excitation. J Biomech 31:693–703.PubMedCrossRefGoogle Scholar
  21. Valero-Cuevas FJ, Towles JD, Hentz VR (2000) Quantification of fingertip force reduction in the forefinger following simulated paralysis of extensor and intrinsic muscles. J Biomech 33:1601–1609.PubMedCrossRefGoogle Scholar
  22. van Ingen Schenau GJ, Bobbert MF (1993) The global design of the hindlimb in quadrupeds. Acta Anat (Basel) 146:103–108.CrossRefGoogle Scholar
  23. van Soest AJ, Schwab AL, Bobbert MF, van Ingen Schenau GJ (1993) The influence of the biarticularity of the gastrocnemius muscle on vertical-jumping achievement. J Biomech 26:1–8.PubMedCrossRefGoogle Scholar
  24. Welmer AK, Holmqvist LW, Sommerfeld DK (2006) Hemiplegic limb synergies in stroke patients. Am J Phys Med Rehabil 85:112–119.PubMedCrossRefGoogle Scholar
  25. Winter DA (1990) Biomechanics and motor control of human movement, 2nd Edition. New York: Wiley.Google Scholar
  26. Yoshikawa T (1990) Foundations of robotics: analysis and control. Cambridge: The MIT Press.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Biomedical EngineeringThe University of Southern CaliforniaLos AngelesUSA

Personalised recommendations