Skip to main content
Springer Nature Link
Log in

Optimization of two-joint arm movements: a model technique or a result of natural selection?

  • Original Paper
  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

The fossil record of early hominids suggests that their Arm length, and presumably stature and weight, had a tendency to increase. Using the minimum jerk principle and a related formulation of averaged specific power, ASP, with regard to selected two-joint Arm movements, the current paper explores relationships between ASP, hand trajectory length (or Arm length, or body mass) and mean movement speed, deriving relationships which indicate that ASP is proportional to cubic mean movement speed, but inversely proportional to hand trajectory length (or Arm length, or 1/3 power of body mass). Accordingly, an `ecological niche’ is modeled in a three-parameter space. Either ASP maximization for fixed movement time, or ASP minimization for fixed mean movement speed, taken as selective optimization criterion, allows the increasing of human Arm length during evolution, regardless of the arm-to-forearm length ratio.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

ASP:

Averaged specific power

References

  • Aiello L., Dean C. (1990). An introduction to human evolutionary anatomy. Academic, London

    Google Scholar 

  • Bevington PR., Robinson DK. (1992). Data reduction and error analysis for the physical sciences, 2nd edn. WCB/McGraw-Hill, Boston

    Google Scholar 

  • Brüwer M., Cruse H. (1990). A network model for the control of the movement of a redundant manipulator. Biol Cybern 62:549–555

    Article  PubMed  Google Scholar 

  • Burdet E. (2000a). Learning impedance to stabilize unstable dynamics: direct evidence in multijoint movements. Society for Neuroscience Abstracts

  • Burdet E. (2001). The central nervous system stabilizes unstable dynamics by learning optimal impedance. Nature 414:446–449

    Article  PubMed  CAS  Google Scholar 

  • Burdet E., Osu R., Franklin DW., Yoshioka T., Milner TE., Kawato M. (2000b). A method for measuring endpoint stiffness during multi-joint arm movements. J Biomech 33:1705–1709

    Article  CAS  Google Scholar 

  • Churchill SE., Smith FH. (2000). A modern human humerus from the early aurignacian of Vogelherdhohle (Stetten, Germany). Am J Phys Anthropol 112(2):251–273

    Article  PubMed  CAS  Google Scholar 

  • d’Avella A., Saltiel P., Bizzi E. (2003). Combinations of muscle synergies in the construction of a natural motor behavior. Nat Neurosci 6(3):300-308

    Article  PubMed  CAS  Google Scholar 

  • Draper NR., Smith H. (1998). Applied regression analysis, 3rd Edn. Wiley, New York

    Google Scholar 

  • Esteki A., Mansour JM. (1996). An experimentally based nonlinear viscoelastic model of joint passive moment. J Biomech 29(4):443–450

    Article  PubMed  CAS  Google Scholar 

  • Flash T., Hogan N. (1985). The coordination of arm movements: an experimentally confirmed mathematical model. J Neurosci 5(7):1688–1703

    PubMed  CAS  Google Scholar 

  • Fu KS., Gonzales RC., Lee CSG. (1987). Robotics: control, sensing, vision, and intelligence. McGraw-Hill, New York

    Google Scholar 

  • Gomi H., Kawato M. (1997). Human arm stiffness and equilibrium-point trajectory during multi-joint movement. Biol Cybern 76:163–171

    Article  PubMed  CAS  Google Scholar 

  • Goodall J. (1986). Chimpanzee of Gombe: patterns of behaviour. Harvard University Press, Cambridge

    Google Scholar 

  • Hasler EM., Herzog W., Wu JZ., Muller W., Wyss U. (1999). Articular cartilage biomechanics: theoretical models, material properties, and biosynthetic response. Crit Rev Biomed Eng 27(6):415–88

    PubMed  CAS  Google Scholar 

  • Hollerbach JM., Flash T. (1982). Dynamic interactions between limb segments during planar arm movement. Biol Cybern 44:67–77

    Article  PubMed  CAS  Google Scholar 

  • Lacquaniti F., Terzuolo C., Viviani P. (1983). The law relating the kinematic and figural aspects of drawing movements. Acta Psychol 5:115–130

    Article  Google Scholar 

  • Landau L., Lifchitz E. (1966). Mechanique. Mir, Moscow

    Google Scholar 

  • Massone L., Bizzi E. (1989). A neural network model for limb trajectory formation. Biol Cybern 61:417–425

    Article  PubMed  CAS  Google Scholar 

  • Mathers K., Henneberg M. (1995). Were we ever that big?. Gradual increase in hominid body size over time. HOMO 46:141–173

    Google Scholar 

  • Morasso P. (1981). Spatial control of arm movements. Exp Brain Res 42(2):223–227

    Article  PubMed  CAS  Google Scholar 

  • Morasso P., Sanguineti V. (1997). Movement dynamics in speed/accuracy trade-off. Behav Brain Sci 20:319

    Article  Google Scholar 

  • Mussa Ivaldi FA., Morasso P., Zaccaria R. (1988). Kinematic networks. A distributed model for representing and regularizing motor redundancy. Biol Cybern 60(1):1–16

    CAS  Google Scholar 

  • Mussa-Ivaldi FA., Hogan N., Bizzi E. (1985). Neural, mechanical, and geometric factors subserving arm posture in humans. J Neurosci 5(10):2732–2743

    PubMed  CAS  Google Scholar 

  • Mussa-Ivaldi FA., Bizzi E. (2000). Motor learning through the combination of primitives. Philos Trans R S Biol Sci 355:1755–1769

    Article  CAS  Google Scholar 

  • Nelson WL. (1983). Physical principles for economies of skilled movements. Biol Cybern 46:135–147

    Article  PubMed  CAS  Google Scholar 

  • Pheasant S. (1996). Bodyspace: anthropometry, ergonomics and the design of work, 2nd edn. Taylor and Francis, London

    Google Scholar 

  • Plamondon R. (1995a). A kinematic theory of rapid human movements: Part I. Movement representation and generation. Biol Cybern 72:295–307

    CAS  Google Scholar 

  • Plamondon R. (1995b). A kinematic theory of rapid human movements: Part II. Movement time and control. Biol Cybern 72:309–320

    Article  CAS  Google Scholar 

  • Polk JD. (2002). Adaptive and phylogenetic influences on musculoskeletal design in cercopithecine primates. J Exp Biol 205:3399–3412

    PubMed  CAS  Google Scholar 

  • Pontryagin LS., Boltyanskii VG., Gamkrelidze RV., Mishchenko EF. (1962). The mathematical theory of optimal processes. Interscience Publisher Inc, New York

    Google Scholar 

  • Popescu AI. (1999). Bionics, biological systems and optimal design principle. Acta Biotheor 46:299–310

    Article  CAS  Google Scholar 

  • Preuschoft H. (1971). Body posture and mode of locomotion in early Pleistocene Hominids. Folia Primatologica 14:209–240

    Article  CAS  Google Scholar 

  • Rose MD. (1991). The process of bipedalization in hominids. In: Coppens Y., Senut B (eds). Origine(s) de la bipédie chez les hominidés. CNRS, Paris pp. 37–48

    Google Scholar 

  • Ruff CB., Trinkaus E., Walker A., Larsen CS. (1993). Postcranial robusticity in Homo . I.Temporal trends and mechanical interpretation. Am J Phys Anthropol 91:21–53

    Article  PubMed  CAS  Google Scholar 

  • Secco EL. (2001). Movement control of a 3 d.o.f. artificial finger: dynamic learning and execution of the natural movement. PhD dissertation, Pavia

  • Secco EL., Scheidt R., Patton J., Mussa-Ivaldi FA. (2003). Misrepresentation of limb dynamics induced by the suppression of visual errors. Society of Neuroscience, New Orleans

    Google Scholar 

  • Shadmehr R., Mussa-Ivaldi FA. (1994). Adaptive representation of dynamics during learning of a motor task. J Neurosci 14:3208–3224

    PubMed  CAS  Google Scholar 

  • Suzuki M., Matsunami K., Yamazachi Y., Mizuno N. (1996). Application of the minimum jerk model to formation of the trajectory of the centre of mass during multijoint limb movements. Folia Primatol 66:240–252

    Article  PubMed  CAS  Google Scholar 

  • Taylor CR. (1985). Force development during sustained locomotion: a~determinant of gait, speed and metabolic power. J Exp Biol 115:253–262

    PubMed  CAS  Google Scholar 

  • Taylor CR., Heglund NC., McMahon TA., Lonney TR. (1980). Energetic cost of generating muscular force during running: a comparison of large and small animals. J Exp Biol 86:9–18

    Google Scholar 

  • Taylor CR., Schmidt-Nielsen K., Raab JL. (1970). Scaling of energetic cost of running to body size in mammals. Am J Physiol 219:1104–1107

    PubMed  CAS  Google Scholar 

  • Todorov E., Jordan M. (2002). Optimal feedback control as a theory of motor coordination. Nat Neurosci 5(11):1226–1235

    Article  PubMed  CAS  Google Scholar 

  • Uno Y., Kawato M., Suzuki R. (1989). Formation and control of optimal trajectory in human multijoint Arm movement—minimum torque-change model. Biol Cybern 61:89–101

    Article  PubMed  CAS  Google Scholar 

  • Valandro L., Caimmi R., Colombo L. (2003). What is hidden behind the concept of energy transformation in ecosystems. Ecol Model 170:185–191

    Article  Google Scholar 

  • Wang WJ., Crompton RH., Gunther MM. (2003). Optimum ratio of upper to lower limb lengths in hand-carrying of a load under the assumption of frequency coordination. J Biomechan 36:249–252

    Article  CAS  Google Scholar 

  • Wang WJ., Crompton RH. (2003). Size and power required for motion with implication for the evolution of early hominids. J Biomech 36:1237–1246

    Article  PubMed  CAS  Google Scholar 

  • West GB., Brown JH. (2004). Life’s universal scaling laws. Phys Today 57:36–42

    Article  Google Scholar 

  • Winter DA. (1990). Biomechanics and motor control of human movement. Wiley, New York

    Google Scholar 

  • Witte H., Recknagel S., Preuschoft H. (1991). Human body proportions explained on the basis of biomechanical principles. Zeitsch Morphol Anthropol 78:407–423

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Universitá di Pavia, Via Ferrata, 1, 27100, Pavia, Italy

    Emanuele Lindo Secco, Giovanni Magenes & Benedetto Salvato

  2. Dipartimento di Biologia, Università di Padova, Via U. Bassi, 58/B, 35121, Padova, Itlay

    Luca Valandro

  3. Dipartimento di Astronomia, Università di Padova, Vicolo dell‘Osservatorio, 5, 35122, Padova, Italy

    Roberto Caimmi

Authors
  1. Emanuele Lindo Secco
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Luca Valandro
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Roberto Caimmi
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Giovanni Magenes
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. Benedetto Salvato
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Emanuele Lindo Secco.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Secco, E.L., Valandro, L., Caimmi, R. et al. Optimization of two-joint arm movements: a model technique or a result of natural selection?. Biol Cybern 93, 288–306 (2005). https://doi.org/10.1007/s00422-005-0003-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00422-005-0003-2

Keywords