Advertisement

Conjunct rotation: Codman’s paradox revisited

  • Sebastian I. Wolf
  • Laetitia Fradet
  • Oliver Rettig
Special Issue - Original Article

Abstract

This contribution mathematically formalizes Codman’s idea of conjunct rotation, a term he used in 1934 to describe a paradoxical phenomenon arising from a closed-loop arm movement. Real (axial) rotation is distinguished from conjunct rotation. For characterizing the latter, the idea of reference vector fields is developed to define the neutral axial position of the humerus for any given orientation of its long axis. This concept largely avoids typical coordinate singularities arising from decomposition of 3D joint motion and therefore can be used for postural (axial) assessment of the shoulder joint both clinically and in sports science in almost the complete accessible range of motion. The concept, even though algebraic rather complex, might help to get an easier and more intuitive understanding of axial rotation of the shoulder in complex movements present in daily life and in sports.

Keywords

Shoulder Joint Modelling Axial rotation Convention Gimbal lock 

References

  1. 1.
    American Academy of Orthopaedic Surgeons (1965) Joint motion. Method of measuring and recording. Churchill Livingstone, EdinburghGoogle Scholar
  2. 2.
    Cheng PL (2006) Simulation of Codman’s paradox reveals a general law of motion. J Biomech 39:1201–1207. doi: 10.1016/j.jbiomech.2005.03.017 CrossRefGoogle Scholar
  3. 3.
    Cheng PL, Nicol AC, Paul JP (2000) Determination of axial rotation angles of limb segments—a new method. J Biomech 33:837–843. doi: 10.1016/S0021-9290(00)00032-4 CrossRefGoogle Scholar
  4. 4.
    Codman EA (1934) Normal motions of the shoulder joint. In: The shoulder—rupture of the supraspinatus tendon and other lesions in or about the subacromial bursa, Krieger Publishing, Malabar, FloridaGoogle Scholar
  5. 5.
    Doorenbosch CA, Harlaar J, Veeger DH (2003) The globe system: an unambiguous description of shoulder positions in daily life movements. J Rehabil Res Dev 40:147–155. doi: 10.1682/JRRD.2003.03.0149 Google Scholar
  6. 6.
    Grood ES, Suntay WJ (1983) A joint coordinate system for the clinical description of three-dimensional motions: application to the knee. J Biomech Eng 105:136–144CrossRefGoogle Scholar
  7. 7.
    Kapandji IA (1980) Physiologie articulaire, 5th edn. Librairie Maloine, ParisGoogle Scholar
  8. 8.
    Masuda T, Ishida A, Cao L, Morita S (2008) A proposal for a new definition of the axial rotation angle of the shoulder joint. J Electromyogr Kinesiol 18:154–159. doi: 10.1016/j.jelekin.2006.08.008 CrossRefGoogle Scholar
  9. 9.
    Miyazaki S, Ishida A (1991) New mathematical definition and calculation of axial rotation of anatomical joints. J Biomech Eng 113:270–275. doi: 10.1115/1.2894884 CrossRefGoogle Scholar
  10. 10.
    Pearl ML, Harris SL, Lippitt SB, Sidles JA, Harryman IDT, Matsen IFA (1992) III: A system for describing positions of the humerus relative to the thorax and its use in the presentation of several functionally important arm positions. J Shoulder Elbow Surg 1:113–118. doi: 10.1016/S1058-2746(09)80129-8 CrossRefGoogle Scholar
  11. 11.
    Tupling SJ, Pierrynowski MR (1987) Use of cardan angles to locate rigid bodies in three-dimensional space. Med Biol Eng Comput 25:527–532. doi: 10.1007/BF02441745 CrossRefGoogle Scholar
  12. 12.
    Wolf SI, Rettig O (2005) Rotation in ball joints—a solution for the Codman paradoxon. Proceedings of biomechanics of the lower limb in health disease and rehabilitation. Salford, UK, 5–7 Sept 2005Google Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2009

Authors and Affiliations

  • Sebastian I. Wolf
    • 1
  • Laetitia Fradet
    • 1
  • Oliver Rettig
    • 1
  1. 1.Orthopädische Universitätsklinik HeidelbergUniversity of HeidelbergHeidelbergGermany

Personalised recommendations