A robotic model for Codman's paradox simulation and interpretation

Bertrand Tondu

doi:10.1016/j.crme.2018.04.016

A robotic model for Codman's paradox simulation and interpretation

Bertrand Tondu ¹

¹ Institut national de sciences appliquées, Université de Toulouse, 31077 Toulouse cedex 4, France

Comptes Rendus. Mécanique, Volume 346 (2018) no. 9, pp. 855-867.

Résumé

A robotic approach based on Denavit–Hartenberg parametrization is proposed for simulating and interpreting Codman's paradox. A 3-degree-of-freedom robot model of the glenohumeral joint, driving the arm reduced to its long humerus, is considered for simulating the two-step rotational sequence of Codman's paradox. We propose to use the classical distinction made in robotics between the joint space, i.e. the inner space of joint angles, and the operational space, i.e. the outer physical space, for interpreting this historical version of the paradox, as there is some kind of confusion between these two spaces to be considered for arm movement definition. In its extended form, developed by MacConnail, the three-step rotational sequence of Codman's paradox would highlight the motor redundancy of the shoulder joint, necessitating for its simulation, according to our robotic approach, a 4-axis model of the shoulder spheroid joint. Our model provides a general prediction of the conjunct rotation angle in full accordance with clinical observation for a two-step or three-step version of Codman's paradox. The relation of the paradox with a possible general law of motion is finally discussed.

Reçu le : 2018-01-25
Accepté le : 2018-04-30
Publié le : 2018-06-28

DOI : 10.1016/j.crme.2018.04.016

Mots clés : Codman's paradox, Roth's proof, Shoulder motor redundancy

Affiliations des auteurs :

Bertrand Tondu ¹

¹ Institut national de sciences appliquées, Université de Toulouse, 31077 Toulouse cedex 4, France

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Bertrand Tondu. A robotic model for Codman's paradox simulation and interpretation. Comptes Rendus. Mécanique, Volume 346 (2018) no. 9, pp. 855-867. doi : 10.1016/j.crme.2018.04.016. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.04.016/

Bibliographie
Cité par

[1] E.A. Codman The Shoulder. Rupture of the Supraspinatus Tendon and Other Lesions in or about the Subacromial Bursa, 1984 (Reprint of Supplemented Edition, Robert E. Kreiger Publishing Company, Malabar, FL, USA, 1934)

[2] E.Y.S. Chao Justification of triaxial goniometer for the measurement of joint rotation, J. Biomech., Volume 13 (1980), pp. 989-1006

[3] P.L. Cheng; A.C. Nicol; J.P. Paul Determination of axial rotation angles of limb segments – a new method, J. Biomech., Volume 33 (2000), pp. 837-843

[4] P.L. Cheng Simulation of Codman's paradox reveals a general law of motion, J. Biomech., Volume 39 (2006), pp. 1201-1207

[5] P.L. Cheng Response to Dr. Stepan and Dr. Otahal: a mathematical note on the simulation of the Codman's paradox, J. Biomech., Volume 39 (2006), pp. 3082-3084

[6] J. Denavit; R.S. Hartenberg A kinematic notation for lower-pair mechanisms based on matrices, J. Appl. Mech. (1955), pp. 215-221

[7] C.A.M. Doorenbosch; J. Harlaar; D.J. Veeger The globe system: an unambiguous description of shoulder positions in daily life movements, J. Rehabil. Res. Dev., Volume 40 ( March/April 2003 ) no. 2, pp. 147-156

[8] E.S. Grood; W.J. Suntay A joint coordinate system for the clinical description of three-dimensional motions; application to the knee, J. Biomech. Eng., Volume 105 (1983), pp. 137-144

[9] A.M. Hill; A.M.J. Bull; A.L. Wallace; G.R. Johnson Qualitative and quantitative descriptions of gleno-humeral motion, Gait Posture, Volume 27 (2008), pp. 177-188

[10] A. Kapandji The Physiology of Joints, Upper Limb, vol. 1, Churchill Livingstone, 2002

[11] M.A. MacConaill Rotary movements and functional décalage with some reference to rehabilitation, Br. J. Phys. Med. Ind. Hyg. ( March 1950 ), pp. 50-56

[12] M.A. MacConaill Joint movement, Physiotherapy, November issue (1964), pp. 359-367

[13] M.A. MacConaill Mechanical anatomy of motion and posture, Therapeutic Exercise: The Third Volume of Physical Medicine Library, Elizabeth Licht, Publisher, New Haven, CT, USA, 1965, pp. 47-89

[14] W.J. Mallon On the hypotheses that determine the definitions of glenohumeral joint motion: with resolution of Codman's pivotal paradox, J. Shoulder Elb. Surg., Volume 21 (2012), p. e4-e19

[15] T. Masuda; A. Ishida; L. Cao; S. Morita A proposal for a new definition of the axial rotation angle of the shoulder joint, J. Electromyog. Kinesiol., Volume 18 (2008), pp. 154-159

[16] R.P. Paul Robot Manipulators: Mathematics, Programming and Control, MIT Press, Cambridge, Massachusetts, 1981

[17] Med. Eng. Phys., 20 (1998), p. 639

[18] A. Pettofrezo Matrices and Transformations, Prentice–Hall, 1966 (Reprinted by Dover, New York, 1966 and 1978)

[19] J.C. Politti; G. Goroso; M.E. Valentinuzzi; O. Brano Codman's paradox of the arm rotations is not a paradox: mathematical validation, Med. Eng. Phys., Volume 20 (1998), pp. 257-260

[20] B. Roth The kinematics of motion through finitely separated positions, Trans. ASME, J. Appl. Mech., Volume 34 (1967) no. 3, pp. 591-598 (Series E)

[21] B. Roth Finite-position theory applied to mechanism synthesis, Trans. ASME, J. Appl. Mech., Volume 34 (1967) no. 3, pp. 599-605 (Series E)

[22] V. Stepan; S. Otahal Is Codman's Paradox really a Paradox? Letter to the Editor, J. Biomech., Volume 39 (2006), pp. 3080-3082

[23] W.J. Suntay; E.S. Grood; F.R. Noyes; D.L. Butler A coordinate system for describing joint positions, Adv. Bioeng. (1978), pp. 59-62

[24] B. Tondu Industrial robotics joint space is a vector space, C. R. Mecanique, Volume 331 (2003), pp. 357-364 (in French with an abridged English version)

[25] S.I. Wolf; L. Fradet; O. Rettig Conjunct rotation: Codman's paradox revisited, Med. Biol. Eng. Comput., Volume 47 (2009), pp. 551-556

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