The question of using the nonorthogonal joint coordinate system (JCS) to report joint moments has risen in the literature. However, the expression of joint moments in a nonorthogonal system is still confusing. The purpose of this paper is to present a method to express any 3D vector in a nonorthogonal coordinate system. The interpretation of these expressions in the JCS is clarified and an example for the 3D joint moment vector at the shoulder and the knee is given. A nonorthogonal projection method is proposed based on the mixed product. These nonorthogonal projections represent, for a 3D joint moment vector, the net mechanical action on the JCS axes. Considering the net mechanical action on each axis seems important in order to assess joint resistance in the JCS. The orthogonal projections of the same 3D joint moment vector on the JCS axes can be characterized as “motor torque.” However, this interpretation is dependent on the chosen kinematic model. The nonorthogonal and orthogonal projections of shoulder joint moment during wheelchair propulsion and knee joint moment during walking were compared using root mean squares (rmss). rmss showed differences ranging from 6 N m to 22.3 N m between both projections at the shoulder, while differences ranged from 0.8 N m to 3.0 N m at the knee. Generally, orthogonal projections were of lower amplitudes than nonorthogonal projections at both joints. The orthogonal projection on the proximal or distal coordinates systems represents the net mechanical actions on each axis, which is not the case for the orthogonal projection (i.e., motor torque) on JCS axes. In order to represent the net action at the joint in a JCS, the nonorthogonal projection should be used.
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e-mail: guillaume.desroches@gmail.com
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November 2010
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Expression of Joint Moment in the Joint Coordinate System
Raphaël Dumas
e-mail: guillaume.desroches@gmail.com
Raphaël Dumas
Université de Lyon
, F-69622 Lyon, France; Université Lyon 1
, F-69622 Villeurbanne, France; INRETS
, UMR T9406, Laboratoire de Biomécanique et Mécanique des Chocs, F-69675 Bron, France
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Raphaël Dumas
Université de Lyon
, F-69622 Lyon, France; Université Lyon 1
, F-69622 Villeurbanne, France; INRETS
, UMR T9406, Laboratoire de Biomécanique et Mécanique des Chocs, F-69675 Bron, Francee-mail: guillaume.desroches@gmail.com
J Biomech Eng. Nov 2010, 132(11): 114503 (4 pages)
Published Online: October 12, 2010
Article history
Received:
March 18, 2010
Revised:
September 2, 2010
Posted:
September 10, 2010
Published:
October 12, 2010
Online:
October 12, 2010
Citation
Desroches, G., Chèze, L., and Dumas, R. (October 12, 2010). "Expression of Joint Moment in the Joint Coordinate System." ASME. J Biomech Eng. November 2010; 132(11): 114503. https://doi.org/10.1115/1.4002537
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