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Technical Briefs

Expression of Joint Moment in the Joint Coordinate System

[+] Author and Article Information
Guillaume Desroches1

 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

Laurence Chèze

 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

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, Franceguillaume.desroches@gmail.com

1

Corresponding author.

J Biomech Eng 132(11), 114503 (Oct 12, 2010) (4 pages) doi:10.1115/1.4002537 History: Received March 18, 2010; Revised September 02, 2010; Posted September 10, 2010; Published October 12, 2010; Online October 12, 2010

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.

FIGURES IN THIS ARTICLE
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Copyright © 2010 by American Society of Mechanical Engineers
Topics: Knee
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References

Figures

Grahic Jump Location
Figure 1

(a) Nonorthogonal and (b) orthogonal projections of M on e1

Grahic Jump Location
Figure 2

Time normalized evolution of the orthogonal (dotted/dashed lines) and nonorthogonal (solid lines) projections of the shoulder joint moment on the first axis (a), second axis (b), and third axis (c) over the propulsive cycle of wheelchair propulsion. The gray shaded lines depict the transition between the push and recovery phases.

Grahic Jump Location
Figure 3

Time normalized evolution of the orthogonal (doted/dashed lines) and nonorthogonal (solid lines) projections of the knee joint moment on the first axis (a), second axis (b), and third axis (c) over the gait cycle. The gray shaded lines depict the transition between the stance and swing phases.

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