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. Author manuscript; available in PMC: 2014 Jul 22.
Published in final edited form as: J Biomech. 2013 Nov 20;47(1):269–276. doi: 10.1016/j.jbiomech.2013.11.014

Table 2.

Joint force and moment calculations. The following variables were used: Ḣ: rate of change of angular momentum, ā: acceleration of center of mass (COM), F̅: force, M̅: moment, r̅: moment arm from COM to distal and proximal joint, and ḡ: gravity (9.81m/s2). Subscripts denote the following: SW: SmartWheel, H: hand, W: wrist, F: forearm, E: elbow, UA: upper arm, or GH: glenohumeral.

Joint Force Moment
Wrist F̅W = massH(āH + ḡ) − F̅SW M̅W = ḢH − M̅SW + r̅DisH × F̅SW − r̅ProxH × F̅W
Elbow F̅E = massF(āF + ḡ) − F̅Wrist M̅E = ḢF − M̅Wrist + r̅DisF × F̅Wrist − r̅ProxF × F̅E
Glenohumeral F̅GH = massUA(āUA + ḡ) − F̅Elbow M̅GH = ḢUA − M̅Elbow + r̅DisUA × F̅Elbow − r̅ProxUA × F̅GH