Table 2.

Joint coordinate systems suggested for in vivo measurements of whole-arm movements, chosen from among the multiple definitions advocated by the ISB recommendations [10]

Joint	Axis	Angle	Description	Positive direction	Origin (0 deg)	ISB equivalent
Shoulder (humerus relative to thorax)	$Y\hspace{0.17em}\left(Y_A\right)$	${\alpha }_s$	Plane of elevation	(positive $Y$)	(anatomical position)	e1 of humerus rel. to thorax, ${\gamma }_h$ (2.4.7)
	$X^{\prime }\left(\mathrm{Int}.\right)$	${\beta }_s$	Elevation	(positive $X\prime$)	(anatomical position)	e2 of humerus rel. to thorax, ${\beta }_h$ (2.4.7)
	$Y^{″}\left(Y_B\right)$	${\gamma }_s$	Axial rotation	Internal rotation	(anatomical position)	e3 of humerus rel. to thorax, ${\left({\gamma }_h\right)}_2$ (2.4.7)
Elbow-forearm (forearm relative to humerus)	$Z\hspace{0.17em}\left(Z_B\right)$	${\alpha }_e$	Elbow flexion–extension	Flexion	Fully extended	e1 of elbow/forearm joint, ${\alpha }_{\text{HF}}$ (3.4.1)
	$X^{\prime }\left(\mathrm{Int}.\right)$	${\beta }_e$	Carrying angle	(positive $X\prime$)	$Y_C$ in $X_B-Y_B$ plane	e2 of elbow/forearm joint, ${\beta }_{\text{HF}}$ (3.4.1)
	$Y^{″}\left(Y_C\right)$	${\gamma }_e$	Forearm pronation–supination	Pronation	Fully supinated	e3 of elbow/forearm joint, ${\gamma }_{\text{HF}}$ (3.4.1)
Wrist (third metacarpal relative to forearm)	$Z\hspace{0.17em}\left(Z_C\right)$	${\alpha }_w$	Wrist flexion–extension	Flexion	third metacarpal parallel to line from US to EL-EM midpoint	e1 of wrist joint, $\alpha$ (4.4.1)
	$X^{\prime }\left(\mathrm{Int}.\right)$	${\beta }_w$	Wrist radial–ulnar deviation	Ulnar deviation		e2 of wrist joint, $\beta$ (4.4.1)
	$Y^{″}\left(Y_D\right)$	${\gamma }_w$	Wrist axial rotation	(positive $Y″$)	$X_D$ in $X_C-Y_C$ plane	e3 of wrist joint, $\gamma$ (4.4.1)

Each JCS is defined by axes of rotation, listed in order from first to third rotation axis. The rotation axes are given in terms of axes of the BCS of the distal segment and, in parentheses, in terms of axes embedded in the proximal and distal segments.8 Given are also the names of the angles of rotation used in this paper, along with their descriptions and explanations of which direction is positive and where the angle begins. Finally, the last column lists the equivalent axes and angles defined in the ISB recommendations (with references).