Table 5.

Bone coordinate system definitions based on anatomical landmarks (left foot). m(a,b) = midpoint between a and b.

bone	first axis	temporary axis	second axis	third axis
calcaneus	${\mathbf{X}}_{\mathrm{CAL}}=|1\to 2|$	${\mathbf{t}}_{\mathrm{CAL}}=|3\to 4|$	${\mathbf{Y}}_{\mathrm{CAL}}={\mathbf{t}}_{\mathrm{CAL}}\times {\mathbf{X}}_{\mathrm{CAL}}$	${\mathbf{Z}}_{\mathrm{CAL}}={\mathbf{X}}_{\mathrm{CAL}}\times {\mathbf{Y}}_{\mathrm{CAL}}$
talus	${\mathbf{X}}_{\mathrm{TAL}}=|5\to 6|$	${\mathbf{t}}_{\mathrm{TAL}}=|7\to 8|$	${\mathbf{Z}}_{\mathrm{TAL}}={\mathbf{X}}_{\mathrm{TAL}}\times {\mathbf{t}}_{\mathrm{TAL}}$	${\mathbf{Y}}_{\mathrm{TAL}}={\mathbf{Z}}_{\mathrm{TAL}}\times {\mathbf{X}}_{\mathrm{TAL}}$
cuboid	${\mathbf{X}}_{\mathrm{CUB}}=|9\to 10|$	${\mathbf{t}}_{\mathrm{CUB}}=|11\to 12|$	${\mathbf{Y}}_{\mathrm{CUB}}={\mathbf{t}}_{\mathrm{CUB}}\times {\mathbf{X}}_{\mathrm{CUB}}$	${\mathbf{Z}}_{\mathrm{CUB}}={\mathbf{X}}_{\mathrm{CUB}}\times {\mathbf{Y}}_{\mathrm{CUB}}$
navicular	${\mathbf{Y}}_{\mathrm{NAV}}=|13\to 14|$	${\mathbf{t}}_{\mathrm{NAV}}=|13\to 15|$	${\mathbf{X}}_{\mathrm{NAV}}={\mathbf{Y}}_{\mathrm{NAV}}\times {\mathbf{t}}_{\mathrm{NAV}}$	${\mathbf{Z}}_{\mathrm{NAV}}={\mathbf{X}}_{\mathrm{NAV}}\times {\mathbf{Y}}_{\mathrm{NAV}}$
tibia	${\mathbf{Y}}_{\mathrm{TIB}}=|m(18,19)\to m(16,17)|$	${\mathbf{t}}_{\mathrm{TIB}}=|m(17,18)\to m(16,19)|$	${\mathbf{Z}}_{\mathrm{TIB}}={\mathbf{t}}_{\mathrm{TIB}}\times {\mathbf{Y}}_{\mathrm{TIB}}$	${\mathbf{X}}_{\mathrm{TIB}}={\mathbf{Y}}_{\mathrm{TIB}}\times {\mathbf{Z}}_{\mathrm{TIB}}$
MT	${\mathbf{X}}_{\mathrm{MT}}=|m(23,24)\to m(m(20,21),22)|$	${\mathbf{t}}_{\mathrm{MT}}=|21\to 23|\times |21\to 20|$	${\mathbf{Y}}_{\mathrm{MT}}={\mathbf{t}}_{\mathrm{MT}}\times {\mathbf{X}}_{\mathrm{MT}}$	${\mathbf{Z}}_{\mathrm{MT}}={\mathbf{X}}_{\mathrm{MT}}\times {\mathbf{Y}}_{\mathrm{MT}}$