Herman J. Woltring

11-13-1989, 03:27 AM

Dear Biomch-l readers,

Within the CAMARC project (see below), the question has been posed on how to

standardize body segment co-ordinate systems. There seem to be a variety of

these, e.g., Z is the longitudinal axis in an oblong segment like thigh, shank

or foot, X is the medio-lateral axis, and Y the anterior-posterior axis. I

would be grateful for any pointers to relevant standardization proposals in

the litterature or elsewhere, and information on how (and why!) you define

your own coordinate systems.

Related to this is the notorious question on how to define joint angles via

Cardan ("Euler") angles `a la Grood & Suntay (they defined a mechanization of a

particular Cardanic convention, with the flexion/extension axis imbedded as the

1st rotation axis in the proximal segment, the endo-/exo-rotation axis imbedded

as the 3rd axis in the distal segment, and ab-/ad-duction the `floating' axis

perpendicular to the two other axes but imbedded in neither segment. See their

paper in the Journal of Biomechanical Engineering 105(1983), 136-144 for further

details, and the Letter to the Editor by Andrews in the Journal of Biomechanics

17(1984)2, 155-158.

Alternatively, I have proposed to use the Finite Axis of Rotation which is de-

fined by a unit direction vector N (N'N = 1), and a rotation angle theta ran-

ging between 0 and 180 degrees. Taking the product theta * N we obtain a `vec-

tor' which can be used as an attitude descriptor with respect to the reference

attitude. This representation does not exhibit `gimbal lock' as does the Car-

danic convention `a la Grood & Suntay; furthermore, the three components are

completely symmetrical with respect to each other, unlike Cardanic representa-

tion. I'll be glad to send a copy of a recent paper to anyone interested.

In clinical practise, joint angulation is merely defined in the simple, `planar'

case, where two of the three components in any convention are zero. Thus, we

have the liberty to choose any definition for compound rotations (where at least

two components are non-zero) in such a fashion as to minimize disadvantageous

properties like gimbal-lock; with various manufacturers now proposing their own

standards, there is a chance that de-facto standards are created with less than

optimal properties.

Standardization is becoming an important issue now an increasing number of (cli-

nical) laboratories are beginning to pool data in order to acquire suitable

databases on normal and pathological movenent.

Apart from naming joint axes and defining rotation parametrizations, there is

the perhaps even more serious problem of how to define segment coordinate sys-

tems from anatomical landmarks. For example, the flexion-extension axis in the

femur is often said to pass through the peaks of the condyles. However, these

peaks are rather flat, so ambiguity may be the result.

Any comments, either on BIOMCH-L or directly to ELERCAMA@HEITUE5.BITNET would

be most welcome.

Herman J. Woltring (CAMARC/Netherlands)

CAMARC ("Computer Aided Movement Analysis in a Rehabilitation Context") is a

project under the Advanced Informatics in Medicine action of the Commission of

the European Communities (AIM/DG XIII-F/CEC), with academic, industrial,

public-health, and independent partners from Italy, France, U.K. and The

Netherlands. Its scope is pre-competitive.

Within the CAMARC project (see below), the question has been posed on how to

standardize body segment co-ordinate systems. There seem to be a variety of

these, e.g., Z is the longitudinal axis in an oblong segment like thigh, shank

or foot, X is the medio-lateral axis, and Y the anterior-posterior axis. I

would be grateful for any pointers to relevant standardization proposals in

the litterature or elsewhere, and information on how (and why!) you define

your own coordinate systems.

Related to this is the notorious question on how to define joint angles via

Cardan ("Euler") angles `a la Grood & Suntay (they defined a mechanization of a

particular Cardanic convention, with the flexion/extension axis imbedded as the

1st rotation axis in the proximal segment, the endo-/exo-rotation axis imbedded

as the 3rd axis in the distal segment, and ab-/ad-duction the `floating' axis

perpendicular to the two other axes but imbedded in neither segment. See their

paper in the Journal of Biomechanical Engineering 105(1983), 136-144 for further

details, and the Letter to the Editor by Andrews in the Journal of Biomechanics

17(1984)2, 155-158.

Alternatively, I have proposed to use the Finite Axis of Rotation which is de-

fined by a unit direction vector N (N'N = 1), and a rotation angle theta ran-

ging between 0 and 180 degrees. Taking the product theta * N we obtain a `vec-

tor' which can be used as an attitude descriptor with respect to the reference

attitude. This representation does not exhibit `gimbal lock' as does the Car-

danic convention `a la Grood & Suntay; furthermore, the three components are

completely symmetrical with respect to each other, unlike Cardanic representa-

tion. I'll be glad to send a copy of a recent paper to anyone interested.

In clinical practise, joint angulation is merely defined in the simple, `planar'

case, where two of the three components in any convention are zero. Thus, we

have the liberty to choose any definition for compound rotations (where at least

two components are non-zero) in such a fashion as to minimize disadvantageous

properties like gimbal-lock; with various manufacturers now proposing their own

standards, there is a chance that de-facto standards are created with less than

optimal properties.

Standardization is becoming an important issue now an increasing number of (cli-

nical) laboratories are beginning to pool data in order to acquire suitable

databases on normal and pathological movenent.

Apart from naming joint axes and defining rotation parametrizations, there is

the perhaps even more serious problem of how to define segment coordinate sys-

tems from anatomical landmarks. For example, the flexion-extension axis in the

femur is often said to pass through the peaks of the condyles. However, these

peaks are rather flat, so ambiguity may be the result.

Any comments, either on BIOMCH-L or directly to ELERCAMA@HEITUE5.BITNET would

be most welcome.

Herman J. Woltring (CAMARC/Netherlands)

CAMARC ("Computer Aided Movement Analysis in a Rehabilitation Context") is a

project under the Advanced Informatics in Medicine action of the Commission of

the European Communities (AIM/DG XIII-F/CEC), with academic, industrial,

public-health, and independent partners from Italy, France, U.K. and The

Netherlands. Its scope is pre-competitive.