Leendert Blankevoort

03-08-1990, 08:46 PM

Dear Biomch-L readers,

Following the discussions on the description of joint motions, I would

like to contribute the following points, which are based on the experiences

we have in our Biomechanics Lab. at the University of Nijmegen. My

intention is not to be in favor of any proposed convention, but to discuss

some items which were not directly addressed as yet and to clarify some

points.

1) JCS vs. Euler/Cardan angles

According to our analyses, the rotations in the JCS system and the Euler/

Cardan angles are equivalent, provided that the rotation sequence is

applied which is implied in the geometric definition in the JCS system.

This can be derived from the equations given in the paper of Grood and

Suntay (1983). For instance, if for the knee flexion, ad-abduction (or

varus-valgus) and internal-external rotation are specified of the tibia

relative to the femur, then in the JCS system the flexion axis is fixed to

the femur, the ad-abduction angle is the floating axis and the internal-

external rotation axis is fixed to the tibia. Using the Euler/Cardan

convention, the rotations are then specified as rotations around the body-

fixed axes of the tibia moving relative to a space fixed femur for which

the rotation sequence flexion, ad-abduction, internal-external rotation is

to be used in order to obtain the same values for the rotations as in the

JCS system. I believe that despite the controversies between Grood and

Woltring, both "chief" discussers can agree on this.

2) Translations

So far much of the attention was paid to the rotations and only little was

said on the translations, probably because the rotations are considered to

be clinically meaningful. However, the anteroposterior translations as

measured in instrumented AP-laxity tests, are important for quantifying AP

laxity and AP stiffness. The value of the translations of one bone

relative to another depend on the choice of the so-called base points,

which generally are identical with the origins of the coordinate systems in

the bones. Thus, special care is to be taken when comparing translational

data between different research groups and between different measurement

devices. When using the finite helical axis description, the translation

along the axis is independent of the choice of the coordinate systems and

represents the "true" translation of one bone relative to another for a

finite motion step. For pure translations however, the helical axis is not

defined, but then the value of the translation does not depend of the

choice of the base point.

3) Variations of the coordinate systems in experiments

As pointed out by Meglan, variations of the orientation of the coordinate

systems relative to the joint anatomy and the variations of the anatomic

reference position account, at least partly, for the differences in the

resulting rotations between joint specimens or between subjects. This was

discussed and illustrated in a paper from our group in the Journal of

Biomechanics in 1988 (Blankevoort et al., 1988). This does not mean that

as long as we are not able to uniquely define coordinate systems in

different joint specimens or different individuals, we should not bother

about the choice of the kinematic convention for the reason that the

variations between the convention are smaller than the observed variations

between joint specimens or individuals. Different kinematic conventions

will introduce systematic differences which have no relation whatsoever

with biologic variations or statistical standard deviations.

4) Mathematics and representation

The present discussion at the list was mainly focussed on how the rotations

are to be represented. Of course, if one is presenting data on joint

angles, then the mathematical background is to be specified. The reader

can then always reconstruct the motion patterns and express them with his

(or hers) own convention. However, most of the reports fail to give all

numbers, e.g. three rotations and three translations, because only those

data is reported which is relevant to the subject of the paper. Some

standardization may be necessary for commercially available measurement

systems to be used on a routine basis in the clinic. However, during the

process of data acquisition and data processing or in the formulations of

kinematic models, one is free to use any of the conventions as long as it

meets the criteria for the data processing and the mathematics of the

model. In the final stage, the kinematics data can be transformed to any

desired system. For instance in gait analysis, one can process the marker

data by some rotation convention which is found to suit best the

requirements for the subsequent dynamic analyses and can represent the

kinematics by use of the JCS or the Woltring system.

5) Future steps

Following the discussions on the list, it became clear to me that because

of the complexity of the description of 3-D joint motions, there remains a

lot of "teaching" to do in the field of Biomehcanics to make clinicians,

anatomists as well as biomechanicians aware of the difficulaties and

pitfalls of kinematics. Basic understanding seems more important than the

normalisation of motion description by adopting some standard convention,

since the consequences of any choice should be properly understood by the

users of such standard system. I am certainly in favor of producing an

extensive paper (or maybe a book?) on the ins and outs of biokinematics,

which should be aimed at a broad audience in the field of biomechanics, to

people with a poor mathematical background as well as people with poor

knowledge of (human) anatomy. I encourage Grood and Woltring to write

something (after they have cleared their confusions).

References

Grood, E.S. and Suntay, W.J. (1983) A joint coordinate system for the

clinical description of three-dimensional motions: applications to the

knee. J. Biomech. Engng 105, 136-144.

Blankevoort, L., Huiskes, R., Lange, A. de (1988) The Envelope of passive

knee joint motion. J. Biomechanics 21, 705-720.

Leendert Blankevoort

Biomechanics Section

Institute of Orthopedics

University of Nijmegen

P.O.box 9101

NL-6500 HB NIJMEGEN

The Netherlands

U462005@HNYKUN11.EARN

Following the discussions on the description of joint motions, I would

like to contribute the following points, which are based on the experiences

we have in our Biomechanics Lab. at the University of Nijmegen. My

intention is not to be in favor of any proposed convention, but to discuss

some items which were not directly addressed as yet and to clarify some

points.

1) JCS vs. Euler/Cardan angles

According to our analyses, the rotations in the JCS system and the Euler/

Cardan angles are equivalent, provided that the rotation sequence is

applied which is implied in the geometric definition in the JCS system.

This can be derived from the equations given in the paper of Grood and

Suntay (1983). For instance, if for the knee flexion, ad-abduction (or

varus-valgus) and internal-external rotation are specified of the tibia

relative to the femur, then in the JCS system the flexion axis is fixed to

the femur, the ad-abduction angle is the floating axis and the internal-

external rotation axis is fixed to the tibia. Using the Euler/Cardan

convention, the rotations are then specified as rotations around the body-

fixed axes of the tibia moving relative to a space fixed femur for which

the rotation sequence flexion, ad-abduction, internal-external rotation is

to be used in order to obtain the same values for the rotations as in the

JCS system. I believe that despite the controversies between Grood and

Woltring, both "chief" discussers can agree on this.

2) Translations

So far much of the attention was paid to the rotations and only little was

said on the translations, probably because the rotations are considered to

be clinically meaningful. However, the anteroposterior translations as

measured in instrumented AP-laxity tests, are important for quantifying AP

laxity and AP stiffness. The value of the translations of one bone

relative to another depend on the choice of the so-called base points,

which generally are identical with the origins of the coordinate systems in

the bones. Thus, special care is to be taken when comparing translational

data between different research groups and between different measurement

devices. When using the finite helical axis description, the translation

along the axis is independent of the choice of the coordinate systems and

represents the "true" translation of one bone relative to another for a

finite motion step. For pure translations however, the helical axis is not

defined, but then the value of the translation does not depend of the

choice of the base point.

3) Variations of the coordinate systems in experiments

As pointed out by Meglan, variations of the orientation of the coordinate

systems relative to the joint anatomy and the variations of the anatomic

reference position account, at least partly, for the differences in the

resulting rotations between joint specimens or between subjects. This was

discussed and illustrated in a paper from our group in the Journal of

Biomechanics in 1988 (Blankevoort et al., 1988). This does not mean that

as long as we are not able to uniquely define coordinate systems in

different joint specimens or different individuals, we should not bother

about the choice of the kinematic convention for the reason that the

variations between the convention are smaller than the observed variations

between joint specimens or individuals. Different kinematic conventions

will introduce systematic differences which have no relation whatsoever

with biologic variations or statistical standard deviations.

4) Mathematics and representation

The present discussion at the list was mainly focussed on how the rotations

are to be represented. Of course, if one is presenting data on joint

angles, then the mathematical background is to be specified. The reader

can then always reconstruct the motion patterns and express them with his

(or hers) own convention. However, most of the reports fail to give all

numbers, e.g. three rotations and three translations, because only those

data is reported which is relevant to the subject of the paper. Some

standardization may be necessary for commercially available measurement

systems to be used on a routine basis in the clinic. However, during the

process of data acquisition and data processing or in the formulations of

kinematic models, one is free to use any of the conventions as long as it

meets the criteria for the data processing and the mathematics of the

model. In the final stage, the kinematics data can be transformed to any

desired system. For instance in gait analysis, one can process the marker

data by some rotation convention which is found to suit best the

requirements for the subsequent dynamic analyses and can represent the

kinematics by use of the JCS or the Woltring system.

5) Future steps

Following the discussions on the list, it became clear to me that because

of the complexity of the description of 3-D joint motions, there remains a

lot of "teaching" to do in the field of Biomehcanics to make clinicians,

anatomists as well as biomechanicians aware of the difficulaties and

pitfalls of kinematics. Basic understanding seems more important than the

normalisation of motion description by adopting some standard convention,

since the consequences of any choice should be properly understood by the

users of such standard system. I am certainly in favor of producing an

extensive paper (or maybe a book?) on the ins and outs of biokinematics,

which should be aimed at a broad audience in the field of biomechanics, to

people with a poor mathematical background as well as people with poor

knowledge of (human) anatomy. I encourage Grood and Woltring to write

something (after they have cleared their confusions).

References

Grood, E.S. and Suntay, W.J. (1983) A joint coordinate system for the

clinical description of three-dimensional motions: applications to the

knee. J. Biomech. Engng 105, 136-144.

Blankevoort, L., Huiskes, R., Lange, A. de (1988) The Envelope of passive

knee joint motion. J. Biomechanics 21, 705-720.

Leendert Blankevoort

Biomechanics Section

Institute of Orthopedics

University of Nijmegen

P.O.box 9101

NL-6500 HB NIJMEGEN

The Netherlands

U462005@HNYKUN11.EARN