unknown user

02-27-1990, 11:49 PM

I guess it's about time that someone besides Herman and Ed commented on

the method of describing the 3D orientation of the body segments relative

to one another.

In the recent complete rewrite of the analysis and display

software for the gait lab here at Ohio State University, I included both

the Grood & Suntay description, which I refer to as the Joint Coordinate

System (JCS), of the joint rotations as well as the standard Pitch-Roll-Yaw

(PRY) euler angles plus calculation of the finite screw across the joint

(the position and orientation of the segments is known in 3D using the marker

position data) using several different algorithms. In addition, the rotation

about the screw axis can be described using Herman's concept of attitude angles

(basically multiply the direction vector of the screw axis by the magnitude of

the rotation about the axis to form a scaled vector) in terms of the proximal

segment local coordinate system (LCS), distal segment LCS, or the JCS. All

these different methods are included because I wanted to compare them on

actual experimentally acquired data plus since there is no standardization at

the moment I decided to use the shotgun approach and try to cover the majority

of the possible orientation description methods.

I did a poster on some of the results for the recent Orthopaedic Research

Society meeting in New Orleans. Interestingly, Murali Kadaba had a poster

right across the aisle which dealt with finite screws also. Basically, the

results using multiple trials of normal subject gait data (we use a marker set

consisting of 21 markers total for the upper and lower body with 3 markers on

most segments) show that for sagittal plane joint angles there really is no

statistically siginificant difference between any of the two rotation angle or

three attitude 1angle schemes used. This was true for all the joints of the

lower body as well as the pelvis, whose angle is not a relative angle but

instead is calculated relative to the global lab coordinate system (GCS). In

the out of plane angles (ab/adduction, in/external, pro/supination, in/eversion)

there were significant differences primarily for the ab/aduction and in/eversion

angles. These differences increase with the magnitude of the flexion angle

which not surprising. The interesting point however is that the attitude

angles are significantly different so the coordinate system in which they are

expressed is critical. Also, the attitude angles expressed in terms of the

JCS were different from the angles calculated with the JCS rotation angle

method.

Based upon these results, plus various other experiments which I have tried

out, it would seem that while the calculation method, i.e. rotation angles or

attitude angles, is important, the coordinate system used to express the

attitude angles is just as important. Which leads to the obvious point that

the positioning of these segment LCS's will have a critical effect upon the

calculated joint angles. I did some perturbation experiments to look at the

sensitivity of the calculated joint angles to slight changes in the orientation

of either or both of the segment LCS's used as input data for the angle

calculation. Each perturbation had some effect upon one or more of the

calculated angles- not surprising. The effects are widely varying however and

it is a relevant concern to identify those effects which are going to most

readily occur with a given marker set and motion system configuration. Even

rigid bodies with more than 3 markers attached to the body segment are

sensitive to this problem since it is difficult to control the position/

orientation of the marker carrier relative to the underlying bones with

accuracy and consistency. This is getting a little of track of the discussion

focusing on rotation angles and finite screw attitude angles... Oh well, I

guess we all have our soap box on one issue or another :-)

At this point, I am inclined to go with the finite screw attitude angle

technique expressed relative to the JCS axes except for the shoulder whose

angles I feel are more properly represented by a spherical angle system. This

was used by Andy An from the Mayo Clinic in a paper at the ORS. I personally

think that the singularity issue ('gimbal lock' if you insist) for the JCS is

theoretically relevant but not really in practice. True, as Herman pointed out,

as the joint approaches this orientation the angles can become inconsistant due

to the fact that both the numerator and denominator of the inverse tangent

approach zero and thus noise in the input data will have a more significant

effect.

But this situation can be detected and corrected numerically (I did just such a

thing until I decided to switch to the spherical system- basically you just

monitor the magnitudes of both numerator and denominator of the inverse tangent

and when they both go below a predetermined threshold, you skip the angle

calculations for that frame of data and then go back later and interpolate the

missing angle back in. It's a kludge but it worked nicely for our situation...)

The finite screw is more proper representation of the actual motion process

occuring in the joint. I.e., the joint is actually rotating about some line in

space not some arbitrarily selected coordinate axes. Unfortunately, this line

of reasoning falls apart when you try to express the screw in more clincally

oriented terms since it must be expressed relative to just such a set of axes

as in the case of the attitude angles concept. I don't think that using either

the proximal or distal LCS as the base for expressing the attitude angles is a

good idea because even though the system axes will orthogonal and hence will

never be singular, the angles are physically meaningful to the clinician. They

are valid descriptors of the joint orientation but since eventually the data is

to be used by a phsycian to make a clinical decision, at least here that is the

case, the data should be in a form with which they are familiar. The JCS axes

pretty much align with the way that the orthopaedist describes/visualizes joint

orientation. There is the singularity problem but that cannot physically occur

in any major extremity joint except the shoulder unless there is a very severe

pathology present.

Even though the screw does represent full 6 DOF motion, if only the attitude

angle representation is desired then the rotation matrix relating the segment

orientations is all that is required since this calculation is a subpart of the

full finite screw calculation. This calculation, I might add, is no more

computational difficult than the standard technique of extracting rotaion

angles from the rotation matrix.

As an aside, the numerical method by which the screw is calculated is

significant as to its sensitivity to noise in the input data. The input data

consists of the position and orientation of one rigid body relative to another

in 3D. This data has noise within it as result of the resolution of the system

used to measure the position/orientation and its method of measuring. We have

used both VICON based marker measuring as well as a 6DOF spatial linkage

designed and built here to collect this information. I have done some

experiments using data from these using the algorithm given in Herman's papers,

which I believe is more or less the same as that of Spoor-Veldpaus (sp?), as

well as using one based upon derivations done by Ken Waldron, who is a

prominent kinematics/robotics researcher at the Mechanical Engineering

Department here at Ohio State. I found that Waldron's method was less

sensitive to noise. In addition, there was a paper recently given at the ASME

conference on Advances in Design Automation-1989 (Univ. of California, Davis)

intitled 'Comparison of Methods for Determining Screw Parameters of Finite

Rigid Body Motion from Initial and Final Position Data' by R.G. Fenton and X.

Shi. This compared 5 different methods, including Spoor-Veldpaus, and

concluded that the best, based upon sensitivity to noise, is one by Bottema

and Roth (of the textbook Theoretical Kinematics fame) while Spoor-Veldpaus

was noise sensitive. I know that there are other versions of the Spoor-

Veldpaus method for use with more than 3 markers to decrease the noise

sensitivity, but based upon its use with straight position/orientation

information of the rigid bodies as input (as I use it) it does not appear to

be the best choice. I will be doing some more work with this area in the

near future, say the next month or two, and if anyone is interested I can post

a follow up.

In summary, I'm trying to stay out of the 'one is better than the other

because...' argument but instead am trying to look at the several methods as

they are used in practice. The only place where a firm decision as to a

single calculation method is critical is for exchange of data between

institutions. That is how all of this got started here at Ohio State. We have

been involved in a Multi-Institutional study of cerebral palsy child gait for a

number of years now that has used sagittal joint angles exclusively. We would

like to expand our focus but before this can happen this matter of joint angle

calculation methods and coordinate system positioning/orienting must be

resolved, at least between the sites involved in the study. For an individual

research group this is not such a critical issue just so long as they establish

a method and stick to it. This issue is more of academic interest in this case.

It is also possible to convert back and forth between the various angle systems

with relative ease as demonstrated by Herman's program, but the matter of the

definition of the coordinate systems is a definite problem...

By the way, that paper on body segment mass/inerita parameters that mentioned

in the fall from Wright-Patterson Air Force Medical Research Laboratory had an

interesting approach to the coordinate system definition problem. The CS's

were defined relative to several easily identifiable bony landmarks for each

body segment. The down side of this method is the need to measure the 3D

location of a lot of points.

Enough said for now. I hope some others might join in on this discussion...

Dwight Meglan

Research Engineer and Phd-in-training (finished product coming to a journal

near you sometime in 1990/91 ;-)

meglan%gait1@eng.ohio-state.edu

In the current spirit of disclaimers, the above text was not written by anyone,

to anyone, about anyone, or for anyone no matter what the text actually says:-)

the method of describing the 3D orientation of the body segments relative

to one another.

In the recent complete rewrite of the analysis and display

software for the gait lab here at Ohio State University, I included both

the Grood & Suntay description, which I refer to as the Joint Coordinate

System (JCS), of the joint rotations as well as the standard Pitch-Roll-Yaw

(PRY) euler angles plus calculation of the finite screw across the joint

(the position and orientation of the segments is known in 3D using the marker

position data) using several different algorithms. In addition, the rotation

about the screw axis can be described using Herman's concept of attitude angles

(basically multiply the direction vector of the screw axis by the magnitude of

the rotation about the axis to form a scaled vector) in terms of the proximal

segment local coordinate system (LCS), distal segment LCS, or the JCS. All

these different methods are included because I wanted to compare them on

actual experimentally acquired data plus since there is no standardization at

the moment I decided to use the shotgun approach and try to cover the majority

of the possible orientation description methods.

I did a poster on some of the results for the recent Orthopaedic Research

Society meeting in New Orleans. Interestingly, Murali Kadaba had a poster

right across the aisle which dealt with finite screws also. Basically, the

results using multiple trials of normal subject gait data (we use a marker set

consisting of 21 markers total for the upper and lower body with 3 markers on

most segments) show that for sagittal plane joint angles there really is no

statistically siginificant difference between any of the two rotation angle or

three attitude 1angle schemes used. This was true for all the joints of the

lower body as well as the pelvis, whose angle is not a relative angle but

instead is calculated relative to the global lab coordinate system (GCS). In

the out of plane angles (ab/adduction, in/external, pro/supination, in/eversion)

there were significant differences primarily for the ab/aduction and in/eversion

angles. These differences increase with the magnitude of the flexion angle

which not surprising. The interesting point however is that the attitude

angles are significantly different so the coordinate system in which they are

expressed is critical. Also, the attitude angles expressed in terms of the

JCS were different from the angles calculated with the JCS rotation angle

method.

Based upon these results, plus various other experiments which I have tried

out, it would seem that while the calculation method, i.e. rotation angles or

attitude angles, is important, the coordinate system used to express the

attitude angles is just as important. Which leads to the obvious point that

the positioning of these segment LCS's will have a critical effect upon the

calculated joint angles. I did some perturbation experiments to look at the

sensitivity of the calculated joint angles to slight changes in the orientation

of either or both of the segment LCS's used as input data for the angle

calculation. Each perturbation had some effect upon one or more of the

calculated angles- not surprising. The effects are widely varying however and

it is a relevant concern to identify those effects which are going to most

readily occur with a given marker set and motion system configuration. Even

rigid bodies with more than 3 markers attached to the body segment are

sensitive to this problem since it is difficult to control the position/

orientation of the marker carrier relative to the underlying bones with

accuracy and consistency. This is getting a little of track of the discussion

focusing on rotation angles and finite screw attitude angles... Oh well, I

guess we all have our soap box on one issue or another :-)

At this point, I am inclined to go with the finite screw attitude angle

technique expressed relative to the JCS axes except for the shoulder whose

angles I feel are more properly represented by a spherical angle system. This

was used by Andy An from the Mayo Clinic in a paper at the ORS. I personally

think that the singularity issue ('gimbal lock' if you insist) for the JCS is

theoretically relevant but not really in practice. True, as Herman pointed out,

as the joint approaches this orientation the angles can become inconsistant due

to the fact that both the numerator and denominator of the inverse tangent

approach zero and thus noise in the input data will have a more significant

effect.

But this situation can be detected and corrected numerically (I did just such a

thing until I decided to switch to the spherical system- basically you just

monitor the magnitudes of both numerator and denominator of the inverse tangent

and when they both go below a predetermined threshold, you skip the angle

calculations for that frame of data and then go back later and interpolate the

missing angle back in. It's a kludge but it worked nicely for our situation...)

The finite screw is more proper representation of the actual motion process

occuring in the joint. I.e., the joint is actually rotating about some line in

space not some arbitrarily selected coordinate axes. Unfortunately, this line

of reasoning falls apart when you try to express the screw in more clincally

oriented terms since it must be expressed relative to just such a set of axes

as in the case of the attitude angles concept. I don't think that using either

the proximal or distal LCS as the base for expressing the attitude angles is a

good idea because even though the system axes will orthogonal and hence will

never be singular, the angles are physically meaningful to the clinician. They

are valid descriptors of the joint orientation but since eventually the data is

to be used by a phsycian to make a clinical decision, at least here that is the

case, the data should be in a form with which they are familiar. The JCS axes

pretty much align with the way that the orthopaedist describes/visualizes joint

orientation. There is the singularity problem but that cannot physically occur

in any major extremity joint except the shoulder unless there is a very severe

pathology present.

Even though the screw does represent full 6 DOF motion, if only the attitude

angle representation is desired then the rotation matrix relating the segment

orientations is all that is required since this calculation is a subpart of the

full finite screw calculation. This calculation, I might add, is no more

computational difficult than the standard technique of extracting rotaion

angles from the rotation matrix.

As an aside, the numerical method by which the screw is calculated is

significant as to its sensitivity to noise in the input data. The input data

consists of the position and orientation of one rigid body relative to another

in 3D. This data has noise within it as result of the resolution of the system

used to measure the position/orientation and its method of measuring. We have

used both VICON based marker measuring as well as a 6DOF spatial linkage

designed and built here to collect this information. I have done some

experiments using data from these using the algorithm given in Herman's papers,

which I believe is more or less the same as that of Spoor-Veldpaus (sp?), as

well as using one based upon derivations done by Ken Waldron, who is a

prominent kinematics/robotics researcher at the Mechanical Engineering

Department here at Ohio State. I found that Waldron's method was less

sensitive to noise. In addition, there was a paper recently given at the ASME

conference on Advances in Design Automation-1989 (Univ. of California, Davis)

intitled 'Comparison of Methods for Determining Screw Parameters of Finite

Rigid Body Motion from Initial and Final Position Data' by R.G. Fenton and X.

Shi. This compared 5 different methods, including Spoor-Veldpaus, and

concluded that the best, based upon sensitivity to noise, is one by Bottema

and Roth (of the textbook Theoretical Kinematics fame) while Spoor-Veldpaus

was noise sensitive. I know that there are other versions of the Spoor-

Veldpaus method for use with more than 3 markers to decrease the noise

sensitivity, but based upon its use with straight position/orientation

information of the rigid bodies as input (as I use it) it does not appear to

be the best choice. I will be doing some more work with this area in the

near future, say the next month or two, and if anyone is interested I can post

a follow up.

In summary, I'm trying to stay out of the 'one is better than the other

because...' argument but instead am trying to look at the several methods as

they are used in practice. The only place where a firm decision as to a

single calculation method is critical is for exchange of data between

institutions. That is how all of this got started here at Ohio State. We have

been involved in a Multi-Institutional study of cerebral palsy child gait for a

number of years now that has used sagittal joint angles exclusively. We would

like to expand our focus but before this can happen this matter of joint angle

calculation methods and coordinate system positioning/orienting must be

resolved, at least between the sites involved in the study. For an individual

research group this is not such a critical issue just so long as they establish

a method and stick to it. This issue is more of academic interest in this case.

It is also possible to convert back and forth between the various angle systems

with relative ease as demonstrated by Herman's program, but the matter of the

definition of the coordinate systems is a definite problem...

By the way, that paper on body segment mass/inerita parameters that mentioned

in the fall from Wright-Patterson Air Force Medical Research Laboratory had an

interesting approach to the coordinate system definition problem. The CS's

were defined relative to several easily identifiable bony landmarks for each

body segment. The down side of this method is the need to measure the 3D

location of a lot of points.

Enough said for now. I hope some others might join in on this discussion...

Dwight Meglan

Research Engineer and Phd-in-training (finished product coming to a journal

near you sometime in 1990/91 ;-)

meglan%gait1@eng.ohio-state.edu

In the current spirit of disclaimers, the above text was not written by anyone,

to anyone, about anyone, or for anyone no matter what the text actually says:-)