A Tutorial on the Measurement of Joint Motion
with Application to the Shoulder
University of Delaware Human Performance Laboratory
The Challenge
The challenge associated with measuring
upper extremity motion is to provide
clinicians with:
1) anatomically meaningful
descriptions of position, and
2) a clinically relevant sense of
motion
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Motion of the Shoulder
• Scapula/clavicle relative to the trunk
• Humerus relative to the scapula
• Humerus relative to the trunk
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Marker Set Options
• Marker set similar to those used on lower extremities
• Sparse marker sets (1 shoulder, 1 elbow, 1 or 2 wrist
markers, 1 hand marker)
• More robust marker sets such as the one
recommended by the International Shoulder Group
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Considerations for Marker Placement
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ISG Recommended Marker Locations
Trunk Markers (Dorsal Side)
• C7
• T8
Scapula Markers (Dorsal Side)
• Acromioclavicular joint
• Angulus Acromialis
• Trigonum Spinae Scapulae
• Inferior Angle of Scapula
Humerus Markers
• Glenohumeral center of rotation
• Medial and lateral epicondyles
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ISG Recommended Marker Locations
Trunk (Ventral Side)
• Suprasternal Notch
• Xiphoid Process
Scapula Markers (Ventral Side)
• Ventral point of Coracoid
• Process
Clavicle Markers
• Acromioclavicular joint
• Sternoclavicular joint
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ISG Recommended Marker Locations
Humerus Markers
• Glenohumeral center of
rotation
• Medial and lateral
epicondyles
Wrist & Hand
• Radial Styloid
• Ulnar Styloid
• 2nd Metacarpal Head
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Determination of Glenohumeral Center of Rotation
Translation from Acromioclavicular marker
• Determine shoulder coordinate system
• Translate AC marker a fixed distance along the shoulder’s Yaxis
Spherical (or Helical) fitting
• Measure motion of the elbow joint center (or epicondyle
marker) relative to the shoulder coordinate system using the
AC marker as the point of origin
• Sphere centroid relative to AC marker in the shoulder
coordinate system approximates glenohumeral center of
rotation
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ISG Recommended Coordinate Systems
Trunk
• Y-vector from midpoint of
T8-Xiphoid to midpoint of
C7-Suprasternal Notch
• X-vector from Y crossed
onto vector from Xiphoid to
T8
• Z-vector from X crossed
onto Y
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ISG Recommended Coordinate Systems
Scapula
• X-vector follows Scapular
Spine
• Vector from Scapular Spine
marker to Inferior Angle
marker crossed onto the Xvector creates the Z-vector
• Y-vector from Z crossed
onto X-vector
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ISG Recommended Coordinate Systems
Upper Arm
• Y-vector from midpoint of
medial and lateral
epicondyles to the center of
rotation of the Glenohumeral
head
• Z-vector from medial to
lateral epicondyle vector
crossed onto Y-vector
• X-vector from Y-vector
crossed onto Z-vector
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Distal Arm Segment Coordinate Systems
Forearm (Proximal)
• Y-vector from wrist center to elbow center
• Z-vector from upper arm X-vector crossed
onto forearm Y-vector
• X-vector from Y-vector crossed onto Z-vector
Forearm (Distal)
• Y-vector from wrist center to elbow center
• Z-vector from Ulnar to Radial Styloid vector
crossed onto Y-vector
• X-vector from Y-vector crossed onto Z-vector
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Distal Arm Segment Coordinate Systems
Hand
• Y-vector from hand marker (2nd met head)
to wrist center
• Z-vector from Ulnar to Radial Styloid
vector crossed onto Y-vector
• X-vector from Y-vector crossed onto Zvector
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Modifications to ISG Marker Locations
Remove the following
markers from the
Dorsal side:
• Angulus Acromialis
• Trigonum Spinae
Scapulae
• Inferior Angle of
Scapula
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Modifications to ISG Marker Locations
Remove the following
markers from the
ventral side:
• Sternoclavicular
joint
• Ventral point of
Coracoid Process
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Modification to ISG Coordinate Systems
Scapula (Shoulder)
• X-vector from midpoint of
C7 and Suprasternal Notch
to the Acromion Process
marker
• Z-vector from shoulder Xvector crossed onto trunk
Y-vector
• Y-vector from shoulder Zvector crossed onto
shoulder X-vector
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Methods of Measuring Arm Orientation
Relative to the Trunk or Shoulder
•
•
•
•
•
•
Joint Coordinate Angles (Grood & Suntay)
Euler or Cardan Angles
Helical Axis Decomposition (described by Woltring)
Instantaneous Helical and Euler Angles
Rotation Matrices
Quaternions, Angle-axis, Rodriguez vectors
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Representative Coordinate Systems
R=X
G=Y
B=Z
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Review of Analysis Methods
Review of Cross-Products
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Review of Analysis Methods
Grood and Suntay Approach
• Select 1 vector from the trunk
• Select 1 vector from the upper arm
• The angle formed by the two vectors represents one
•
•
of the anatomical angles
Cross the vector from the trunk onto the vector from
the upper arm
The resulting intermediate vector provides remaining
orientation information depending on the segment to
which it is referenced
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Review of Analysis Methods: Grood & Suntay
The angle between Yarm and Ytrunk represents the
amount of shoulder abduction
• Select 1 vector from
•
•
the trunk
Select 1 vector from
the upper arm
The angle formed by
the two vectors
represents one of the
anatomical angles
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Review of Analysis Methods : Grood & Suntay
Yarm crossed onto Ytrunk results in an
orthogonal Intermediate Vector
Cross the vertical vector
from the trunk onto the
vector representing the
long axis of the upper arm
to create the intermediate
vector
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Review of Analysis Methods : Grood & Suntay
Intermediate Vector with Respect to the
Trunk’s Coordinate System
The intermediate vector
indicates the amount of
horizontal
flexion/extension when
viewed in the trunk’s
coordinate system.
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Review of Analysis Methods : Grood & Suntay
Intermediate Vector with Respect to the
Arm’s Coordinate System
The intermediate vector
indicates the amount of
internal and external
rotation when viewed in
the arm’s coordinate
system.
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Review of Analysis Methods : Grood & Suntay
Other Combinations of Vectors
Other combinations of vectors can be used to
determine angles using Grood and Suntay’s
method. For example, we could use the trunk’s
Z vector and the arm’s Y vector to calculate
shoulder angles as well. Each combination of
vectors will give you different results for one or
more of the joint angles.
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Review of Analysis Methods
Euler Angles
A second approach to describing joint
orientation involves the use of Euler angles.
Euler angles are easily interpreted but are prone
to discontinuities at 90 degree and 180 degree
crossings, depending on the rotation order that is
being used. For the legs, the order of rotation is:
1) Flexion/Extension, 2) Ab/Adduction, and 3)
Int/Ext Rotation
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Review of Analysis Methods
Euler Angles
There are 12 different rotation sequences that
can be used in this approach. They are:
XYZ
YXZ
ZXY
XZY
YZX
ZYX
XYX
YXY
ZXZ
XZX
YZY
ZYZ
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Review of Analysis Methods
Calculation of Euler Angles
• Use YZY order of rotation as recommended by the
•
•
•
•
International Shoulder Group
Start with an intermediate coordinate system aligned
with the trunk coordinate system
Rotate the intermediate coordinate system about the
trunk’s Y axis (angle = horiz flex/ext)
Rotate the intermediate coordinate system about its
own Z axis (angle = ab/adduction)
Rotate the intermediate coordinate system about the
arm’s Y-axis (angle = int/ext rotation)
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Review of Analysis Methods: Euler Rotations
Y-Z-Y Euler Rotation Sequence
1) Rotate the intermediate
coordinate system about
the arm’s Y-axis (angle =
int/ext rotation
2) Rotate the intermediate
coordinate system about
the intermediate Z-axis
(angle = ab/adduction)
3) Rotate the intermediate
coordinate system about the
trunk’s Y axis (angle = horiz
flex/ext
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YZY Euler Sequence
(ISG Recommendation)
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ZXY Euler Sequence
(Adduction/Abduction Priority)
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XZY Euler Sequence (Flexion/Extension
Priority)
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Review of Analysis Methods
Angles from Helical Axis Decomposition
• Find the axis about which the trunk coordinate
system can be rotated to match the orientation
of the arm coordinate system
• Unitize the axis, and multiply it by the
magnitude of rotation
• Resolve the resulting vector into the
appropriate coordinate system
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Review of Analysis Methods: Helical Axis Decomposition
Angles from Helical Axis Decomposition
Find the axis about
which the trunk
coordinate system can
be rotated to match the
orientation of the arm
coordinate system
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Review of Analysis Methods
Alternative Approaches to Measuring
Shoulder Orientation
Quaternions, Angle-Axis representation, and Rodriguez
vectors
• All in the family of helical axis
• Do not relate directly to anatomical conventions
• Can be converted into Euler angles
Rotation Matrices
• Used in all other methods of calculating joint angles
• By themselves, cannot be interpreted into meaningful
anatomical angles
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Alternative Approaches to Measuring
Shoulder Orientation
Instantaneous Helical and Euler Angles
• Determine starting orientation of limb segment
• Calculate joint angle change between frames
• Integrate results
Advantages
• Provides excellent sense of motion
Drawbacks
• Resultant orientations aren’t exact
• Need accurate reference orientation
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Angle Measures at the Elbow
• Segments on either side of the elbow share a
common flexion/extension axis
• No measure of internal/external rotation
• Euler approach using same rotation order as
the legs will work fine (F/E, Ab/Add)
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Angle Measures at the Wrist
• Segments on either side of the wrist share a
common flexion/extension axis
• No measure of internal/external rotation
• Euler approach using same rotation order as the
legs will work fine (F/E, Ab/Add)
• Calculating the angle between the proximal and
distal forearm coordinate systems provides the
pronation/supination angle
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Application of Methods at the Shoulder
Given:
• Clearly defined marker sets
• Well defined segment coordinate systems
• Several methods of measuring orientations
We could easily believe that:
Describing orientation of the upper arm
relative to the scapula or trunk should pose
a simple problem
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Shoulder Orientation Measured during Walking
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Shoulder Orientation Measured during Abduction/Adduction
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Shoulder Orientation Measured during Flexion/Extension
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Shoulder Orientation Measured during Int/Ext Rotation(Adducted)
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Shoulder Orientation Measured during Int/Ext
Rotation(Abducted)
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Shoulder Orientation Measured during Horizontal Flex/Ext
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Shoulder Orientation Measured during Codman’s Motion
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Shoulder Orientation Measured during Circumduction
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Shoulder Orientation Measured during Overhand Throw
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Summary of Analysis Methods
Abduction
Flexion
H. Flexion
IE Abducted
IE Adducted
Circumduction
Codman
Throw
Walk
YZY (ISG)
ZXY (Ab/Ad)
X-
X
X
X
XZY (F/E)
Helical
X
X
X
X
X
X
X
X
X
X
XX
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Using Instantaneous Approaches
• Instantaneous Helical or Euler angles
• Both provide excellent sense of motion
• Both require an initialization point
• Neither provide accurate orientation angles
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Other Approaches to Getting Better Results
• Change the arm’s reference position to what
would normally be considered 90 degrees of
abduction
• Cut out sections of the curve where
discontinuities in motion occur, and then
interpolate for the missing data
• Splice results from different rotation
sequences together depending on the arm’s
location relative to the trunk
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Final Recommendations for
Measurement of the Shoulder
• View the results using each of the
measurement approaches, giving greater
weight to the approach that best measures the
dominant arm motion
• Select the approach that makes the most sense
clinically
• Report the method used
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Acknowledgements
• Scott Coleman, for his help with the graphics
and animations
• John Henley, for his willingness to serve as a
sounding board for numerous unusual
measurement strategies
• Dave Hudson, for letting me use pictures of
him shot in profile
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The End