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Hi! This is Hen-Yu Lien. I post a question about the definition of Euler
and Cardan Rotation. Thank you all for the responses, they were all very
helpful. I got lots of great references, but I can not post them all
because they will take too much space of your mail box. The following
messages answered my question directly, they are as followed. Again,
thank you all for the answer, they are very helpful.
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Director, Gait & Biomechanics Lab (DR. GREGORY S. RASH)
Phone: (502) 582-7657
I beleive you have a Qualysis system with AutoGait3D. If so the terms
are
wrong in the version of AutoGait3D that you have & have since been
switched to
Floating & fixed. They are both Cardan with the Euler being a special
case.
Keven Campbell wrote the software & the angle calculations using Euler
are the
same as described by Kadaba & Davis in their respective publications.
This is
a method which uses the Euler y-x-z rotations which correspond to
flexion/
extension, abd/add & int/ext rotation. The 1st rotation of the moving,
or
distal, segment about the y axis. A new orientation of the embedded
coordinate
system is determined (x1, y1, z1) and the second rotation is performed
about
the embedded x1 axis. Again a new orientation of the moving, or distal,
axis i
s determined (x2, y2, z2) and the final rotation is made about the
embedded z2
axis. This is a floating axis system... In what the program you have
calls
Cardan (now called fixed) the system is always fixed in the proximal
segment.
In this method the distal segment is rotated from its initial position
about th
the proximal segment y axis to account for flex/ext producing a new
distal
embedded coordinate system x1, y1, z1. The second rotation is about the
proximal segment x coordinate axis accounting for adb/add and producing
a new o
rientation of the distal coordinate system x2, y2, y3. The final
rotation
was performed about the proximal z axis accounting for the int/ext
rotation
angle.
I to was unsure of what the difference was when I got my Qualysis system
but
found the company very helpful in explaining the difference. However,
being
the questioning type individual I am I wanted to see what the difference
was
on paper so I conducted a study & it was presented at the NASGCMA
meeting
in Birmingham in 1996. The Abstract is in Gait & Posture4(2) pg 176.
We
found that there was no clinicallly significant difference in the two
methods.
I use what your version of the program calls the Cardan method because I
beleive it to be an advantage to always work from a fixed proximal
segment.
I hope this helps & I can't beleive you were unable to get an answer
from the
Qualysis guys (Andy & Mike).
------------------------------------------------------------------------------
------------------------------------------------------------------------------------
Dear Hen-Yu,
In planar motion, if you assume that plane of motion is the x-y
plane, it implies that a free segment has the ability to
translate
along the x-direction and the y-direction. It also means that it
can rotate about the z-direction. A total of 3 degrees of
freedom.
On the other hand, in a three dimension motion, a free segment
translates along and rotatates about the x, y, and z directions.
Hence it is said to have 6 degrees of freedom, 3 translational
and 3 rotational. If you displace a segment from point "A" to
point "B", you move the segment along the known directions x, y,
and z, the order of the translation is not important, any
sequence
always land on "B". This is not the case for rotation, the sequence
of rotaion must be observed. You can verify that by rotating a
book
about one of its edges by 90 deg. followed by a 90 deg. rotation
about a second edge then another 90 deg. rotation about the
third
edge. The final orientation of the book will not be the same
for different sequence of rotations. The reason for that is
simple;
a rotation about one axis always re-orients the other two axes.
For the x,y,z axes there are 12 possible rotation sequences:
1) x-y-z; 5) y-x-z; 9) z-x-y;
2) x-z-y; 6) y-z-x; 10) z-y-x;
3) x-y-x; 7) y-x-x; 11) z-x-z;
4) x-z-x; 8) y-z-y; 12) z-y-z
All of these sequences are called Eulers' angles. Some of these
rotation sequences were studied in details by notible scientists
such that the rotational sequences are named after them. For
example, the sequence "1)" is called Cardans angles, the
sequence
"11)" is called the zxz Euler's and soforth.
Regards,
Milad Ishac,
Neural Control lab,
University of Waterloo, Ontario, Canada
------------------------------------------------------------------------------
------------------------------------------------------------------------------
A general description of the differences between these types of analysis
are that the Proximal (or Cardan) rotations use a joint coordinate
system that uses the rotation in each of the three planes to orient the
more distal limb in relation to the more proximal limb. Simply, this
uses the cross product of two vectors to determine the final
perpendicular axis. Euler rotations use an intermediate set of axes to
generate the limb orientations that do not necessarily align with a
particular anatomical structure. Either method is accepted within the
gait community since the kinematic differences are small, on the order
of 1 to 2 degrees (as cited by Kevin Campbell, Ph.D. from the AutoGait
user manual).
Qualisys, Inc.
Andrew Mahar
Research Biomechanist
and Cardan Rotation. Thank you all for the responses, they were all very
helpful. I got lots of great references, but I can not post them all
because they will take too much space of your mail box. The following
messages answered my question directly, they are as followed. Again,
thank you all for the answer, they are very helpful.
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Director, Gait & Biomechanics Lab (DR. GREGORY S. RASH)
Phone: (502) 582-7657
I beleive you have a Qualysis system with AutoGait3D. If so the terms
are
wrong in the version of AutoGait3D that you have & have since been
switched to
Floating & fixed. They are both Cardan with the Euler being a special
case.
Keven Campbell wrote the software & the angle calculations using Euler
are the
same as described by Kadaba & Davis in their respective publications.
This is
a method which uses the Euler y-x-z rotations which correspond to
flexion/
extension, abd/add & int/ext rotation. The 1st rotation of the moving,
or
distal, segment about the y axis. A new orientation of the embedded
coordinate
system is determined (x1, y1, z1) and the second rotation is performed
about
the embedded x1 axis. Again a new orientation of the moving, or distal,
axis i
s determined (x2, y2, z2) and the final rotation is made about the
embedded z2
axis. This is a floating axis system... In what the program you have
calls
Cardan (now called fixed) the system is always fixed in the proximal
segment.
In this method the distal segment is rotated from its initial position
about th
the proximal segment y axis to account for flex/ext producing a new
distal
embedded coordinate system x1, y1, z1. The second rotation is about the
proximal segment x coordinate axis accounting for adb/add and producing
a new o
rientation of the distal coordinate system x2, y2, y3. The final
rotation
was performed about the proximal z axis accounting for the int/ext
rotation
angle.
I to was unsure of what the difference was when I got my Qualysis system
but
found the company very helpful in explaining the difference. However,
being
the questioning type individual I am I wanted to see what the difference
was
on paper so I conducted a study & it was presented at the NASGCMA
meeting
in Birmingham in 1996. The Abstract is in Gait & Posture4(2) pg 176.
We
found that there was no clinicallly significant difference in the two
methods.
I use what your version of the program calls the Cardan method because I
beleive it to be an advantage to always work from a fixed proximal
segment.
I hope this helps & I can't beleive you were unable to get an answer
from the
Qualysis guys (Andy & Mike).
------------------------------------------------------------------------------
------------------------------------------------------------------------------------
Dear Hen-Yu,
In planar motion, if you assume that plane of motion is the x-y
plane, it implies that a free segment has the ability to
translate
along the x-direction and the y-direction. It also means that it
can rotate about the z-direction. A total of 3 degrees of
freedom.
On the other hand, in a three dimension motion, a free segment
translates along and rotatates about the x, y, and z directions.
Hence it is said to have 6 degrees of freedom, 3 translational
and 3 rotational. If you displace a segment from point "A" to
point "B", you move the segment along the known directions x, y,
and z, the order of the translation is not important, any
sequence
always land on "B". This is not the case for rotation, the sequence
of rotaion must be observed. You can verify that by rotating a
book
about one of its edges by 90 deg. followed by a 90 deg. rotation
about a second edge then another 90 deg. rotation about the
third
edge. The final orientation of the book will not be the same
for different sequence of rotations. The reason for that is
simple;
a rotation about one axis always re-orients the other two axes.
For the x,y,z axes there are 12 possible rotation sequences:
1) x-y-z; 5) y-x-z; 9) z-x-y;
2) x-z-y; 6) y-z-x; 10) z-y-x;
3) x-y-x; 7) y-x-x; 11) z-x-z;
4) x-z-x; 8) y-z-y; 12) z-y-z
All of these sequences are called Eulers' angles. Some of these
rotation sequences were studied in details by notible scientists
such that the rotational sequences are named after them. For
example, the sequence "1)" is called Cardans angles, the
sequence
"11)" is called the zxz Euler's and soforth.
Regards,
Milad Ishac,
Neural Control lab,
University of Waterloo, Ontario, Canada
------------------------------------------------------------------------------
------------------------------------------------------------------------------
A general description of the differences between these types of analysis
are that the Proximal (or Cardan) rotations use a joint coordinate
system that uses the rotation in each of the three planes to orient the
more distal limb in relation to the more proximal limb. Simply, this
uses the cross product of two vectors to determine the final
perpendicular axis. Euler rotations use an intermediate set of axes to
generate the limb orientations that do not necessarily align with a
particular anatomical structure. Either method is accepted within the
gait community since the kinematic differences are small, on the order
of 1 to 2 degrees (as cited by Kevin Campbell, Ph.D. from the AutoGait
user manual).
Qualisys, Inc.
Andrew Mahar
Research Biomechanist