# degrees of freedom

Hello,

there are two things, i don’t quite understand. Could someone please try to
explain to me the following:

1.) I am not quite sure about the degrees of freedom all in all. I understand
that joints reduce the possible DOFs. But what about let’s say a ball joint
allowing 3 rotational DOFs with parallel added rotational springs? Then the
rotation is still allowed, but not really free. There is a clear relationship
between moment and rotation, i. e. it should not be counted as “free” as the
rotation can be calculated from the outer forces and moments. Are my
thinkings correct?

2.) related to the spine rythm of the standing model: Am i right that there
are 7 ball joints modelled in the lumbar region which would allow 21
rotational degrees of freedom, but the spine rythm reduces them to 3 by
distributing them to the 21? Doesn’t this mean a higher stiffness?

When we consider only the rotations in the sagittal plane: Normally there
would be 7 DOF in the plane, but now there is only 1 DOF. The segments are
then not so flexible regarding the whole lumbar region. Is this true?

Thanks,

Thomas

Hi Thomas

First of all you can find some more info on how joints eliminate DOF
at http://www.anybodytech.com/679.0.html.

Question 1: Let me try to explain. As you write a ball joint has 3
rotational DOF. If you add the parallel springs the joint would still
have 3 DOF. So how can we remove a DOF from the system? Well try
taking a look at a human hip joint. In many ways it is similar to your
example. The hip joint has 3 DOF and if you put a big cast on it that
don’t allow it to flex/extend but still to abduct/adduct and
eversion/inversion, then you would only have 2 DOF left.

Question 2:
The spine rhythm is made in order to constrain all the DOF in the
back, as you mention there are a lot of DOF in the back. All the
rhythms does; is that it takes the DOF and binds them together, saying
that for example in the sagital plane where there would be 7 DOF,
those are merged into 1, by for example saying that each joint will
move 1/7 of the full motion. So the single DOF that is left in the
model, controls the 7 DOF by means of a rhythm.

I hope this explains it a bit, it is kind of hard to explain in
text;-) However if you have any other questions please feel free to
write again.

Best regards
Christian, AnyBody Support

— In anyscript@yahoogroups.com, Thomas Zander <thomas.zander@…> wrote:
>
>
> Hello,
>
> there are two things, i don’t quite understand. Could someone please
try to
> explain to me the following:
>
> 1.) I am not quite sure about the degrees of freedom all in all. I
understand
> that joints reduce the possible DOFs. But what about let’s say a
ball joint
> allowing 3 rotational DOFs with parallel added rotational springs?
Then the
> rotation is still allowed, but not really free. There is a clear
relationship
> between moment and rotation, i. e. it should not be counted as
“free” as the
> rotation can be calculated from the outer forces and moments. Are my
> thinkings correct?
>
> 2.) related to the spine rythm of the standing model: Am i right
that there
> are 7 ball joints modelled in the lumbar region which would allow 21
> rotational degrees of freedom, but the spine rythm reduces them to 3 by
> distributing them to the 21? Doesn’t this mean a higher stiffness?
>
> When we consider only the rotations in the sagittal plane: Normally
there
> would be 7 DOF in the plane, but now there is only 1 DOF. The
segments are
> then not so flexible regarding the whole lumbar region. Is this true?
>
> Thanks,
>
> Thomas
>

Hi Christian,

it is clear that torsional springs do not remove DOFs completely from a joint,
but together with a spring, the joint’s position is not undefined any longer.
A pure joint does not allow for calcuating the position as all positions are
equal. But together with a spring, one position is prominent: the position
were there is no force in the spring. This is the position of the lowest
energy.
In other words: Similar to a ball joint that equals the translations of two
bodies, a torsional spring equals their rotations except for a constant,
which is the moment divided by the stiffness.
If a spring does not remove/reduce DOFs: How can a large model like the
standing model have a balanced number of DOFs and drivers? You mention that
there is more than one rythm. Are they introduced in order to balance the
number of DOFs and drivers?
I think, i understood the principle of the spine rythm correctly, but my doubt
is if they create stiffness? Isn’t one DOF stiffer than 7? I have the feeling
that the loads necessary to deflect the lumbar spine are too high and wanted
to replace the spine rythm by torsional springs in the joints.
The natural spine doesn’t know anything about a spine rythm. What is missing
in AnyBody in order to be able to remove the rythm?

many regards, Thomas

Christian wrote:
> Hi Thomas
>
> First of all you can find some more info on how joints eliminate DOF
> at http://www.anybodytech.com/679.0.html.
>
> Question 1: Let me try to explain. As you write a ball joint has 3
> rotational DOF. If you add the parallel springs the joint would still
> have 3 DOF. So how can we remove a DOF from the system? Well try
> taking a look at a human hip joint. In many ways it is similar to your
> example. The hip joint has 3 DOF and if you put a big cast on it that
> don’t allow it to flex/extend but still to abduct/adduct and
> eversion/inversion, then you would only have 2 DOF left.
>
> Question 2:
> The spine rhythm is made in order to constrain all the DOF in the
> back, as you mention there are a lot of DOF in the back. All the
> rhythms does; is that it takes the DOF and binds them together, saying
> that for example in the sagital plane where there would be 7 DOF,
> those are merged into 1, by for example saying that each joint will
> move 1/7 of the full motion. So the single DOF that is left in the
> model, controls the 7 DOF by means of a rhythm.
>
> I hope this explains it a bit, it is kind of hard to explain in
> text;-) However if you have any other questions please feel free to
> write again.
>
> Best regards
> Christian, AnyBody Support
>
> — In anyscript@yahoogroups.com, Thomas Zander <thomas.zander@…> wrote:
> > Hello,
> >
> > there are two things, i don’t quite understand. Could someone please
>
> try to
>
> > explain to me the following:
> >
> > 1.) I am not quite sure about the degrees of freedom all in all. I
>
> understand
>
> > that joints reduce the possible DOFs. But what about let’s say a
>
> ball joint
>
> > allowing 3 rotational DOFs with parallel added rotational springs?
>
> Then the
>
> > rotation is still allowed, but not really free. There is a clear
>
> relationship
>
> > between moment and rotation, i. e. it should not be counted as
>
> “free” as the
>
> > rotation can be calculated from the outer forces and moments. Are my
> > thinkings correct?
> >
> > 2.) related to the spine rythm of the standing model: Am i right
>
> that there
>
> > are 7 ball joints modelled in the lumbar region which would allow 21
> > rotational degrees of freedom, but the spine rythm reduces them to 3 by
> > distributing them to the 21? Doesn’t this mean a higher stiffness?
> >
> > When we consider only the rotations in the sagittal plane: Normally
>
> there
>
> > would be 7 DOF in the plane, but now there is only 1 DOF. The
>
> segments are
>
> > then not so flexible regarding the whole lumbar region. Is this true?
> >
> > Thanks,
> >
> > Thomas

Dr. Thomas Zander
Biomechanik-Labor
Campus Virchow Klinikum
http://www.biomechanik.de
Tel.: +49(0)30 450 55 22 36

Hi Thomas

I think you have to look at it in another perspective. The DOF does
not have anything to do with muscles or springs.
For instance the amount of DOF does not change if you use a bodymodel
with no muscles or one with all muscles.
When talking inverse dynamics the motion or posture is always
described and from that the muscle forces can be calculated.

The spine ryhtme links the spine DOF so it is easier to control. You
can just remove the constraints if you want to control exactly how the
angle between each joint should be. This is kind of complicated and
you would need for instance a set of markers for each segment.

I would actually say that the human spine does have some kind of
ryhtme, each joint is constrained by ligaments and cartilage.

I hope this helped you a bit, else please write again.

Best regards
Christian, AnyBody Support

— In anyscript@yahoogroups.com, Thomas Zander <thomas.zander@…> wrote:
>
>
> Hi Christian,
>
> it is clear that torsional springs do not remove DOFs completely
from a joint,
> but together with a spring, the joint’s position is not undefined
any longer.
> A pure joint does not allow for calcuating the position as all
positions are
> equal. But together with a spring, one position is prominent: the
position
> were there is no force in the spring. This is the position of the
lowest
> energy.
> In other words: Similar to a ball joint that equals the translations
of two
> bodies, a torsional spring equals their rotations except for a
constant,
> which is the moment divided by the stiffness.
> If a spring does not remove/reduce DOFs: How can a large model like the
> standing model have a balanced number of DOFs and drivers? You
mention that
> there is more than one rythm. Are they introduced in order to
balance the
> number of DOFs and drivers?
> I think, i understood the principle of the spine rythm correctly,
but my doubt
> is if they create stiffness? Isn’t one DOF stiffer than 7? I have
the feeling
> that the loads necessary to deflect the lumbar spine are too high
and wanted
> to replace the spine rythm by torsional springs in the joints.
> The natural spine doesn’t know anything about a spine rythm. What is
missing
> in AnyBody in order to be able to remove the rythm?
>
> many regards, Thomas
>
>
> Christian wrote:
> > Hi Thomas
> >
> > First of all you can find some more info on how joints eliminate DOF
> > at http://www.anybodytech.com/679.0.html.
> >
> > Question 1: Let me try to explain. As you write a ball joint has 3
> > rotational DOF. If you add the parallel springs the joint would still
> > have 3 DOF. So how can we remove a DOF from the system? Well try
> > taking a look at a human hip joint. In many ways it is similar to your
> > example. The hip joint has 3 DOF and if you put a big cast on it that
> > don’t allow it to flex/extend but still to abduct/adduct and
> > eversion/inversion, then you would only have 2 DOF left.
> >
> > Question 2:
> > The spine rhythm is made in order to constrain all the DOF in the
> > back, as you mention there are a lot of DOF in the back. All the
> > rhythms does; is that it takes the DOF and binds them together, saying
> > that for example in the sagital plane where there would be 7 DOF,
> > those are merged into 1, by for example saying that each joint will
> > move 1/7 of the full motion. So the single DOF that is left in the
> > model, controls the 7 DOF by means of a rhythm.
> >
> > I hope this explains it a bit, it is kind of hard to explain in
> > text;-) However if you have any other questions please feel free to
> > write again.
> >
> > Best regards
> > Christian, AnyBody Support
> >
> > — In anyscript@yahoogroups.com, Thomas Zander <thomas.zander@>
wrote:
> > > Hello,
> > >
> > > there are two things, i don’t quite understand. Could someone please
> >
> > try to
> >
> > > explain to me the following:
> > >
> > > 1.) I am not quite sure about the degrees of freedom all in all. I
> >
> > understand
> >
> > > that joints reduce the possible DOFs. But what about let’s say a
> >
> > ball joint
> >
> > > allowing 3 rotational DOFs with parallel added rotational springs?
> >
> > Then the
> >
> > > rotation is still allowed, but not really free. There is a clear
> >
> > relationship
> >
> > > between moment and rotation, i. e. it should not be counted as
> >
> > “free” as the
> >
> > > rotation can be calculated from the outer forces and moments. Are my
> > > thinkings correct?
> > >
> > > 2.) related to the spine rythm of the standing model: Am i right
> >
> > that there
> >
> > > are 7 ball joints modelled in the lumbar region which would allow 21
> > > rotational degrees of freedom, but the spine rythm reduces them
to 3 by
> > > distributing them to the 21? Doesn’t this mean a higher stiffness?
> > >
> > > When we consider only the rotations in the sagittal plane: Normally
> >
> > there
> >
> > > would be 7 DOF in the plane, but now there is only 1 DOF. The
> >
> > segments are
> >
> > > then not so flexible regarding the whole lumbar region. Is this
true?
> > >
> > > Thanks,
> > >
> > > Thomas
>
>
>
> –
> _________________
> Dr. Thomas Zander
> Biomechanik-Labor