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Finally get to the kinematics that we're really interested
in, which is the kinematics of your hapkits.
So to remind you, this is what the hapkit looks like.
And what I've drawn on the screen is just a very simple
kinematic representation of it.
And the important variables are as follows.
We have drawn the pulley, the motor pulley itself, and some
of our documentation, I think, we'll call this the drive
pulley or the motor drive.
In any case, it has a radius, r pulley, and we also have the
angle, theta pulley, and you could define as positive
whatever you want, in terms of what is positive theta or a
negative theta.
I've just defined directions that are convenient so that a
positive rotation of the pulley will result in a
positive rotation of the next item that it's attached to.
In this case, that's the sector.
So you can imagine if this pulley rotates like this, then
this is actually going to cause the
sector to go this way.
OK.
So this larger sector pulley has a radius of, r sector, and
that is pinned here in the middle, and that doesn't
finish our kinematics yet, though.
There's actually another step.
Because what we're really interested in is what's going
on up here, at the handle.
So the person might actually--
here's my sideways drawing of fingers grabbing on to the
end-- a person will be grabbing on to this end point
with their fingers, and so what we're really interested
in is what is the motion of the handle?
And we call it x handle, even though it's not a perfectly
straight movement, It is movement over an arc.
So that's why this is drawn as an arc, because the tip the
hapkit right here is going to move in an arc.
But x handle represents the length along that arc.
And the main reason why we think of it as a change in
position, rather than a change of angle, is that when we
write code to render interesting haptic virtual
environments that you can feel, it's much easier,
especially for beginners, to think about it in terms of
translations rather than rotations.
OK.
So let's get back to the kinematics of this device.
So this would be the first kinematic equation, which just
says that the radius times the theta of the pulley equals the
radius of the sector times the theta of the sector.
And this is just because these two are meshed by
the friction drive.
And the other equation is that the handle, the position of
the handle, is going to be r handle times
theta of the sector.
Because you can see that the rotation of the sector here is
going to be the same as the rotation of
this handle up here.
So if you combine these two equations together, and you
get this kind of motion that I just animated, you will have x
handle equals r handle times r pulley divided by r sector
times theta pulley.
And so you can see how a change in angle of the motor
pulley is going to cause a change in
position of the handle.
And I'll animate that one more time for you.
All right.
And if you design a haptic device from scratch, you can
pick r handle, r pulley, and r sector to be the values that
you want, to create the relationship that you desire
between the angle of the motor and the
position of the handle.
Your haptic device has already physically been built for you,
so you can actually measure these quantities, and figure
out what this relationship will be.
So just a quick example of the real physical haptic paddle
just showing some different positions.
You can't really see it on here how the pulley is
rotating, but in this case, if a pulley rotates a certain
amount of time, then the sector is also going to move a
certain amount.
And similarly, this handle will also move.
So going from this position to this position, the arrows of
movement of angles will be as shown.
And then you could also keep going, and eventually get to
this position of the handle.
And just quickly, to look at the hapkit from the side,
we're now actually looking sideways at the hapkit, and
this is the friction drive right here.
So you can see the pulley here.
A rotation of this pulley, theta pulley, is going to
cause the rotation about this axis, which now I'll draw this
way, of theta sector.
And because the hapkit is a one-degree of freedom device,
these equations back on the last slide, this equation
here, is the only kinematic equation that you'll need to
get from motor input to motion of the handle.