Hello, this is Rob from PracticalPrecision.com.
In this video, we look at designing and modeling
a kinematic mount - one of the most useful
and powerful tools in precision machine design
and optomechanical engineering - in CAD, using
SolidWorks.
You can download this model and learn more
about designing a custom kinematic mount at
practicalprecision.com/model.
A kinematic mount works on the principle that
any two rigid bodies have six relative degrees
of freedom between them: 3 translations and
3 rotations.
Introducing a point of contact between the
two bodies eliminates one of those degrees
of freedom, as in a ball on a surface.
Two points eliminates two degrees of freedom,
as in a ball in a v groove.
And three points eliminates three degrees
of freedom, as is a ball in a trihedral socket.
By combining these elements in different configurations
with no more than 6 points of contact, a kinematic
mount positions and orients two bodies relative
to one another with very high stability and
repeatability.
Constraining fewer than 6 points allows precision
motion in the remaining degrees of freedom.
More than 6 points over-constrains the assembly,
introducing distortion, instability, and uncertainty.
This is a Maxwell-style kinematic mount.
For clarity, I�ve left out a lot of details
that would be present in an real application,
such as features for attaching optics, just
so that we can focus only on the details that
make it a kinematic mount.
A Maxwell-style clamp uses three balls in
three v grooves radiating from a common center
to establish 6 points of contact that fully
locate the the two bodies relative to one
another.
In this design, the ball is press fit into
the top plate so that it can�t move.
But the combined top plate and ball is free
to rotate about the center of the ball, on
the two points of contact with the v groove
in the bottom plate.
In some applications, one or more of these
balls will be replaced with a ball end screw.
Turning the screw will adjust the relative
position of the ball relative to the top plate,
changing the orientation of the top plate
relative to the bottom.
If two of the balls are replaced by adjustment
screws, it�s even possible to get relative
adjustments about two axes, so you can have
a tip tilt system.
Although it�s not quite as intuitive as
if they were in a right angle arrangement.
If all three balls are replaced by ball end
screws, it�s even possible to adjust the
spacing between the plates without changing
the orientation.
Depending on the orientation of your mount,
the magnitude of the load it will carry, and
any external loads such as shock and vibration,
you�ll need a mechanism to positively load
the kinematic components against each other,
so that they don�t separate.
In this case, we�re using three extension
springs located midway between each supports.
Preload can be a critical part of your design.
There can be a delicate balance between sufficient
locking force to hold the mount together against
the combined loads, and excessive force that
significantly deforms the components, defeating
the purpose of using a kinematic mount in
the first place.
Preload mechanisms are one of the topics we
cover in detail on practicalprecision.com.
As I mentioned at the beginning of this video,
you can download this model at practicalprecision.com/model
and freely use it in your own work.
Let�s look at the construction of the model
and how to easily adapt it to different applications.
The model uses top-down design, so that we
can make changes in one place in the assembly,
and those changes will propagate down to the
components.
That place is the Layout component, which
is the first component in the assembly tree.
The Layout Contacts sketch let�s you control
the basic footprint of the mount.
You can change the diameter of the circle
that the supports lie on, and you can change
the angle between the supports.
This equilateral triangle layout is the most
common one you�ll see for a Maxwell mount.
It maximizes usable area; is very stable;
and can be less sensitive to transient thermal
effects due to its symmetry.
But in some applications, there can be practical
reasons for changing this.
The most common reason is that an equilateral
layout simply won�t fit in the space available.
Changing the layout is as simple as changing
the diameter and angle dimensions.
An everything else changes accordingly.
We may also want to change the ball diameter
and the contact angle with the v groove.
We can make those changes using the ContactCrossSection
sketch.
The ball diameter and the contact angle could
be infinitely variable just like the spacing
and the angle between the supports are.
But as a practical matter, precision balls
are only readily available in discrete diameters,
as are tools for machining smooth surfaces
at particular angles.
So in this model, we have a fixed number of
ball diameter and contact angle combinations,
with diameters ranging from 6 to 10 mm and
angles of 120 and 135 degrees.
We�re going to change from currently 6 mm,
135 degrees to 10 mm, 120 degrees.
You�ll notice that regardless of ball diameter
and the angle, we maintain a 0.5 mm offset
between the center of the ball and the bottom
flat on the top plate.
Since the ball is press fit into this hole,
that just ensures that the widest part makes
contact with the hole and that we get a press
fit.
Similarly, on the bottom, we have a fixed
0.5 mm distance between the contact points
between the ball and the v groove and the
top of the plate.
And, again, 0.5 mm clearance from the bottom
of the ball to the bottom of the groove.
That just accounts for manufacturing tolerances.
How do you determine the right contact angle
and diameter?
This is a critical aspect of your design,
affecting the performance, stability, and
operating life of the mount.
There are at least three considerations in
the designing the kinematic interface.
One of the disadvantage of the kinematic mounts
is that we are supporting whatever combination
of design load and external load that there
is on at most six points.
And they are points, not pads.
That does result in very high contact stresses
that we call Hertzian stresses.
Contact stress is a function of the geometry
and the load.
What�s an acceptable level depends on the
material properties of the components.
The main variable you have to play with is
the diameter of the ball.
The larger, the lower the stress.
For smooth, linear operation and long life,
the ball needs to be able to slide easily
on the contact points.
That�s a function of friction and all that
that normally entails, but also of geometry,
in particular, the steepness of this angle.
You can imagine as the contact angle gets
steeper and steeper, you could reach a point
where, under the operating load, the ball
could actually wedge and bind
But steeper angles also have benefits.
They�re more resistant to lateral loads.
If the ball does become unseated due to shock,
vibration, or other external load, it will
more readily fall back into place.
And overall, the repeatability is higher with
steeper angles.
So, in addition to the first order design
concern of, "Does it fit?" and designing a
preload mechanism that performs its function
without introducing excessive deflection,
We also have the related and sometimes contradictory
design parameters of contact stress; friction
and freedom of movement; and stability.
Visit practicalprecision.com/model to find
additional help and resources for designing
a kinematic mount that satisfies all of these;
download this CAD model and others; and sign
up for a course in kinematic mount design
with me, Rob at Practical Precision.
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