In this video, we concentrate
on the machine itself:
how to set up,
adjust,
and calibrate
the machine for use.
Let’s look at the five main things
we can set when using the analyzer
The amplitudes of the sinusoids
we’re summing
the horizontal scaling
the vertical scaling
choosing sines or cosines
and lastly adjusting the pen
so it writes correctly.
Let’s start with setting
the twenty amplitude bars.
As we saw in earlier videos
this lever’s position
on the rocker arms
determines the value
of the coefficient.
We set that position precisely
using this tool
it’s a small brass bar
with an adjustable stop.
The brass bar has markings
that go from 0 to 10
in increments of one-tenth.
The stops slides along the bar
and can be fixed at precise points.
Here we slide the stop up to five
place the tool on the rocker arms
and push the amplitude bar into place.
When I slide the stop
all the way up to a
large number, like ten,
I slide the amplitude bar
out to reach the end of the tool.
Recall this measuring stick
goes from 0 to 10.
So how do we set negative amplitudes?
We set the measuring stick
to the magnitude we want
and use it on the opposite end
of the rocker arms.
On the left are the
positive coefficients
and on the right side
are negative coefficients.
The amount of horizontal scaling
depends upon how fast
this platen moves
as the crank is turned.
This platen can move slowly
at a medium pace
or very fast.
This gear train that moves the platen
consists of these six gears.
The first gear is on
the shaft of thecrank.
A chain connects this first gear
to the second gear
which you can see up
close here.
On the same shaft
as this second gear,
and sitting just behind it,
is a third gear.
It has twelve teeth
and engages the fourth gear.
This fourth gear has a 120 teeth.
Behind and attached
to the fourth gear
is the fifth gear.
This gear has twelve teeth and
engages the rack
which is the sixth gear.
You can see from the back
how the rack runs
the full length of the platen.
I can adjust the
horizontal scaling by changing
the first and second gears.
First, remove this tapered pin
and pull off the crank handle.
Next unscrew the nut that holds
the other gear in place,
and then unlatch this gear system
so it disengages from the rack.
Here’s the same motion
but from a different angle.
Notice how the chain is now slack
and so can be removed.
The machine came with four gears
one small
two medium
and one large.
I’ll remove a medium gear
from the crankshaft
and replace it with
the small gear
and then replace
the medium gear above it
with the large gear.
Then affix that gear with the nut
replace the chain
attach the handle
secure it with a pin
and then relatch the gears.
Now, let’s look at three gear combinations
large and small,
medium and medium,
and small and large
and see how each
translates the platen.
I’ll start with the
large-small gear configuration.
When it reaches half way
I’ll start the medium-medium gear set.
Notice the pens move up and down
in sync.
When the first gear set is
three quarters of the way
I’ll start the third gear set.
They finish all at the same time.
This large-small gear set yields
twice as many periods as the
medium-medium gear set.
And the small-large yields
half as many.
In contrast to the horizontal scaling
the analyzer uses a
different method to
scale up and down.
At the top of the analyzer,
the vertical scaling is
determined by the magnifying lever.
This cylindrical rod extends
from the pivoted summing bar.
The position of this knob
on the lever determines
the vertical scaling of the output.
When the knob is toward the end, the
amplitude is at a maximum.
When the knob is about half way
the amplitude is reduced
and when I place it all the way inward
the amplitude is at a minimum.
A second rod perpendicular to the
first controls the
vertical offset of the output.
This knob slides up and down
and the wire wrapped around
the end connects the rod
to the inner hub
of the magnifying wheel
which in turn is
connected to the pen.
Lets look at the pen
and the knob simultaneously.
We’ll mark the current position,
and move the knob up.
Notice a small movement of the knob
yields a large movement of the pen
because a set of concentric wheels
connect the wire attached to the
knob and the wire attached to the pen.
The diameter of the outer wheel is
five times that of the inner wheel,
and so the pen moves vertically with
five times the magnitude
of the knob’s motion.
We can set the analyzer to use
either sines or cosines.
We do that by configuring
these gears
the cone gear set,
the cylinder gear set
and the pinion gear.
Recall that when we use the machine
the gears on the cone engage
the gears on the cylinder.
To change between sines and cosine
we need to disengage
the two sets of gears.
Unscrewing this knob allows
the cone gear set to swing away
from the cylinder.
You can see it more easily
from the top.
This action completely disengages
the cone and cylinder gears.
Notice that each gear has a notch
and can be rotated independently.
The goal is to put the sinusoids
associated with each gear in phase.
You can see that sinusoid’s motion
from the side
As I rotate the gear
the rocker arm above moves in sync.
Internal cams drive
the connecting rods up and down.
When the notches are aligned
the cams and the connecting rods
are also aligned.
Aligning the notches is a bit tedious
but only takes a few minutes.
Once they’re aligned
I can position the gears for
sines or cosines by
engaging the cylinder gear
with this pinion.
This lever pushes the pinion into
contact with the cylinder gear set.
Notice the notch.
When all the notches are
in this position
the machine is set for sines.
If I rotate the gears 90 degrees
this sets the gears for cosines.
Again, if the notches are on the side
the machine calculates sines
and if they’re on the top
the machine calculates cosines.
Why is this?
When the notches are at the top
the rocker arms are
at their maximum travel.
That’s like a sinusoid starting
at its peak which is
equivalent to a cosine.
When at the bottom
the rocker arms
are at their lowest point of travel
which is like a sinusoid starting
at its trough
this is like a negative cosine.
And when the notches are on the side,
this is a middle position which is
equivalent to a sine.
If we set the amplitude bars
for a square wave,
and set the machine
for cosines
we get this even function.
It’s even because it is
mirrored about the y-axis.
And, then, keeping the
amplitude bars the same
but setting the gears for sines
we get this odd function.
It’s odd because it is
rotated 180 degrees about the origin.
The output of the machine is
recorded by a pen mechanism.
This brass pen holder
which looks authentic
was made in our shop because
the original is long lost.
A long, square brass rod rests gently
in an open bracket
its top attached by a wire
to the outer rim of
the magnifying wheel.
I attach the pen to this brass block.
A square rod, with a cylindrical end
fits into the block,
and a set screw secures it.
A removable rectangular frame
secures the pen to the brass block.
Here I attach the frame
insert the mini-sharpie pen
and secure it.
I orient the pen about 45 degrees
against the direction of travel
of the platen.
And then press it up lightly
against the paper.
As I turn the crank
the pen smoothly
writes the function.
Oddly, if the pen is perpendicular
to the direction of travel
the plot tends to have
flat peaks and troughs.
And if the pen is oriented with the
direction of travel
it’s even worse.
This particular machine
with gears to produce twenty frequencies
was likely built around 1915
and is a descendant of the first analyzer
that Albert Michelson ever built.
He used what he learned from
that first model to construct
an 80 gear machine
and even planned to build a
model with one thousand gears.
What a wonder that machine
would have been!
I’m Bill Hammack
the engineer guy.
That’s the last in this series on
Albert Michelson’s harmonic analyzer.
If you want deeper insight into
this machine check out this video
to learn about the 128 picture book
that goes through every part of the machine.
The page by page video will guide you
through the entire book from
cover to cover.