 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 sinusoid we're summing, the horizontal scaling, the vertical scaling, choosing the sines or cosines, and lastly, adjusting the pin so it writes correctly. Let's start with setting the 20 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 1 tenth. The stop slides along the bar and can be fixed at precise points. Here we slide the stop up to 5, 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 10, 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 on how fast this platen moves as the crank is turned. The platen can move slowly. At a medium pace, they're very fast. This gear train that moves the platen consists of these six gears. The first gear is on the shaft of the crank. A chain connects this first gear to the second gear, which you can see up close here. On the same shaft as the second gear and sitting just behind it is a third gear. It has 12 teeth and engages the fourth gear. This fourth gear has 120 teeth. Behind and attached to the fourth gear is the fifth gear. This gear has 12 teeth and engages the rack, which is the sixth gear. You can see from the back how the rack runs a 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 a 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 a large small gear configuration. When it reaches halfway, I'll start the medium, medium gear set. Notice the pins 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 halfway, 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 pin. Let's look at the pin 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 pin because a set of concentric wheels connect the wire attached to the knob and the wire attached to the pin. The diameter of the outer wheel is five times that of the inner wheel and so the pin 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 set engage the gears on the cylinder. To change between sines and cosines, we need to disengage the two sets of gears. Unstrewing 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 sinusoids motion from the side. As they 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 rod are also aligned. Aligning the notches is a bit tedious, but it 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 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 around 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's rotated 180 degrees about the origin. The output of the machine is recorded by a hen 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. It's 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 in fits into the block and a set screw secures it. A removable rectangular frame secures the pin to the brass block. Here I attach the frame, insert the mini-sharpy pin, and secure it. I orient the pin 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 pin smoothly writes the function. Oddly, if the pin is perpendicular to the direction of travel, the plot tends to have flat peaks and troughs. And if the pin is oriented with the direction of travel, it's even worse. This particular machine, with gears to produce 20 frequencies, was likely built around 1915 and is a descendant of the first analyzer that Albert Michelson never built. He used what he learned from that first model to construct an 80-gear machine and even planned to build a model with 1,000 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-page 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.