Chapter 8 Movement vs Force

Things happen as we gear up in the going train. Rotational speed increases and the force or torque available at each wheel decreases. What does this mean and how does it happen? A clock wheel is just a modified lever with two sides and a pivot point called a fulcrum, like a seesaw. A long board balanced in the center on an arbor or shaft that will rotate. If the length of the two sides of the seesaw are equal then the force applied to one side will equal the force on the other and the movement of one side will equal the movement on the other. This is called a one-to-one ratio. Now if we move the weight on the left towards the pivot point the situation changes. If a ten pound weight is one foot from the fulcrum on the left side it will only take one pound to balance it ten feet from the fulcrum on the right side. This is a ten-to-one ratio. It looks like we lost power, but we didn't. We converted the force into movement, or distance traveled. On the left, if the ten pound weight moves one foot the one pound weight on the right will move ten feet. The actual amount of power stays the same. We just convert some of the force into movement. On the left, ten pounds times one foot of movement equals ten foot pounds. On the right, one pound times ten feet of movement equals the same, ten foot pounds. In a clock, the pinion acts as the short side of the lever, with the wheel acting as the long side. The arbor is the fulcrum, or the pivot point. The difference between levers and wheels is that wheels continuously interact with each other, and the movement is rotational rather than linear. We start with a large power source in the great wheel and transfer it to the pinion of the second wheel, from the second wheel to the pinion of the third wheel, and so forth. Each time we do this, the driving force, or torque, is reduced, but the rotational distance traveled in each stage is increased. Here we have two levers connected together in the same manner that one clock wheel would drive another. In this case, each lever has a ten-to-one ratio. As before, the lever on the left starts with a ten-pound weight on the left side of the pivot point, and is offset by a one-pound weight ten feet away. We are converting the ten pounds of force on the left to one pound of force moving ten times the distance on the right side of the first lever. Now we add a second lever in place of the one-pound weight. The effective force on the left, or input, side of the second lever is one pound coming from the first lever, and ten feet away on the second lever, this one pound of force is offset by one-tenth of a pound. We've also again multiplied the distance moved by ten, which gives us an end-to-end movement of one hundred to one. Of course this is impractical in straight levers, but this one hundred to one total ratio, and much more, is done in the simplest clock by turning the levers into the rotation of pinions and wheels. Here we see two clock wheels with five-to-one ratios working together. A one-tooth movement of the first pinion moves the outer edge of the first wheel five teeth. Since the first wheel directly engages the second pinion, the second pinion is forced to move five teeth, which moves the outer edge of the second wheel twenty-five teeth, but with one twenty-fifth of the starting torque, or force. Also notice that we multiply the ratio of the levers, not add to get the overall end-to-end ratio. Two ten-to-one ratio levers working together create a one hundred-to-one total ratio, not twenty-to-one. Two five-to-one ratio levers create a twenty-five-to-one ratio, not ten-to-one. We'll cover this again when we get into the motion works. Let's look at how the power and torque is distributed through the going train. Here we have the going train with levers superimposed over the wheels. Here is a typical wheel train with the wheels replaced by levers. I've calculated the torque or pressure applied to each wheel starting with a ten-pound driving weight all the way up to the escape wheel. The final force available at the escape wheel to drive the pendulum, after the force of a ten-pound weight is converted to rotational speed through the going train, is one point four grams. That's less than the weight of a U.S. nickel. This is not much force to keep the pendulum moving. If you want a practical demonstration of the loss of torque through the wheel train, take the winding key and feel the force of the spring or weight as you wind the clock. Now touch the escape wheel. You can stop it with a feather. So why do we care about all this force and torque stuff? The answer is friction. Friction is the most common cause of a mechanical clock stopping. As the lubrication dries up, parts wear and everything gets coated with dirt, friction increases until there's not enough force left to overcome it. And the clock finally stops.