I’m an electronics and computer engineer by trade. I don’t know as much about mechanical engineering as I’d like (or should), but I’m increasingly impressed by the masterful mechanisms fashioned and formed by masterful mechanical artificers.

I’ve previously made mention of the book 507 Mechanical Movements: Mechanisms and Devices by Henry T. Brown (the original version was published in 1868, but the link given here is to an unabridged printing of the 18th Edition from 1906).

One topic that keeps on tweaking (what I laughingly call) my mind is that of clockwork and gears. As an aside, people in the UK commonly use the term “cog” as being interchangeable with “gear,” but a cog is really another name for a tooth on a gear (the term “cogwheel” is an acceptable synonym for “gear” or “gear wheel”).

Your knee-jerk reaction may be that gears are a rudimentary technology, but I would beg to disagree. Defining the shape of the cogs (teeth) on the gear is an artform in and of itself. And (for the uninitiated), wrapping your brain around the way in which even a simple gear train works can be a mindboggling exercise.

The simplest of gear wheels—the ones we all think of when someone says “gear wheel”—are known as “spur gears.”

A simple gear train is one in which there is only one gear wheel on each shaft. The simplest of these has only two gear wheels. Consider the example below. Let’s assume the gear on the left is the input (imagine it’s being driven by a motor), while the gear on the right is the output (imagine it’s being used to drive something else.

Simple gear train (5 -> 10 teeth) (Click image to see a larger version)

One way to specify the gear ratio of this system is by dividing the number of teeth on the driven (output) gear, which is 10 in this example, by the number of teeth on the driving (input) gear, which is 5 in this case. This gives us a gear ration of 10:5, which we would boil down to 2:1.

Another way to look at this is that the input gear needs to rotate two times to make the output gear rotate once. This means that the output shaft will rotate at half the speed (in revolutions per unit of time) but with twice the torque (twisting force).

Note that I created all the illustrations shown here using the free tool on the Gear Generator website. This is an awesome aid, including the ability to animate your creations, but we digress…

Now consider what happens when we add a third gear to our simple train as illustrated below. This additional gear is called an “idler gear.” This serves two purposes. Without the idler gear, the input and output shafts would rotate in opposite directions. With the addition of our idler gear, the input and output shafts rotate in the same direction.

Simple gear train (5 -> 10 -> 10 teeth) (Click image to see a larger version)

Another reason for adding an idler gear is to increase the distance between the other gears. Another way to look at this is that it can bridge the gap between two gears that are too far apart to mesh directly.

In the example above, our idler gear has 10 teeth, just like our output gear. What would happen if we were to increase the number of teeth to 15 as shown below? Would this change the speed or torque of the output shaft?

Simple gear train (5 -> 15 -> 10 teeth) (Click image to see a larger version)

Now suppose we were to add a second idler gear with 7 teeth as shown below. Apart from changing the rotational direction of the output shaft (which will once again be in opposition to the input), would this change the speed or torque of the output shaft?

Simple gear train (5 -> 15 -> 7 -> 10 teeth) (Click image to see a larger version)

Amazingly enough (well, it amazes me), the number of idler gears and the number of teeth on those gears has no effect on the gear ratio (and hence the speed and torque) of the system. Irrespective of how many idler gears we have, the gear ratio of the simple gear train is determined only by the number of teeth on the output gear divided by the number of teeth on the input gear.

While this may be intuitive to those of a mechanical bent, it requires my mind to perform mental gymnastics, and my mind is not as limber as it used to be.

Things get even more interesting when we start to consider compound gear trains, which involve multiple gear wheels being attached to the same shaft. Consider the example below. The shaft in the middle is carrying a small gear and a medium-sized gear.

Compound gear train (Click image to see a larger version)

Also, the smallest gear wheel and the largest gear wheel have the smallest teeth, while the two medium gear wheels have larger teeth. And, just for giggles and grins, the largest gear wheel has its teeth on the inside edge rather than the outside edge.

So, what’s the gear ratio of this beast? I haven’t got a clue (feel free to work it out and post the answer in the comments below). Happily, my friend Steve Manley pointed me toward the INTEGRAL PHYSICS YouTube Channel. Amongst many other offerings, this has some fantastic gear-related videos as shown below.

You would think that this would be enough to keep mechanical engineers busy and off the streets at night, but no! Instead, they are running around creating even more arcane and esoteric gear-related constructs, like logarithmic gears (see my Lusciously Lovely Logarithmic Gears blog), hyperboloidal gears, double helical bevel gears, elliptical gears, hypoid gears, helicon gears, spiroid gears, and more (check out this YouTube Short Video to see these in action)

In closing, you might also be interested in my somewhat related Is This the Best Useless Machine Ever blog that dazzles us with more mechanical motions than can possibly be good for us.

So, what say you? Do you have any thoughts you’d care to share on any of this? And are you aware of any YouTube videos that would confuse me even more (in a good way, not just because they are bad videos)?