
You've probably never noticed, but (nearly*) all bicycles place the chain and associated components on the right side, not the left.
If every bike is built that way, there must be a good reason right? Some sound mechanical explanation?
To anwer we'll visit horses, swords, the rule of the road, and the Wright brothers. Read on.
Rule of the Road
It's difficult to pinpoint the exact moment the bicycle as we know it evolved out of the high wheel penny-farthing, but in England in 1879 Henry Lawson patented a "bicyclette" featuring a rear wheel chain drive on the right side.
The Science Museum has an awesome gallery
A few short years later John Kemp Starley, another Brit, released a rear wheel chain drive bike that would become the model for the modern bicycle.
65% of the world's population travels on the right side of the road, but Starley and Lawson being English, would have traveled on the left. A right side crank on left side travel would keep the dirty chain towards the road rather than the sidewalk, potentially allowing for cleaner mounting and dismounting.
It's a decent theory, but the evidence doesn't support it.
Righty-Tighty
Some 20 years after Lawson's bicyclette, in Dayton, Ohio, the Wright brothers (yup, the flying ones) were building and selling bicycles. It's believed they introduced reverse, or lefty-tighty threading to the bicycle. Prior to that, all threads were righty-tighty, some of which could loosen while pedaling if placed on the bike's left side.

A Wright brothers bicycle on display at the National Air and Space Museum. Creative Commons.
While it's true a left side cog and hub threading would require some additional engineering, it was certainly doable.
This is a better theory, but the evidence doesn't support it.
The Cavalry
Now let's talk about swords.
If you wear a sword, it hangs from your left hip, so it can be more easily drawn with the right hand, because most people are right handed. If you wear a sword and need to ride a horse, you mount the horse from its left side, swinging your right leg over, to keep the sword out of the way.
So because of swords, horses were mounted on the left. Because of horses, it's been suggested, bicycles were mounted on the left. If so, a right side drivetrain would keep the frame between you and the greasy chain.
That makes sense, but bikes are more manageable than horses, and few riders wear swords. This is the most interesting theory, but the evidence doesn't support it either.
The Chicken and the Egg
Drivetrain components are on the right side of the bike because they've always been on the right side of the bike. It's arbitrary. Beyond that, no one really knows.

*There are a few exceptions of course. Tandem bikes have chains and chainrings on both sides of the frame. BMX bikes are also often ambidextrous to allow tricks on a chosen side without damaging the crankset.

