We are discussing alternative steeds (to horses) over at worldbuilding.se. I boldly proclaimed that in ancient times, the bike could easily have replaced the steed if they had some Da Vinci level of tech nailed down. (Disregard the various animal-as-motor ideas. That's just goofing.)
Has anyone here ever tried a bicycle made with late medieval technology in rough terrain? Could they survive long in terrain?
Wooden carriage wheels have existed for thousands of years and have mainly been used on bumpy terrain without too much trouble. Smooth tarmac or concrete roads didn’t exist until very recently after all. So I don’t think wheels will be your limitation.
The bigger question is if you can manufacture a bicycle drivetrain (chain, sprockets and possibly freewheel, though I guess you could use a belt drive) and make the bike comfortable and ergonomic enough. Early bikes were pennyfarthings for that very reason.
They also required quite a bit of advanced machining. A crankarm and pedals is not something your medieval village blacksmith can just hammer out.
Some of the other answers mentioned technologies that are prerequisites for bicycles. However, the deciding technology that prevented the widespread use of bicycle technology were cost effective methods to build durable and maintainable roads.
Karl Drais invented the Laufmaschine (aka vélocipède bicycle) as early as 1817, because he couldn't afford to feed his horse and because he was living near a stretch of excellent road going into Mannheim. He sold a couple of his inventions to nobility or the like. Think of (grown up) princes riding around in formal gardens. Except for Drais and a few others it wasn't even useful for most of the gentry. Bicycles were a fad in other nations in the following years, and then forgotten until the 1860s.
What changed in between were Macadam roads and railways. Up until the 1850 the ne plus ultra for goods transport were canals. In early industrialisation from 1600, digging canals was a priority for any prince or monarch developing their dominion. Railways were considerably cheaper and faster to build. They freed up funds and workforce for road building. But they also increased demand for overland transport, and thus made good roads economically feasible.
Before the development of Macadam roads, metalled (i.e. gravel roads) were possible but expensive and degraded very quickly. The key was water management by compacting the surface, camber, ditches, and stable foundations. If you have to rebuild the damn thing after every decent downpour, you don't have the funds or workforce to extend a road network.
When you imagine a 17c 'highway', think of two adjacent MTB single trails and not a rough gravel road. Old roads were built for carts. Two ruts for the wheels separated by a very nutrient-rich trampled morass. That's where the ox goes.
Bicycles don't do well on such rough terrain. Mountain bikes (MTB) with fat tyres are good for going downhill and having hilarious fun. Pneumatic tyres were invented in 1847. Until 1876, the Portuguese had a rubber monopoly and it was a rare commodity. Even with modern tyres, MTBs aren't much faster than trail hiking for long distances though.
Without any application, inventions are forgotten. At best they may become a fad, like Drais' 'dandy horse'. But they do not last.
You need to go another 1000 years back in time to make bicycles great again.
Many of the pre-collapse Greek and Roman roads were quite viable for bicycles:
This state includes some amount of neglect, but a road that's been used occasionally.
While falling short of Dutch bike paths, it's nothing you won't encounter in Paris-Roubaix.
A few were outright comfortable:
Ancient roads remain popular cycling paths even today.
But even without a road, on rough terrain, chariots were stable enough to shoot from:
It's hard to think of anything that would prevent a bicycle from being used in the developed parts of Greek or Roman civilizations. The horse was simply more performant (if more expensive and fuel-hungry), just as the car has been more performant (if more expensive and fuel-hungry) than the horse over the last century. And how the easier-to-ride scooters and electric bicycles are displacing pedal power today.
Could a bicycle be built with then-available materials?
Modern department store bikes aka BSOs are typically made out of some unspecified grade of steel and weigh 16-20 kg. Basic construction steel, the kind used in medium-rise building frames, ranges from 200 to 280 MPa yield and about 320-380 MPa ultimate. Reasonably good steels like AISI 4130 allow for steel bikes in the 12-15 kg range. 4130 steel has a tensile strength of 360 MPa yield and 560 ultimate.
Bronze has tensile strength ranging from 70 to 1000 MPa, with an average of 280 MPa for yield and 470 MPa for ultimate strength. So, bronze is about 20% weaker than decent bike steel, but 20% stronger than cheap steel. All in all, even ancient bronze should be on par with what BSOs are made out of, but 10% heavier per unit weight. Bronze lugs are well within what was commonly made at the time.
Wood, of course, hasn't changed much over the years. Strong, high-quality wood was in high demand for ships, polearms and shields. So a bike with bronze lugs and bronze or wooden frame members would likely be in the same weight range as modern BSOs, i.e. within 20 kilograms. All-wood construction was achievable pretty much throughout history, but has less performance potential.
One issue is that, before the industrial revolution, a bronze-lugged bike would likely cost more than a basic rideable horse. Fresh-air exercise was also definitely easier to come by, as well, making the bike's benefits less attractive. Even if you had the means to build a sophisticated vehicle, whipping a horse was seen as a classier activity than exercising your calves.
I'm no historian, but the tech of the 17th century would be incapable of making
However the concept of wheels and axles existed, as well as the idea of reducing friction between axle and a wagon. Though this was probably nothing fancier than "lubricate it with grease" and the two parts wear into each other.
The dandyhorse/drasinine is a plausible example of tech of the time. This would let someone ride down a slope, and would make it possible to "stride" across a level path faster than walking.
There's no chance of riding this proto-bike up any noticeable gradient. You'd have to get off and walk while pushing.
Another consideration is that Asphalt or Concrete was not used for roads or paths, so any track is going to be plain dirt at best, and it is possible the tracks will have rocks and roots. The proto-bike won't be at all comfortable to ride.
Even in the 19th century it looked like this, with iron wheels and no brakes. The rider pushed off the ground with their feet, like a modern kid's balance bike. There are no pedals or even foot-pegs
In summary, this is no use in your presumed time period because of limitations. It can't go up hill like a horse, nor carry much, and can't really function as transport.
It's a toy, in this form. Sure someone could have come up with the same basic idea a hundred years earlier, but no better than this early design.
The bicycle was a good idea for a lot longer than it was a practical idea. So there is a long history of proto-bicycles before the 'modern' bicycle. A series of inventions in the 1800s allowed the development of what is broadly agreed as the modern bicycle -- the Rover Safety Bicycle (1885) plus the Dunlop pneumatic bicycle tyre (1888).
The Safety Bicycle is named because it was safer than the Penny Farthing high wheeler (1870), which very readily tipped the rider onto their head. The Penny Farthing included the wire-spoked wheel (1849), which had solved the problem of heavy and thus slow wheels.
Some Penny Farthing also included an axle with radial ball bearings (1869), which allowed the wheels to spin freely. The ball bearings, cup and race are beyond the ability of a village blacksmith in the small size used on the Penny Farthing.
The Safety Bicycle could have two same-sized wheels because of the gradual development of another invention, the bush roller chain (1880). This is an item of precision manufacturing, beyond the skill of a village blacksmith.
The Safety Bicycle incorporated the previous inventions of the wire wheel, hub bearings and sprung saddle (1865).
As you can see, practical bicycles are relatively recent, because they are a high technology item requiring precision manufacturing. This trend continues even now, with bicycles using carbon fibre or aluminium welded frames, in shapes designed to minimise air resistance using computers and wind tunnels, aluminium gears made to tight tolerances, mechatronic gear shifting, tyres with exotic puncture-proof materials, GPS cycle computers, rechargeable LED lighting, breathable synthetic clothing.
I hope I've illustrated how the modern concept of a bicycle -- two equal-sized wheels, with the rear wheel driven by a roller chain, with light easy rolling wheels -- requires too much technology from the 1800s to be in a late mediaeval world.
A (nearly) parallel development of the bicycle has occurred in the Eastern Democratic Republic of Congo in the form of the cargo chukudu.
While this does have the added infrastructural disadvantage of tropical levels of rain, something like this could have been the pinnacle of development in Europe until the advent of the high-quality wrought iron noted in other responses.
This design is a choice - potentially economic. Africa is awash with car wrecks and there is no shortage of steel bar from suspension components if it were deemed better.
VO₂max, or the maximum possible volume of oxygen that we can consume, is the maximum power your aerobic system can generate (we burn O₂ to generate energy). It can be expressed in absolute terms of liters of O₂ per minute, or it can be divided by body weight (usually called relative VO₂max; think of it like W/kg).
What does this have to do with anything? Well, the VO₂maxes of a sample of racehorses ranged from 123-172 ml O₂/min kg. The maximum values we've measured in humans are in the 90s. Moreover, horses are a lot bigger than humans, so their total power is a lot greater.
It seems likely to me that the VO₂maxes of draft horses are similarly larger than the VO₂maxes of average humans, and that their power relative to bodyweight at a sustainable sub-maximum effort is similarly larger than humans. Unless the walking/running economy for horses is a lot worse than for cycling humans (e.g. what % of that energy is converted to forward motion, the balance being wasted as heat and sound), then I would assume that horses would be able to cover long distances faster than human cyclists - on the Worldbuilding post, someone commented about the man v horse marathon. This is the point they were trying to make but with distance running, not cycling.
In addition, bicycles were first introduced in the 19th century, so at least 100 years ahead of the period mentioned. Bicycle technology developed considerably since invention, whereas technology related to horses was stable because we had horses for a long, long time. The point here is that a bicycle made in the 1700s might be less capable than the first bicycles. Hence, at the time of the story, horses may have the technological advantage over bikes - it's just that bikes will develop faster later on.
One particular issue that I'd want to know about is steel quality. Yes, we have had steel for quite some time before the 1500s. However, in the 1500-1700s, I don't know if we had the ability to mass produce high-quality steel. We might not have been able to remove all the impurities, and steel might not have been as homogeneous as today (i.e. you could get some parts of a block that have lower carbon content and are weaker). Bicycle chains take a lot of force. People have built wooden bicycles in the modern era, but the chain is a critical link in the system.
Because of these two issues, you might not be able to build a bicycle to survive rough terrain in the 1700s, and it would likely be inferior to horses for transport.
Let me play devil's advocate for a moment. Horses were associated with status: a chevalier rode a cheval. In Rome, equestrian was a member of the social class that was immediately below a senator. Riding a bike wouldn't have the same cachet.
