I am a Fool (hence Mike Fule) with a team of Morris dancers. I have attended and conducted many workshops on Fooling and Fool-related skills and ideas. I have come into contact with a few semi-professional clowns (and a few professional semi-clowns;) ) in connection with this.
A Fool is not a clown, but there are similarities.
Clowning is a skill. Clowning is what a clown does. Unicycling is a skill. IF a particular clown happens to possess the skill of unicycling, THEN the clown might choose to incorporate the unicycle into his or her act. Other than that, there is no substantial traditional connection between clowns and unicycles.
As others have suggested on this thread, and elsewhere, it seems likely that the public has conflated the idea of the clown and the unicycle because they both appear in the circus, and they are both absurd.
An additional factor is the recent (last few decades) growth of street circus, and the concept of ‘circus skills’ as a challenging and rewarding hobby for children from 7 to 77 (etc.).
Gone are the days when people were happy to do one thing and do it well. Now, as soon as one skill is learned, another beckons. This is why so many people (including me!) have experimented not only with unicycles, but also with stilts, slack ropes, juggling, fire eating and clowning. In the traditional circus, skills were taken more seriously. Specialisation was the norm. Skills were passed down through families. People did not trespass on the acts of their colleagues.
A clown is a character. There are several categories of clown - the American hobo clown; the grotesque; the white face; Pierot; and so on. Within the show, each clown would have a role - one would be in charge; the other would be down trodden; another would be rebellious. A traditional bit of clowning ‘business’ would revolve around something as simple as the ‘boss’ clown telling the others what to do, and the others failing to do it, through a mixture of stupidity and mischief. The aim was to entertain, not to impress with ‘circus skills’.
Clowns were often low ranking in the circus hierarchy, although some individuals made their names and fortunes. Sometimes clowning would be a ‘second string’ for other performers, who would regard their main act as (say) knife throwing, but would put on the clown suit and makeup for the rest of the show. The quality of their clowning performance might reflect this.
But the modern ‘clown’ is often a different thing altogether. It is a student collecting charity money in a bucket, and wearing a hired clown suit; it is a bored man in a colourful suit and daft hat, tying balloons into amusing shapes; it is someone spicing up a drab unicycling act by wearing stripey trousers and shouting when he wobbles; it is the strange character bouncing around at burger bars, pretending to like children… and so on.
Not all modern clowns are this bad; there are, no doubt, many excellent modern clowns. However, it is the “clowns of all trades”, who often have little or no concept of how to amuse or entertain an audience, who rely on the long list of props - a list which so often contains a unicycle.
A unicycle is not actually a very useful prop for a clown. I have used a unicycle on and off (ho ho) in my Fooling performances for 15+ years. Riding it often attracts attention (good); wobbling and waving my arms and making ‘Oooooer!’ noises provokes a laugh (OK); a few little tricks (idling one footed etc.) provoke a good response (great); but anything cleverer isn’t really Fooling - or clowning.
I can’t leap up onto a picnic table, or do a 360 degree unispin. Even if I could, however, I would not do it as part of a Fooling (or clowning) performance. A Fool/clown is there to entertain and amuse, not to impress.
So, ladies and gentlemen of the jury, I put it to you that whilst clowning and unicycling are both skilled activities, and are both found in traditional and street circus, they are essentially unrelated, and only overlap occasionally because the modern performer so often works on every skill except the most important one: the skill of entertaining. Unicycling is to clowns what fire eating is to knife throwing. I rest my case.
I would, however, link unicycling with juggling - they are performing skills which go naturally together (for people who are cleverer than I am!).