Ok ducklings, let's talk about frame for a tick.
In any performance arena, you have to be aware of the space, space designated for the performance, space designated for the audience, how easy it is to move back and forth between the two, etc. So if you're on a good ol proscenium stage, there's the stage up above the audience, maybe an apron of stage jutting out a little beyond the arch, the audience facing the stage on one side, probably some room on the floor used by the audience as an aisle, and maybe some stairs to and from the stage. The audience has expectations about what the performers will do, how close the performers will come to them, and how they can do their part to react politely by applauding and laughing at the appropriate times.
If you're in a circus ring, you're dealing with an audience in the round, the audience is sitting right next to the partition dividing the performance space and the seats, and the audience has a very difference expectation of what the performers might do and how much they the audience might be involved.
This is of course just dealing with live performance and doesn't take into account outdoor shows, site specific shows, street performance, or anything of that. These are just the areas I plan to focus on here.
But let's consider film, too. In a film you can change the setting in each shot and deal with any sort of depth and scale you'd like. But no matter how many different shots you have and how many different depths and set ups and all that, the filmmaker is always confined to the frame of the screen.
SO, having said all that, for a clown in any space it's her job to redefine the space she occupies. If she appears in a space, you don't want to see her treating it how it's meant to be treated, you want to see her do things that no ordinary person will do with it. If the piano is on the other side of the room from the bench, you move the piano to the bench (Grock, 1880-1959). So in any frame, the clown should defy the audience's expectations, occupy space not meant to be occupied by the performer, treat audience members in a way they don't expect, so forth.
But how they choose to redefine the space is what makes each performer memorable and unique. Let's look at one of my faves, Buster Keaton.
Probably the biggest difference between Keaton and Chaplin, because it's sort of hard to talk about one without the other, is that while Chaplin was a strange man in a normal world, Keaton was a normal guy in a crazy bizarre world. Both were directors and so were responsible for the looks of many of their films and the construction of their film worlds. Buster tended to place himself next to giant machines or mammoth landscapes to emphasize his lil size and he largely drew his comedy from the geometry of each shot. Anything that's not in the shot doesn't exist in that moment. Often there's a lot of perfectly symmetrical shots, representing order, and then along comes Keaton who can't help but disrupt such mathematical perfection. Observe:

The Garage, 1920

The Haunted House, 1921

Neighbors, 1920
That particular movie deals with a forbidden romance so this shot bisected with the fence happens a lot. This shot has a nice unbalance happening as Keaton tries to get things to be as they should.
And a super classic fave...

Before

and After! Steamboat Bill Jr, 1928
Fun fact! They only ever did one take of this shot because it was so freakin dangerous. They got it done that one time and despite Keaton's nerves of steel (he proudly boasted that he broke every bone in his body at some point in his life) he didn't feel the need to do it again.
Nothing is accidental in any Keaton shot. And in such a geometrically constructed world, Keaton's acrobatics are all the more emphasized and celebrated.
I mean seriously, check this out:
Thanks Dr. Moon Rat for that lovely tribute.
Let's not forget people, the kid did all his own stunts.
If you're interested in a further discussion of this, check out The Body in Hollywood Slapstick by Alex Clayton. He does a whole chapter on this subject. (I realize I've mentioned this book before in a less flattering context, but don't read that chapter. Just read the one about Keaton.)