Ludwik, You should look at "Bicycles & Tricycles - An Elementary
Treatise on Their Design and Construction" by Archibald Sharp.
The 1896 edition of the book was reprinted by MIT Press and it
should be in any good library (it's in mine). "Bicycling Science"
by Frank Rowland Whitt and David Gordon Wilson is another MIT
Press book (2d ed. 1982) with useful information.
The problem is not trivial, but it is resolvable. The geometry
is quite tricky. You will have to articulate your wheel on a
tricycle or else go to a bicycle model. Forget about simplified
treatments of the sort you find in Serway. They won't answer
real world questions.