I'm on my way to a Mechanical Engineering BS, and my courseloads have gone through statics, dynamics, fluids, CAD, among others. The help you're asking for involves all these disciplines, and more.
For instance, have you considered the fact that all these components you're trying to design are not solid, and rather, are all deformable? (Bending) Therefore, everything that's designed has an associated factor of safety associated with it; to put it simply, you design components to be at least X times as strong as the loads for which it is designed for. Because component failure is inevitable- all materials can be characterized as brittle or ductile. And even if ductile materials aren't stressed to an outright breaking point, permanent (plastic) deformation occurs which changes the original shape.
The deformation problems are what you should be concentrating on after getting a nice, regular, static problem. This is the stuff that CivE's and such contemplate when designing stationery bridges, trusses, etc, which you may argue is what a frame is. Which is why you need to have a basic design in order to use equations in the first place..
That's the big picture. The devil's in the details. While working on a Formula SAE car this year, one of the tierod ends (a bolt with an eye through it) sheared off during testing, taking a wheel with it. Would you be able to calculate the forces on your "tie rod end" - axles, points of contacts, etc? Never mind stress concentration factors (They increase when you have a groove in the material..) So, that's the shear part of kinematics; are you prepared to do those calculations as well? How safe is your design? What is the maximum load it can handle? Etc, etc.
This is what major bicycle manufacturers do to come up with new designs. In fact, I highly doubt that any major company ever guesses-and-checks new products anymore. The people you cite to come up with ultralight aircraft who do not do any calculations to come up with there designs are on the same level as the Wright brothers, only with modern-day tools. (The first attempts at heavier than air flight were fraught with danger...)
And regarding the design engineer you spoke of; even if he forgot the exact formulas, what difference does it make if he can go to his bookshelf and pull out his references? I shelled out a lot of bucks for these texts, and I'm thinking of keeping them for reference. Likewise, these programs of which you speak aren't magical; they require someone at the keyboard to actually know what they're doing to get meaningful results. (Pro Engineer, from personal experience, needs a guru at the keyboards to make sense of its idiotic interface)
If you're still determined to forge onward with your project, good luck to you and perhaps you could enlighten us with a basic sketch of your design. Just adding a watermark would validly copyright your creation, IIRC.