> a simple mechanical equivalent or example of the kind of bootstrapping as we know it.
I suppose we all know that Baron Münchhausen was able to fly by pulling on his own bootstraps. Or hair. Or so it is said in books by Raspe and Bürger. That IS where the term comes from. And appears to be a purely mechanical process.
Joystick controlled vehicle. Push on the joystick, an amplification system (engine) moves the vehicle forward.
The tricky part is: we normally ride such a vehicle.
Get off and walk alongside, pushing the joystick. You must walk a mile to move the vehicle a mile.
Now get in. Push the joystick, vehicle moves forward, bootstraps your butt and arm. Now you can move the vehicle a mile with a peak motion of one inch.
Heck, this even works with a conventional automobile foot throttle. Except it is nearly inconceivable that you would move a car by walking alongside with your hand on the foot pedal. (I've done it on a tractor, and it IS awful stupid, and I still limp.)
> one possible example might be power steering on an automobile
Yes. You apply motion to the steering link. If the amplifier (pump and piston) are failed, you must apply large force. If the pump works, the initial motion opens a valve and applies oil pressure to a piston, following your motion, until the valve is closed. Force is greatly reduced.
That may be the clearest example. I think in most cases of mechanical boostrapping, the bootstrapping is so nearly indispensible that the machine would not be useful without bootstrapping, and we tend not to see it as such.
Here's another though not usually implemented as bootstrapping. A rudder (airplane or boat) is usually hinged at its leading edge. If the pilot/captain lets-go, the rudder tends to self-straighten, which is often the best thing to do. However on large planes/ships this leads to large steering forces. An alternate is to pivot the rudder part-way from front to back. The area ahead of the pivot tends to cancel the pivot-force exerted by the area behind the pivot, but the total boat-turning force stays high. If you pivot near halfway (more or less depending on edge effects), the turning effort tends to zero: infinite bootstrap. If you pivot behind center (or run a powerboat in reverse carelessly), the least turn tends to want to slam the rudder all the way: positive feedback. You need a couple more conditions for outright oscillation, but the potential is there.
A conventional butterfly throttle works with a halfway pivot and turning effort is near-zero despite air stream; high bootstrapping. Classic US choke flaps are off-center butterfly throttles (above the fuel jet for mixture enrichment) so that at high air-flow (where choke enrichment is not needed) they may self-straighten against a light spring; partial bootstrapping.
