I am looking for research on mechanical or electronic input devices
with a dial or cylindar knob design. Examples of such interfaces would
be the Intermatic security timer (EJ341C), the Melnor 3015 Aqua
Timer, a kitchen timer that needs to be turned past 20 before being
set at 10 minutes, or some programmable lawn sprinklers.

I am interested in:
How such devices got designed that way in the first place. 
Historical background.

A few good references for these questions would be a big help.

I don't have any concrete information on the subject, but can offer
some conjecture.

I think that the reasoning for the kitchen timer is probably quite
different from the others.

Strictly from a logical standpoint it makes a lot of sense.  Inside
that timer there is likely a coiled up spring which drives an
oscilating gear, much like a pendulum. An example of this type of
spring mechanism (though probably not exactly what you're looking for)
is shown at http://home.howstuffworks.com/inside-clock.htm

It is probably simpler to just mount the knob directly in line with a
both the winding and setting mechanism, rather than having seperate
controls for both.  You have to turn it past a certain point in order
to give the spring enough winding to allow it to count down properly.

In the case of the other timers, it is probably more to do with the
fact that they're periodic,  doing the same thing in a set pattern. 
For this kind of repeating patern it would be easier to mechanically
set your times on a cylendar which can continue to turn day after day,
than it would be to have an extra mechanism to restart the timer.

Thank you for taking the time to respond to my questions.