On Sun, 25 Dec 2016 19:19:15 +0000 (UTC), Frank Baron advised:

Specifically, what is the patent saying the single-spring apparatus
accomplishes?

The "treading force" is the pressure exerted on the pedal,
and "urging the pedal" means operating it.

I wasn't sure if the terms were "directional" since what we're trying to
figure out is why Toyota uses this method, and what the difference is in
the patent description for the two spring method (which we don't have in
our vehicles) and the one spring method (which is what we have).

Since our vehicle diagrams look almost exactly like those in the patent, we
think the rationale as to WHY Toyota used such a complex mechanism will be
described in the patent (if we only understood what the patent says).

Here is our vehicle diagram:
http://i.cubeupload.com/2Bsddp.gif

Here is the patent diagram (which is almost exactly the same):
http://i.cubeupload.com/wYA3iD.jpg

While some of us have re-engineered the bushings, the bushings still fail:
http://i.cubeupload.com/8lgaVh.jpg

Given the re-engineered bushings still fail, most of us have simply
dispensed with the torsion spring altogether, replacing it with a linear
spring instead:
http://i.cubeupload.com/pSB77I.jpg

We've spent some effort on finding just the right geometries for that
linear spring:
http://i.cubeupload.com/FaKA4k.jpg

But, we're really shooting blind if we don't know WHY Toyota used such a
complex torsion spring setup when we know they knew all about the linear
springs (since all the attachment points already exist!).
http://i.cubeupload.com/WO7trl.jpg

Given what you've said, which is that "urging" is merely operating the
pedal, and "treading" is the force applied, then we can convert this quote:
https://www.google.com/patents/US4907468

"The present invention relates to an apparatus for reducing the /treading/
force required to operate a pedal, such as the clutch pedal of an
automobile. More specifically, the present invention relates to an
improvement of the means for /urging/ the pedal."

To this quote:
"The present invention relates to an apparatus for reducing the /amount of/
force required to operate a pedal, such as the clutch pedal of an
automobile. More specifically, the present invention relates to an
improvement of the means for /operating/ the pedal [initially]."

It's important to get the interpretation correct because the pedal has
multiple modes of travel, from the initial pressure to the ending release
to the various points in the arc in between (which the patent discusses in
similarly cryptic engineering terms).

In summary, it seems that the patent mostly refers to the purpose in being
to alleviate STARTING (urging) force - would you concur?