I forgot to mention one obvious and major source of nonlinearity in
a Duo-Art (or almost any) expression regulator, namely, the nonlinear
relation of a pneumatics force per inch of vacuum versus its amount
of closure.

We know that a fully open pneumatic, when fed a certain vacuum level,
produces much more force than it will on that same vacuum after it is
partly closed.  This is because much of its force is produced by the
cloth sides' being pulled inwards, causing their edges to pull the
pneumatics boards closed.  The geometry is such that the sides are
more effective when the pneumatic is fully open.

In a regulator setup, such as a Duo-Art, where the pneumatic
balances the output vacuum against a linear spring, you will get a
concave-upwards curve of vacuum versus spring displacement.  Going from
intensity 0 to 1 requires little vacuum increase to move the spring so
much, but from 14 to 15 requires a lot more vacuum change to move the
now nearly closed pneumatic the same distance.

This is all to the good (unless you really are trying to get a linear
vacuum versus expression code plot).  In practice, what I seem to
recall when I adjusted my D-A years ago, is that the first intensity
step moved the pneumatic board quite a bit, and succeeding steps each
moved it less.  This would tend to flatten the curve, making it more
nearly linear.

Anyway, the pneumatic is a built-in source of nonlinearity, over which
we have little control, unlike the side linkages, which can be phased
to bend the curve in various ways.

Mike Knudsen