I've been doing some conceptual design work on a vertical broadband
sensor, and I have a few questions. By reading past archives of the
PSN-L I noticed that Sean-Thomas Morrissey was a contributor to this
list, and there was some discussion about his STM-8 vertical
leaf-spring design.

1.) My first question is about deriving the transfer function. I tried
to derive it myself, but from first principles, but what I got isn't
what is shown in Sean-Thomas' work. I think the problem is my
understanding of what the input and output of the transfer function
are. Here's my logic for the transfer function:

You can't=A0measure the position of the Earth's surface from a
stationary reference frame, and you can't measure the position of the
mass from a stationary reference frame. Only the relative position
between the two can be measured. My first postulate is that the force
acting on the mass only depends on the relative position of the mass
and Earth's surface. Combining this postulate with Newton's F=3D ma, I
get:

          s^2 * M * X(s) =3D F(s) * (Y(s) - X(s))

Where M is the mass, X(s) is the position of the mass in a stationary
frame, Y(s) is the position of the ground in a stationary frame. The
only thing we can directly measure is Y(s) - X(s), so I believe the
transfer function is from Y(s) to Y(s) - X(s)/

          Now X(s) =3D Y(s) - (Y(s) - X(s)), substituting in the left
hand side of my above expression:

          s^2 * M * (Y(s) - (Y(s) - X(s))) =3D F(s) * (Y(s) - X(s))

          s^s * M * Y(s) =3D (F(s) + s^2 * M)(Y(s) - X(s))

                                      s^2 * M
          (Y(s) - X(s)) =3D ----------------------- Y(s)
                                F(s) + s^2 * M

Then F(s) would be k + s*eta + K_p  + s * K_d + K_i /s where K_p, K_i,
K_d are the coefficients of a PID controller, k is the mechanical
spring constant, and eta is the mechanical damping, if any.

When I plug this all in I get a somewhat simpler expression.that what
Sean-Thomas had. So I went back on including that fact that the
integrator pole is not zero, and the back EMF generated in the
feedback coil, and wound up with something way more complicated that I
am not going to type out here. Does anybody have any hints?

2.) My second question is about the hinge. Is foil suitable or should
I look at something like a knife edge or ball bearing hinge? I'm
leaning strongly towards foil. How much of an impact does the
flexibility of the foil really have on the period? Given that the
spring constant of the main spring is probably much much larger.
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