On Tue, 4 Apr 2006 10:03:12 -0400, "Glenn Ashmore"
wrote:

Thanks to same day delivery from McMaster I cobbled together the first
prototype last night. I quickly figured out that the spring rate and
initial tension are critical. A rate of 10 lb/in is way to fast. It is not
sensitive enough to prevent the camera moving. Had to cut back to a 5.29
rate with a 6.41 initial tension. Preloaded the spring to 17 pounds and the
arm settled at about 5 degrees up. Rapidly moving the fixed side up and
down 7-8" the camera stayed at the same level but when I moved it up and
stopped the camera followed a bit to quickly and overshot. It needs to
approach the equilibrium point more slowly.

I think I need a rate of about 4.5 to 4.8 and ideally with a higher initial
tension but McMaster doesn't have one in that range that will fit in the
available space and I don't think you can increase the initial tension and
lower the rate at the same time.

Many thanks to Don for the formula. With it working things out on a spread
sheet greatly eased the design.

Resonant frequency is determined only by springrate, regardless of
initial tension. One possibility might be to use a torsion spring,
like a clock spring or the spring from a recoil starter on a small
engine. You can wind in a lot of initial tension without needing a
lot of space.

Another possibility might be to add a "negator" spring. Those are
dished flat strips that wind onto a roller, provide an essentially
constant pull rate regardless of extension. It could provide some of
the bias tension, enabling use of a soft spring to make up the
difference. The springrate of a negator is nearly zero; it's more
like a counterweight but without the mass. That and a soft helper
spring would provide very low resonance frequency.

AxMan Surplus sometimes has those. I'll look when I next visit.
They're about 2 bux if they have 'em.

It sounds like you about have it, though. A little dashpot damper
would cure your overshoot. Just a plastic or metal cylinder with a
leaky piston -- like a screendoor closer without the spring. You can
also make a torsional viscous damper with a disc in a cavity filled
with grease. Somebody, perhaps Airpot, used to make little glass
cylinder dampers with graphite pistons. Very smooth, no stiction,
last forever. Yeah, it *is* Airpot!
http://www.airpot.com/

What a viscous damper does is offer resistance that is proportional to
velocity. That quells overshoot. The reason your car doesn't
continue to bounce after hitting a bump, even though it is a spring
mass system with a resonant frequency, is viscous dampers AKA "shock
absorbers" though they are exactly the opposite. They transmit abrupt
shock but offer very little resistance to slow motion. In the UK
they are called "dampers".