Spring calculation?

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Little side project.  I want to build a vertical stabilizer arm for my
Glidecam camcorder stabilizer.  The theory is similar to the Steadicam.
Picture a 10"x3" parallelogram pinned with bearings at the corners.  Long
dimension is horizontal.  One 3" side is fixed and the other floats and
holds the Glidecam.  A spring runs diagonally between the top end of the
fixed side to the bottom of the floating side.  The moving parts of the arm
weigh 2 lbs and when level the COG is 7" from the fixed end.  The Camcorder
and Glidecam weigh 4.2 lb and the COG is 12.75" from the fixed end.

How do I figure out which spring to use to just maintain the arm slightly
above level?  If the spring rate is to high the stabilization effect will be
diminished and if to low it won't recover fast enough.  The spring can't be
longer than 6" with no tension and will need about 3.5" of extension to
allow the arm to move from 30 degrees above to 30 degrees below level.
There will also be an adjustment screw to pretension the spring.

--
Glenn Ashmore

I'm building a 45' cutter in strip/composite. Watch my progress (or lack
We've slightly trimmed the long signature. Click to see the full one.
Re: Spring calculation?
Hi Glenn,

I'm sure I could figure out the answer to this problem if it wasn't 2
am! If no one has solved it for you by tomorrow I'll have a go (let me
know if I forget).

Best wishes,

Chris


Re: Spring calculation?
Glenn Ashmore wrote:
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It's not the answer to your question, but it might be interesting for you:

http://www.tiffen.com/dynamic%20primer.pdf

Please put a sketch in the dropbox after you make it. I would like to
add one to my (never completed) project list.

Kevin Gallimore

-

Re: Spring calculation?

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I have already found that and used it to rework the Glidecam.  The Glidecam
is basically the front end of  a Steadicam.  With a gimbal and
counterweights it uses balance spreading to give the camcorder some
stability.  I addeded an aluminum camera sled and threaded and knurled
counterweights to make it less bulky and aid in balance adjustment.   Works
great for roll and yaw but I want to mount it on the rail of a sailboat so I
need to deal with bouncing and vibration.  That is what the arm is for.
Just can't swing $20K for a mount for a $1K camcorder.  :-)

--
Glenn Ashmore

I'm building a 45' cutter in strip/composite. Watch my progress (or lack
We've slightly trimmed the long signature. Click to see the full one.
Re: Spring calculation?
wrote:

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I'll assume that the 6" rest length and 3.5" max extension are due to
unmentioned constraints because that's too short for the geometry. The
spring will need a "dead"  extension -- a link or piece of wire 2.29"
long.    

The load moment at level is 67.55 lbf*in.  With the 10" member
horizontal the diagonal  spring is at a 16.7 deg angle from
horizontal.   It will therefore need to exert 23.5 lbf to balance at
level.     Extension at horizontal is 2.15", so spring constant k  is
10.93 lbf/inch.  To balance "slightly above" level the spring constant
will need to be "slightly greater".

Re: Spring calculation?
Thanks!  That may give me enough to navigate McMaster's spring selection.

I actually have about 9" of room but I wanted the no load length 6" or less
to allow for extension and the adjustment mechanism.

--
Glenn Ashmore

I'm building a 45' cutter in strip/composite. Watch my progress (or lack
We've slightly trimmed the long signature. Click to see the full one.
Re: Spring calculation?

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Trying to set this up in a spreadsheet. Is the spring force the
moment/(Sin(A)*arm length)?

--
Glenn Ashmore

I'm building a 45' cutter in strip/composite. Watch my progress (or lack
We've slightly trimmed the long signature. Click to see the full one.
Re: Spring calculation?
wrote:

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Yup.  

Re: Spring calculation?
Glenn Ashmore wrote:
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There are a couple of other things to consider here, if you haven't
already.  One is damping.  With bearings at the corners, your mount will
be very free and in constant motion.  One good bump and your camera will
be bobbing like one of those silly car rear window statues.  You'll need
some form of (adjustable) friction.

Another is accelerations.  Given the size of your boat, they will be
pretty small, I'd guess.  So you won't have a problem with your mount
bottoming out.  But the mount might be too stiff for the small
accelerations that you will have.  You could calculate the deflections
that you will have, given the geometry and Don's spring constant, but I
don't know what numbers you'd use for the accelerations.

Hmm - it just occurred to me that the way to think about your mount is
as a high frequency filter.  Of the spectrum of frequencies that the
boat is moving at, you want to camera to only move at low frequencies.
The camera/mount frequency is mostly a matter of the spring constant:
high spring constant equals high frequency.  A lower spring constant
means more extension, means a longer horizontal arm.  The gotcha, of
course, is *how* low the frequency needs to be and how to calculate the
spring constant and geometry from that.  I'm sure that there's an ME
reading this that can help.

Don't you just hate it when the problem becomes *much* more complicated
that you thought it was.  Sorry about that.

Bob

Re: Spring calculation?
Don Foreman wrote:
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Oh, that sounds bad.  Imagine trying to watch a video that jiggles up
and down at several hertz!  Seasickness in your living room - talk about
capturing the experience on tape.  I'd think an order of magnitude lower
would be better ("sway" rather than "jiggle").  Of course, the "badness"
would depend upon the amplitude and the distance to the taped object.  A
1" amplitude while taping the horizon would be imperceptible, but if
taping a person 6' away, probably pretty bad.

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I don't think that you'd want to pass the high frequencies, e.g.,
vibration - that would give a fuzzy picture, wouldn't it?

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Oh oh - another project for Don  8-)

Bob

Re: Spring calculation? First Prototype results
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.

--
Glenn Ashmore

I'm building a 45' cutter in strip/composite. Watch my progress (or lack
We've slightly trimmed the long signature. Click to see the full one.
Re: Spring calculation? First Prototype results
wrote:

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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".  

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