Spring calculation?

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.

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Glenn Ashmore

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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

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Glenn Ashmore wrote:

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

-

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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. :-)

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Glenn Ashmore

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wrote:

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".

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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.

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Glenn Ashmore

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

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Glenn Ashmore

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wrote:

Yup.

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Glenn Ashmore wrote:

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

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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.

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Glenn Ashmore

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wrote:

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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