Mechanics and Construction > Mechanics and Construction

Servos for Robot arm

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SeagullOne:
I'm constructing an arm for my robot and I want to make sure I got the idea for servo torque right. I've read some other posts about servo torque and its helped a little, but I still want to know a few things:

Suppose I have a servo that has specs of 47 ounces per inch. Suppose I mount this servo for the elbow joint. Now, if the forearm was 9 inches long, this servo would be able to...see that's where I get stuck in my calculations. I understand that as the arm gets longer, it takes more power for the servo to lift it. I want the servo to easily lift a 9 inch forearm made of sheet polyethylene plastic (two sheets cut to similar dimensions and bracketed together to be, say two inches wide). If I use a 47 oz per inch servo, and at a beam of 1 inch it lifts an object of 94 oz, than at 9 inches it would lift the arm if the arm weighed...uh, okay. What's the mathematical equation to calculate the torque of a servo that's measured by oz per inch? Is the torque just halved for each additional inch? Or is it 1/3rd for three inches? That's what I'd like to know, just so I make sure I buy a powerful enough servo.

Can someone please explain this for me, I'm really confused. Thanks.