Our team is working on a 5 foot arm made out of PVC pipe in a scissor lift configuration. The motor needs to be mounted at the beginning of the 5 feet. We are trying to find out how much weight we need to place behind the arm to counter balance the 5 feet of PVC. The back end needs to be as short as possible. How do we find how much weight we need to mount to the back of the arm?
assuming uniform weight distribution (of the PVC arm), the moment will be: (weight of arm)*1/2(length of arm)
once you have that, divide it by the distance from the fulcrum to (roughly) the center of gravity of the counter weight. that will give you the amount of weight you need. this doesn’t factor in the material supporting the counterweight. if you’re concerned about it being slightly off balance because this, you can use the above equation to find the moment of the material supporting the counter balance, subtract it from the moment of the 5 ft PVC arm, and then divide by the distance from the fulcrum to the center of gravity of the counter weight.
final equation:
1/2(distance from fulcrum to end of arm)(weight of arm)=1/2(distance from fulcrum to end of arm supporting counterwieght)(weight of arm supporting counterweight)+(distance from fulcrum to CG of counterweight)*(weight of counterweight)
welcome to the wonderful world of statics.
If it’s in a scissor lift configuration, is there a load at the end of the Pipe? If so, that needs to be figured in as well by multipling the load times the distance from the fulcrum. Watch your units and make sure to gear down your motor so that it works at half it’s stall torque to maximize its efficiency (except for the FP, Drill, and CIM - check Joe Johnson’s / Paul Copioli’s motor presentations in the White Papers section).
I = 1/3 ML^2 if that helps.
Thanks. We will get to work on the equations now.
not really
and its not stats, its mechanics…
if you can send me a diagram of how it works, i#m afraid i dont know what you mean by scissor lift…
No, he really meant statics. Statics is the science of computing forces in things that are not accelerating. It is also useful if you are dealing with motion that is slow enough to be considered static. The essence of Statics is found in the basic equation: the sum of the forces = 0. When you design a bridge you use statics. When you design a slow moving arm, you use statics. When you design a fast moving arm (One where you get a significant amount of “whip”) you use Dynamics.
Stats is usually short for Statistics, the science of making sense of large amounts of individually useless data. 
BTW a scissors lift is a non-trivial statics problem.
Matt,
Am I understanding correctly that you’re planning on deploying your scissor lift other than vertically? In my experience, that’s a bad idea. You might be able to ameliorate problems if you have some (extreme) precision machining capabilities. But even if you do, you might want to reconsider your design.
Consider that each joint in your mechanism will have some slop in it. This causes sag when the lift is deployed non-vertically. And each stage in your scissor mechanism compounds the sag. If you have very many stages, you will have a LOT of sagging going on out at the end of your arm.