## Elegant Solutions – Why does this balance?

From the Eng-Tips forum

Why does the mechanism shown below balance when the load applied to each platform is the same, even when the lever arms from the pivot are different?

Equal load; unequal lever arm

It “looks wrong” but an analysis shows that the applied moment is balanced by the moment in the support rod.  One of the Eng-tips respondants came up with an even simpler analysis however, showing without any calculation at all that the mechanism will be in equilibrium for equal loads with any position of the loads:

 handleman (Automotive) 7 Dec 09 14:06

### “Use energy method.  By inspection (due to parallelogram) the platforms stay flat during motion.  Therefore, vertical displacement at any point on either platform is equal.  Same vertical displacement, same potential energy.”

Update – an interesting link from the Eng-Tips thread: The Roberval Balance

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### 1 Response to Elegant Solutions – Why does this balance?

1. Leon says:

The cans sit on the load bar, which is supported by the uprights, and the uprights are pinned into the beams (which are horizontal).

The mechanism is symmetric so we can ignore its own weight and torque.

The torque from each load bar that is converted to tension and pressure in the beams puts these tension/pressure directly though the axis of rotation of the beam, so counts as zero torque.

The turning of the uprights does not create any vertical forces on the beams.

The only vertical force is the can, balancing vertical forces, this must be the only vertical force the beam is holding up (additional to the mechanisms own mass)

So the weight of the cans on each side is delivered to the center beams (beams = horizontal) at the pin and since the mechanism is symmetrical the loads create equal and opposite torque on the beams.

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