Roberval Balance

The Roberval balance is a weighing scale presented to the French Academy of Sciences by the French mathematician Gilles Personne de Roberval in 1669.

In this scale, two identical horizontal beams are attached, one directly above the other, to a vertical column, which is attached to a stable base. On each side, both horizontal beams are attached to a vertical beam. The six attachment points are pivots. Two horizontal plates, suitable for placing objects to be weighed, are fixed to the top of the two vertical beams. An arrow on the lower horizontal beam (and perpendicular to it) and a mark on the vertical column may be added to aid in leveling the scale.

The object to be weighed is placed on one plate, and calibrated masses are added to and subtracted from the other plate until level is reached. The mass of the object is equal to the mass of the calibrated masses regardless of where on the plates items are placed. Since the vertical beams are always vertical, and the weighing platforms always horizontal, the potential energy lost by a weight as its platform goes down a certain distance will always be the same, so it makes no difference where the weight is placed. For maximum accuracy, Roberval balances require that their top be placed on the line between the left and right pivot so that tipping will not result in the net transfer of weight to either the left or right side of the scale: a fulcrum placed below the idea pivot point will tend to cause a net shift in the direction of any downward-moving vertical column (in a kind of positive feedback loop); likewise, a fulcrum placed above this point will tend to level out the arms of the balance rather than respond to small changes in weight (in a negative feedback loop).

The vertical column supporting a plate with an offset weight must be in axial compression and flexure. Here the axial compression is carried by the bearing at the top beam in most balance scales, the lower beam just being supported horizontally at midpoint by the body of the scales by a simple peg-in-slot arrangement, so it effectively hangs beneath the top beam and stops the platforms from rotating. The flexural force in the column (a.k.a. bending moment) is taken by a pair of equal and opposite forces in the horizontal beams. So if the offset weight is towards the outside of the platform, further from the centre of the scales, the top beam will be in axial tension and the bottom beam will be in axial compression. These tensions and compressions are carried by horizontal reactions from the central supports, the other side of the scales is not affected at all, nor is the balance of the scales.

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