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.

Roberval balance made by W & T Avery Ltd. in England

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 fulcrum 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).

Detail: note that the bottom horizontal beam is hidden under the protective cover

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.

Principles of operation

Certain presumptions are made in a theoretical Roberval balance. In order for such a balance to appear level in its natural state and be able to balance theoretical masses, the following must be true:

  • The weights of the arms themselves are unequal, or
  • The weights of the vertical columns and/ or pans is unequal
  • As a corollary, because no actual two masses can have exactly the same weight, a highly precise Roberval balance measuring two such imprecise masses should always tip either completely to the left or completely to the right— it does not measure degree of difference, it indicates the existence of difference. These effects must be distinguished from the feedback loops and the friction of the pivot points mentioned above, as those are undesirable effects caused by design weaknesses/ flaws.

Accuracy

The Roberval balance is arguably less accurate and more difficult to manufacture than a beam balance with suspended plates. The beam balance, however, has the significant disadvantage of requiring suspensory strings, chains, or rods. For over three hundred years the Roberval balance has instead been popular for applications requiring convenience and only moderate accuracy, notably in retail trade.

Manufacturers

Well known manufacturers of Roberval balances include W & T Avery Ltd. and George Salter & Co. Ltd. in the United Kingdom and Trayvou in France. Henry Troemner, who designed scales for the United States Department of Treasury, was the first American to use the design.[1]

Notes

  1. Child, Ernest. The Tools of the Chemist. New York: Reinhold Publishing Corporation (1940), p. 88. Cited in John Meeks Shannon and Geraldine Collins Shannon, "The Henry Troemner Company." Robert A. Paselk Scientific Instrument Museum at Humboldt State University.

Bibliography

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