The purpose of the driving mechanism is to increment the numeral wheels of the accumulator with a number of teeth equal to the the input device figure.
Thirty years after Blaise Pascal, Leibniz (1646-1716) conceives a calculator (the stepped reckoner) in which the the calculation and the input of the numbers are two separate things. Such a feature allows (on the contrary of the Pascal calculator) to easily perform the four arithmetic operations. A great number of calculators was based on the Leibniz system as far as 1970. However the realization of the calculator is difficult at this time and the two constructed machines were inoperative. Nevertheless this is the first calculator to materialize the definition of a product of two numbers. The multiplicand is registered once for all at the beginning of the operation and can be added to himself as many time as desired. The mechanism is composed for each order of decimal units of a 9 teeth of increasing lengths disposed on the circumference of a cylinder. The cylinder can slide along its axis, this allows the teeth to mesh with one of the gear wheels of the accumulator and, according to its position, make turn this gear from zero to nine teeth for each rotation of the cylinder.
Leibniz is regarded as the true precursor of mechanical calculation. Animation shows the operation of the Leibniz cylinder in a "modern" calculator (in fact the cylinders don't slide on their axis of rotation, but the gear wheels can be moved along the cylinder).
If QuickTime or RealPlayer is installed on your computer, a click on the photography will show you a Leibniz cylinder at work.
To download QuickTime or RealPlayer, click on the appropriate logo ( For RealPlayer, choose the free download button ) !
In 1878, the swedish Wilgodt Odhner (1845-1905) introduces a special gear wheel mechanism. The teeth of the gear are retractable allowing the wheel to indent from 0 to 9 teeth. The system is patented in Russia then in Germany in 1891. A similar wheel had been imagined by the Venitien Poleni in 1709 for a machine which never worked. The systems with Odhner pinwheels are implemented in a great number of calculators (with levers or keyboard input devices). American Frank S. Baldwin (1838-1925) had conceived in 1875 a machine whith a similar driving mechanism (in the United States this system is called "trainer of Baldwin"). Click on the figure to see an animation of the pinwheel.
In 1911, Baldwin which worked for the Monrœ company reduces the size of the Leibniz cylinder while retaining the principle of operation. The Leibniz cylinder is replaced by 2 cogged wheels, one provided with 4 cogs of increasing length, the second with 5 cogs of same length. The two disks are pushed apart by a spring. The input of a number between 1 and 4 operates only the first disk which acts with the cog-wheel of the accumulator as the Leibniz cylinder did. For the figures from 5 to 9, the second disk becomes active. In a Leibniz calculator, the cylinders axes are parallel to each other and perpendicular to driving axe compeling to make use of beveled gears. In a Monrœ type calculator, all the cogged wheels are on the same axis and have a smaller size than the cylinders of Leibniz. To see the cogged disks in action, click on the picture.
A wheel toothed on the totality of its circumference can rotate of an angle proportional to the figure entered on the input device for each cycle of calculation. This system was developed by Christel Hamann (1870-1948) in 1925 and is implemented in calculators which bear its name and manufactured by Deutche Telefon Werke. This principle had been imagined by Leupold in 1727. For more details and animation, click on the picture.
Another system allowing a motion proportional to the figure registered in the input device is implemented in the mercedes calculators. It consists of 9 parallel toothed racks attached to a same lever H perpendicular to their direction.They are articulated on the lever at such distances of the rotation axe that, when the first one advances of one tooth, the second advances of 2, and so on. A figure entered to the input device engages a gear with the corresponding toothed rack (figure 5 positions a gear on the toothed rack n° 5).When an addition is carried out, the lever H swivels around H ', and rocks in K to return to its starting position. During the return path, the contact between the mechanism and the accumulator dials ceases. This principle had been used by Leupold in 1727, Grant en1871, Selling in 1886 and Christel Hamann in 1910 for the calculators Mercedes Euklid. If you want to see the animation (252 ko), click on the picture.
The following movie shows how the toothed racks work.
Toothed racks of the Mercedes EUKLID 29 (120 ko)
The two following movies are examples of disengaging mechanisms of the numeral wheels of the accumulator when yhe toothed racks go back.
Mercedes EUKLID 29 (330 ko) Mercedes EUKLID 8 (120 ko)
Another type of driving mechanism gives increasing angular velocities to the numeral wheels of the accumulator. The wheel associated with a figure equal to 9 revolves 9 times more quickly than a wheel associated with figure 1. This technic was used in some Marchant calculators.
