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Mechanics, Artilleryand Robotics of the Russian Mathematician Paphnuty Chebyshev

The most important direction in any science the Russian mathematician Chebyshev considered practical application of discoveries, to which he devoted a lot of time.

Artillery Ballistics

What is the flying range of a missile? How to account for the velocity of the missile, its mass, attitude angle? Many mathematicians created calculation formulas for artillery, for example, Didion, but only Chebyshev took into account in his formula not just air resistance but different air resistance at different speeds of the missile (Chebyshev formula). It is important to note that the Chebyshev formula had a small number of parameters, that is, an ordinary Russian officer could use it in everyday practice.

Probability theory of Chebyshev allowed calculating how many missiles will reach the target, which ensured that real goals could bet set for artillery batteries and significant cost savings.

Chebyshev Mechanisms

Chebyshev from a young age loved to design mechanisms. If you add to this his beautiful mathematical mind – as a result you will get the creation of mechanism of the three points, which converts a circular motion of a wheel into a linear one.

Ladies bike (free-wheeling stroller) by Chebyshev

Ladies bike (free-wheeling stroller) by Chebyshev was set in motion using the arms of a lady sitting in it (1895, the Chicago exhibition, a drawing from the book by V. Prudnikov)

Moreover, the deviation in the transformation process was so small that the invention by Chebyshev allowed creating even fine feed mechanisms –watches. Furthermore, if the scheme could be widely used in steam engines of the time, it would have had exceptional success because it far exceeded empirical mechanisms of that time, including because of the simplicity and accuracy of its movement. Chebyshevs team engine was demonstrated at the World Exhibition in 1878 (USA).

Also, of course, very interesting is  his “plantigrade”, “plantigrade machine” or “step-walker” by Chebyshev, which began a new era of walking mechanisms (before the invention of Chebyshev walking mechanisms were not viable).

Plantigrade machine today can be assembled easily using Lego:

Altogether Chebyshev designed and built more than 40 different mechanisms.

Chebyshev Adding Machine

Before the era of computers (by the way, the mathematical apparatus developed by Chebyshev, is used in modern computer programs) all calculations were carried out on adding machines – mechanical adding machines. However, during Chebyshev era they had so many glaring weaknesses that in 1978 Chebyshev designed his own adding machine (it is exhibited in the Paris National Museum of Arts and Crafts). Originally the mechanism could add and subtract, but later Chebyshev added to it the functions of multiplication and division.

Chebyshev adding machine

Chebyshev adding machine (photo from the book by V. Prudnikov)

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