Abstract: Equilibria in mechanics can be treated very easily by using simple energy considerations, which can be reduced in many cases to pure geometry, especially in the homogeneous field of gravity. Energy has to be known only as something needed for lifting any object. Nothing has to be known about forces or torques. A very astonishing machine is Roberval's balance, but by simple changes it shows any kinds of equilibria and any kinds of balances. Also hydrostatic experiments can be explained easily as examples of stable equilibria, i.e. as cases, where no water can go to a lower position. Even Heron's fountain can be explained in this way. Models of the machines can be made with construction kits like Maerklin (iron) or fischertechnik, but also by cardboard, where the parts are connected with patent-fasteners. The possible movements in these models can be measured by a ruler and compared with each other. Forces are to behave inversely to the geometric displacements in any equilibrium. This holds for nutcrackers as for any balance type and for special pincers with a gear which is increasing during closing them.

This picture shows a very strange balance, called after Roberval (1602-1675). If two equal weights are hanging on both sides, we observe an equilibrium (more exactly an indifferent one). It doesn't matter when one of the weight is shifted along the horizontal arm.This is quite different from the familiar balance with a singe axis, where such a shift would change the equilibrium totally. This "normal" balance is explained usually by the concept of torque as a product of the weight and its distance from the axis (more exactly as a vectorial or cross product). Some years ago a colleage told me that believed at first of a joke when he got a paper about the Roberval balance to be published in a journal for physics education. Only after doing the experiment he became convinced of the reality of the astonishing behaviour.An explanation of the Roberval balance in terms of torque equilibria is quite complex, because there are six axes. Poinsot introduced in the 19th century additional virtual forces and torques to reduce it in a certain manner to a normal balance. Such sophisticated explanations are not leading to deeper insights or the more general rules.A certain poet (I think he was Strindberg, but I am not sure) had a negative opinion about physicists: They are explaining not-understandable phenoma by not-understandable natural laws.He was right, but he neglected two central points: Physicists are explaining millions of not-understandable phenomena by only very few not-understandable natural laws, and they are able to predict them by these laws.The Roberval balance is more than an astonishing toy which may be explained a posteriori by a special sophisticated theory, but it should be the key pattern to find a quite general concept to predict a lot of mechanic phenomena and machines, even the most important of them.

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