Mathematically, you would use the principle of virtual work to calculate the force between them.
2.
It includes the principle of virtual work for rigid bodies as a special case where the internal virtual work is zero.
3.
The principle of virtual work states that in equilibrium the applied forces are equal and opposite to the reaction, or constraint forces.
4.
In 1717 Jean Bernoulli wrote to Pierre Varignon explaining the principle of virtual work, while in 1726 Daniel Bernoulli wrote of the " composition of forces ".
5.
The result is D'Alembert's form of the principle of virtual work, which is used to derive the equations of motion for a mechanical system of rigid bodies.
6.
The principle of virtual work then states : " External virtual work is equal to internal virtual work when equilibrated forces and stresses undergo unrelated but consistent displacements and strains ".
7.
The principle of virtual work yields a set of linear equations that relate the resultant force-torque six vector, called a wrench is known, then a direct calculation yields the joint torques.
8.
If we assume, that the gears are rigid and that there are no losses in the engagement of the gear teeth, then the principle of virtual work can be used to analyze the static equilibrium of the gear train.
9.
Meanwhile, work flourished at scientific academies on the Continent, led by such mathematicians as Bernoulli, Euler, Lagrange, Laplace, and Lagrange's equations of motion in " M�canique Analytique ", in which the whole of mechanics was organized around the principle of virtual work.
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