the lever amplifies the input force. On the other hand, if the distance a from the fulcrum to the input force is less than the distance b from the fulcrum to the output force, then the lever reduces the input force. The use of velocity in the static analysis of a lever is an application of the principle of virtual work. Virtual work and the law of the lever A lever is modeled as a rigid bar connected to a ground frame by a hinged joint called a fulcrum. The lever is operated by applying an input force FA at a point A located by the coordinate vector rA on the bar. The lever then exerts an output force FB at the point B located by rB. The rotation of the lever about the fulcrum P is defined by the rotation angle θ in radians. Let the coordinate vector of the point P that defines the fulcrum be rP, and introduce the lengths which are the distances from the fulcrum to the input point A and to the output point B, respectively. Now introduce the unit vectors eA and eB from the fulcrum to the point A and B, so The velocity of the points A and B are obtained as where eA⊥ and eB⊥ are unit vectors perpendicular to eA and eB, respectively. The angle θ is the generalized coordinate that defines the configuration of the lever, and the generalized force associated with this coordinate is given by where FA and FB are components of the forces that are perpendicular to the radial segments PA and PB. The principle of virtual work states that at equilibrium the generalized force is zero, that is Thus, the ratio of the output force FB to the input force FA is obtained as which is the mechanical advantage of the lever. This equation shows that if the distance a from the fulcrum to the point A where the input force is applied is greater than the distance b from fulcrum to the point B where the output force is applied, then the lever amplifies the input force. If the opposite is true that the distance from the fulcrum to the input point A is less than from the fulcrum to the output point B, then the lever reduces the magnitude of the input force. See also Balance lever coupling References External links Lever