70 THE HUMAN MOTOR 



50. Machines. A machine is a system employed, either to 

 maintain in equilibrium resistant forces, or to overcome such 

 resistant forces, by other forces, known as moving forces, or 

 powers. 



In the static state, the power is equal to the resistance. In 

 the dynamic state power overcomes resistance. A machine is 

 said to be simple when it comprises a single element, with certain 

 connexions whilst it is called composite like most industrial 

 machines when it is composed of several simple machines work- 

 ing in conjunction. 



The parts of a machine generally have connexions, which limit 

 each part to only one possible movement, which may be denned 

 by a single equation. If, for example, it only turns round an 

 axis, or slides along the length of that axis, the angle of rotation 

 or the value of the translation defines the movement. One or 

 the other of these values is the " parameter " or constant that 

 it is both necessary and sufficient to know. 



Machines are therefore systems with complete connexions, 

 that is to say such, that all their points are determined by a single 

 parameter. 



51. Simple Machines. This name is given to the lever (fig. 84) ; 

 to the inclined plane (fig. 88) ; to the pulley (fig. 92) ; to the 

 hand winch (fig. 91) ; to the wedge (fig. 93), and the 



screw. The conditions of equilibrium of these 

 machines, under the forces which are applied to _... 

 them, external forces and forces of restraint ( 14), M~~ Of 



are given by an important theorem, that of Alembert K|0 ^ 

 relating to virtual work. If any point M of a system 

 is displaced to M 7 it is stated to produce work described as 

 " virtual " to distinguish it from the real work that the forces 

 could cause it to accomplish, for instance, in the direction MM* 

 (fig. 83). 



The theorem of Alembert says : 



' The necessary and sufficient condition for the equilibrium 

 of a system is that for every virtual displacement of the system 

 compatible with its connexions, the sum of the virtual work of 

 the given forces shall be "zero." But the work of the connexions, 

 in the absence of any friction, is zero. Thus a print moving on 

 a plane is subject to a reaction which, being perpendicular to the 

 displacement, produces no work ( 28) . Therefore, it only remains 

 to consider the work of the external forces which must also be 

 zero, according to the theorem of Alembert. In fact, in an 

 equilibria te system with connexions, it is known that all the forces 

 have two resultants ( 15) , of which the work must be zero, because 

 they are themselves both zero. As the virtual work of the one 

 that of the connexions is zero, that of the other the resultant 



