259-] PLANE MOTION. l ^ 



axes perpendicular to this plane is always a single angular veloc- 

 ity about an axis perpendicular to the plane or a single velocity 

 of translation parallel to the plane. 



6. APPLICATIONS. 



258. Kinematics of Machinery. A large majority of the cases 

 of motion that are of importance in mechanical engineering can 

 be reduced to plane motion. 



At first glance the application of theoretical kinematics to 

 machines might seem to lead to rather complicated problems 

 owing to the fact that a machine is never formed by a single 

 rigid body, but always consists of an assemblage of several 

 bodies some of which may even be not rigid (belting, springs, 

 water, steam). The problem is, however, very much simplified 

 by a characteristic of all machines, properly so called, that was 

 first pointed out and insisted upon by recent writers on applied 

 kinematics, in particular by Reuleaux.* This characteristic is 

 the constrainment of the motions of the parts of a machine. 



Thus Professor Kennedy defines a machine as "a combination 

 of resistant bodies whose relative motions are completely con- 

 strained, and by means of which the natural energies at our 

 disposal may be transformed into any special form of work." 



With the latter clause of this definition we are not at present 

 concerned ; it will be considered in kinetics. To explain the 

 former in detail would lead us too far into the domain of applied 

 mechanics. A brief indication of the fundamental ideas must 

 be sufficient. 



259. By considering machines of various types it appears 

 that the bodies, or elements, composing a machine always occur 



*F. REULEAUX, Theoretische Kinematik, Berlin, 1875; translated into English 

 and edited by ALEX. B. W. KENNEDY under the title Kinematics of machinery, 

 London, Macmillan, 1876. Compare also R. WILLIS, Principles of mechanism, 

 London, Longmans, 2d ed. 1870 (ist ed. 1841); F. GRASHOF, Theoretische Ma- 

 schinenlehre, Vol. II., Leipzig, Voss, 1883; L. BURMESTER, Lehrbitch der Kinematik, 

 Leipzig, Felix, 1888; ALEX. B. W. KENNEDY, Mechanics, of machinery, London, 

 Macmillan, 1886; J. H. COTTERILL, Applied mechanics, London, Macmillan, 1884. 



