I4 KINEMATICS. [260. 



in pairs. Thus a single rigid bar will form a lever only when 

 taken in connection with a support, or fulcrum ; a shaft to be 

 used in a machine must rest in bearings ; a screw must turn in 

 a nut. To take a more complex illustration, consider the 

 mechanism formed by the crank and connecting rod of a steam- 

 engine (Fig. 57). It may be regarded as composed of three 

 pairs, two so-called turning pairs at O and A, and a sliding pair 

 at B ; and these three pairs are connected by three rigid bars, 

 called links, OA, AB, OB, the last of which is fixed. 



Fig. 57. 



260. A sliding pair is formed by two bodies so connected that 

 one is constrained to have a motion of translation relatively to 

 the other. A pin moving in a groove or slot, a sleeve sliding 

 along a shaft, are familiar examples. 



A turning pair constrains one body to rotate about a fixed 

 axis in another, as in the case of a shaft turning in its bearings. 



A twisting pair makes one body have a screw motion about 

 an axis fixed in the other. 



These three pairs are the only so-called lower pairs. They 

 are characterized as such by the fact that their elements have 

 surface contact, and that, if either element be fixed, every point 

 of the other is constrained to move in a definite line. In other 

 words, the constraint effected by lower pairing is such as to 

 leave but one degree of freedom (see Art. 37) to either element 

 if the other be fixed. 



261. All other pairs are called higher pairs. The contact in 

 such pairs is usually line contact, and the two bodies have more 

 than one degree of freedom relatively to each other, usually two 

 degrees, so that if one element be fixed, any point of the other 

 is constrained to a surface. 



Higher pairs are of far less frequent occurrence in ordinary 



