APPLICATION OF GRAPHIC METHODS 275 



We shall always assume that a pin of this kind is fixed relatively 

 to one of the elements, so as to reduce the elements of the 

 machine to the smallest number. A joint will be designated by 

 two italic letters, being the names of the elements between which 

 it occurs. Thus in Fig. 1 (p. 279) there are two joints, ab and oc, 

 the pin being fixed on a. All actual joints are surfaces of greater 

 or less extent. They may be divided into three classes : 1st. 

 Joints between a solid and hollow sphere ; this case includes that 

 of a plane resting on a plane. 2nd. A solid prismatic cylinder 

 inside a hollow cylinder. AVhen the cylinder has a circular 

 cross section, relative turning and sliding are both possible. 3rd. 

 A solid screw inside a hollow screw. When the pitch is infi- 

 nite we have one form of case second in which only translation 

 is possible. When the pitch is zero we have a joint which only 

 allows of rotation and is the joint or bearing most commonly met 

 with in machinery. The third case is the most general, and may 

 be considered as including the two others as special forms. The 

 solid and hollow cylinder, which allow simple rotation of one 

 element relatively to another, will be called the pin and eye of a 

 joint. 



A dynamic joint occurs wherever pairing occurs, the word 

 ' pairing ' being used in the sense given it by Professor REULEAUX. 

 The kinematic pair as defined by him differs from the dynamic 

 joint in respect that complete pairing implies closure or complete 

 restraint except in one direction. Moreover, Professor REULEAUX 

 is able to classify pairs with reference to the mode of closure. 

 A dynamic joint implies no restraint other than that given by 

 the force exerted in the line of bearing pressure. All portions 

 of the pair might be cut away, except a surface of sufficient 

 strength round the bearing point ; distinctions between force 

 closure, pair closure, link closure, have no dynamic signification ; 

 and restraint, such as that afforded by collars on bearings, is of 

 no importance dynamically when the machine is properlv de- 

 signed. A short distinction may be made between a dynamic 

 joint and a kinematic pair, by saying that the latter might be 

 self-strained by imperfect fitting, while the former cannot be 

 self-strained. 



In certain cases the surface in contact may approximately 

 be represented by lines, as in what Professor REULEAUX calls 



T 2 



