4 PROFESSOR FLEEMING JENKIN’S APPLICATION OF GRAPHIC METHODS 
between two elements. When the elements are rigid, joints can occur only 
where there is sliding or rolling contact between the elements. A surface of 
separation between a flexible tie and a rigid bar will also be treated as a joint, 
inasmuch as discontinuity of motion may occur at this surface similar to that 
which occurs at a surface of separation between rigid elements. A joint in the 
sense in which the word is here used is essentially a joint between two elements. 
There can be no common joint between three or more elements. In ordinary 
phraseology, we speak of three or more members of a frame as jointed at one 
place, and speak of the joint there as a single joint, meaning that they all abut 
against a single pin; but, in the present paper, each portion of the surface of 
such a pin as bears against a single element will be spoken of as a single joint. 
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 there are two joints, ab and ac, the 
pin being fixed on a. All actual joints are surfaces of greater or less extent. 
They may be divided into three classes :—I1st, Joints between a solid and hollow 
sphere ; this case includes that of a plane resting on a plane. 2d, A solid 
prismatic cylinder inside a hollow cylinder. When the cylinder has a circular 
cross section, relative turning and sliding are both possible. 3d, A solid screw 
inside a hollow screw. When the pitch is infinite we have one form of case 2d 
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 con- 
sidered 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 ; distinc- 
tions 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 properly designed. A short dis- 
tinction 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. 
