Page 111 - Tribology in Machine Design

4 Friction, lubrication and wear in
lower kinematic pairs

4.1. Introduction Every machine consists of a system of pieces or lines connected together in
such a manner that, if one is made to move, they all receive a motion, the
relation of which to that of the first motion, depends upon the nature of the
connections. The geometric forms of the elements are directly related to the
nature of the motion between them. This may be either:
(i) sliding of the moving element upon the surface of the fixed element in
directions tangential to the points of restraint;
(ii) rolling of the moving element upon the surface of the fixed element; or
(iii) a combination of both sliding and rolling.
If the two profiles have identical geometric forms, so that one element
encloses the other completely, they are referred to as a closed or lower pair.
It follows directly that the elements are then in contact over their surfaces,
and that motion will result in sliding, which may be either in curved or
rectilinear paths. This sliding may be due to either turning or translation of
the moving element, so that the lower pairs may be subdivided to give three
kinds of constrained motion:
(a) a turning pair in which the profiles are circular, so that the surfaces of
the elements form solids of revolution;
(b) a translating pair represented by two prisms having such profiles as to
prevent any turning about their axes;
(c) a twisting pair represented by a simple screw and nut. In this case the
sliding of the screw thread, or moving element, follows the helical path
of the thread in the fixed element or nut.
All three types of constrained motion in the lower pairs might be regarded
as particular modifications of the screw; thus, if the pitch of the thread is
reduced indefinitely so that it ultimately disappears, the motion becomes
pure turning. Alternatively, if the pitch is increased indefinitely so that the
threads ultimately become parallel to the axis, the motion becomes a pure
translation. In all cases the relative motion between the surfaces of the
elements is by sliding only.
It is known that if the normals to three points of restraint of any plane
figure have a common point of intersection, motion is reduced to turning
about that point. For a simple turning pair in which the profile is circular,
the common point of intersection is fixed relatively to either element, and
continuous turning is possible.