6 Fundamental concepts
freedom by 6 – f. For a mechanism composed of n links that are connected
with a total of j joints, each of which has f i (i = 1, 2, . . ., j) degrees of
freedom, the mobility of the linkage, m, is
,
or
(2.1)
This is called the Grübler–Kutzbach mobility criterion (Hunt, 1978) or
Kutzbach criterion.
Figure 2.1(a) shows a spatial linkage composed of a chain of four links
and four joints, including one revolute joint (R), one spherical joint (S),
one cylindrical joint (C) and one prismatic joint (P), which is commonly
referred to as an RSCP linkage. According to Eq. (2.1), its mobility is
.
Table 2.2 Some of the higher pair joints
Joint names Number of
degrees of
freedom
Typical form
Comments
Cylindrical
roller
1
Roller rotates about the
instantaneous contact line and
does not slip on the surface.
Spatial point
contact
5
Body can rotate about any
axis through the contact point
and slide in any direction in
the tangent plane.
(a)
(b)
Figure 2.1 (a) an RSCP linkage and (b) an RSSP linkage.