Fundamental concepts 5
of all the links, also known as outputs, with respect to a fixed reference
frame, sometimes referred to as ground. The mechanism becomes a locked
chain, or a conventional structure, if no mobility remains.
In three dimensional space, the number of degrees of freedom of a rigid
link is six: three directional displacements and three directional rotations.
Thus n free links will have 6n degrees of freedom. By fixing one link as
ground, the remaining degrees of freedom are 6(n – 1). A joint with f
degrees of freedom connecting two links reduces the total degrees of
Table 2.1 The lower pair joints
Joint name
Letter
symbol
Number
of degrees
of freedom
Typical form
Sketch symbol
Revolute
joint (hinge,
turning pair
or pin)
R
1
Prismatic
joint (slider
or sliding
pair)
P
1
Screw joint
(helical joint
or helical
pair)
H
1
Cylindrical
joint
(cylindrical
pair)
C
2
Spherical
joint (ball
joint or
spherical
pair)
S
3
Planar joint
(planar pair)
P L
3