Freudenstein and Maki [50] also show that a general
form of the degree-of-freedom equation for both planar and
spatial mechanisms can be written as
J
F = d(n j 1) + Efi Id (2.2)
i
where F = the effective degree of freedom of the assembly
or mechanism,
d = the degree of freedom of the space in which the
mechanism operates (for spatial motion d = 6, and
for planar motion and motion on a surface d = 3),
n = number of links,
j = number of joints,
fi = degree of freedom of i-th joint,
Id = idle or passive degrees of freedom.
The number of degrees of freedom that a manipulator
possesses is the number of independent position variables
which would have to be specified in order to locate all
parts of the mechanism. In the case of serial manipulators,
each joint displacement is usually defined with a single
variable; the number of joints equals the number of degrees
of freedom.
The number of degrees of freedom of multi-loop
manipulator linkages containing multi-degree-of-freedom
self-actuated joints can be determined simply by the
following equation: