n
Fc = E Fi 6(n 1) (2.3)
i=l
where Fc = the number of degrees of freedom of the multi-
loop mechanism,
Fi = the number of degrees of freedom of the i-th
subchain (leg),
n = the number of subchains (legs)
As shown in Fig. 2.10, there are three identical
subchains and each subchain has six degrees of freedom.
Therefore, the number of degrees of freedom of this type of
parallel manipulator can be calculated from Eq. (2.3) as
Fc = (6 + 6 + 6) 6(3 1) = 6
2.5 Inverse Kinematics
When the position of one link, generally the hand, is
specified and it is required to determine the position of
all other links, including the joint variables of actuated
joints which will move the hand to the specified position,
the method is called inverse kinematics. The determination
of the actuated joint variables for a specified position of
the hand is conducted by obtaining a set of equations
relating the actuated joint variables and constant
parameters of the manipulator linkages to the hand position
variables. In general, this set of equations is also