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reduced to one equation of polynomial form in only one joint
variable. For a specified hand position, one proceeds to
find the roots of this displacement polynomial to determine
the joint variable. The degree of this polynomial also
determines the number of possible ways the desired hand
position can be reached.
Generally, the methods employed in solving the inverse
kinematics in robotics are either analytical or numerical.
An analytical solution is one that produces a particular
mathematical equation or formula for each joint variable
(rotation or translation) in terms of known configuration
values (length of the link, twist angle and offset), whereas
a numerical solution generally pertains to the determination
of appropriate joint displacements as the result of an
iterative computational procedure. It is noted that the
equations associated with the inverse kinematic problem are
nonlinear and coupled, and this nonlinear dependence is
basically trigonometric.
As shown in Figs. 2.7 and 2.8, there are five possible
dyads with six degrees of freedom and twelve possible triads
with six degrees of freedom. In order to reduce the number
of links in forming the mechanism and avoid the number of
translational joints greater than three in a loop, we only
consider subchains (R-L)-R-S, (R-L)-P-S, (R-L)-S-R and (R-
L)-S-P as shown in Fig. 2.7 in the following sections.