CHAPTER 6
SOLVING FIVE-DOF MANIPULATORS
One-Dimensional Iterative Technique
With five degrees of freedom, Eq. (2.14) takes the form
A1 A2 A3 A4 A5 = P. (6.1)
and after multiplying both sides of this equation by A1- 1 we obtain
A2 A3 A4 A5 = Q (6.2)
with
Q = A1 P. (6.3)
When G1 is known, matrix Q is fully determined and can be viewed as a pose matrix for a 4-DOF arm whose structure is described by the left hand side of Eq. (6.2) which merely expresses a 4-DOF problem. In Chapter 5, we have seen that a 4-DOF problem can always be solved in closed-form, hence the remaining joint variables can be computed as shown earlier.
Since we only need to know one of the joint variables to solve for the whole solution set, the inverse kinematics problem of five-DOF manipulators reduces to finding the
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