CHAPTER 10
CONCLUSION AND FUTURE WORK
This research has addressed the inverse kinematics problem of non-redundant all-revolute robot manipulators. We first showed how a convenient choice of manipulator frames and proper use of inner-product invariance of rotation transformations can be used to easily reduce the inverse kinematic problem to four simple equations independent of two of the joint variables (Doty, 1986). For four-axis robots, the reduced system of equations can always be solved in closed-form and at most two inverse kinematic solution sets can be found. We have determined that, in general, a 4-DOF arm will yield a unique solution and we identified ten special four-DOF structures for which two solutions can be found.
The same ten 4-DOF special structures, when part of a five-axis robot manipulator are sufficient to insure closedform solutions for the 5-DOF structure. Otherwise, we have shown that the inverse kinematic problem reduces to finding the zeros of a real-valued function of one joint variable. The most kinematically complex 5-DOF arm can therefore be solved by a fast one-dimensional iterative technique such as the regular Newton-Raphson or secant method.
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