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In the analysis of six-degree-of-freedom manipulators, we identified three major classes of 6-DOF arms according to their kinematic complexity. First, the class of closed-form arms in which we find all 6-DOF open kinematic chains with three adjacent joint axes intersecting at a common point (Pieper, 1968) or with three parallel adjacent joint axes. We discovered that the 6-DOF arms with three pairs of two parallel axes and those with two intersecting axes following or preceding two pairs of parallel joint axes had closedform solutions as well.
The next class contains all 6-DOF manipulators that do not allow closed-form solutions but are such that knowledge of one joint variable is sufficient to obtain a complete solution set in closed-form. We determined that all 6-DOF arms that include one of the ten special 4-DOF structures discussed earlier were in this second class. The inverse kinematics problem for these manipulators reduces to finding the zeros of a real valued-function. A one-dimensional
Newton-Raphson or other iterative method can be used to solve the inverse kinematics problem for these robots.
The third class of six-degree-of-freedom robots contains all the manipulators that do not fall into the two preceding classes. For the most kinematically complex sixDOF robot manipulators, the inverse kinematics problem
reduces to solving a nonlinear system of only two equations in only two of the joint variables. Therefore, the robots
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