Abstract
We present a method of determining a solution of the inverse kinematics problem based on $${\mathbb G}_{3,1}$$ for serial robot arm manipulators with an additional condition such as the prescribed gripper trajectory. The algorithm is based on geometrical understanding and $${\mathbb G}_{3,1}$$ calculations. We propose an algorithm for determining the actuating rotations and, furthermore, we discuss different approaches to their segmentation in order to realize the appropriate motion optimally.
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