Kinematic Redundancy Analysis for (2n+1)R Circular Manipulators

摘要

The kinematic analysis of redundant serial manipulators with $2n+1$ revolute joints (integer $n ≥3$ ), which we call circular manipulators, is presented in this article. The structure of the kinematic chain of circular manipulators has special properties that can be seen in the Denavit–Hartenberg parameters: all orthogonal distances are zero, all even-numbered offsets are zeros, but odd-numbered offsets are not. Typical manipulators that fulfill these properties are redundant 7R serial chains ( $n=3$ ) that mimic the human arm, e.g., the lightweight robot arm KUKA LBR iiwa. This 7R circular manipulator has self-motion as rotation around an axis that goes through two fixed points for a fixed pose. First, radical reparametrization is presented based on the swivel angle of the closed-form inverse kinematics solution for the 7R circular manipulator. Second, for a six-dimensional task, the inverse kinematics solution for redundant serial manipulators with $2n+1$ revolute joints ( $n≥3$ ) is reparametrized by the swivel angle and other $2n-6$ rotation parameters. From a geometric point of view, for a circular manipulator with $2n+1$ revolute joints, one can have ${n(n-1)}/{2}$ choices of such circular rotations. Third, we conjecture numerical kinematic singularities for circular manipulators in a recursive formula, confirming $n=5,6,7$ .