English

A DH-parameter based condition for 3R orthogonal manipulators to have 4 distinct inverse kinematic solutions

Robotics 2007-09-05 v1

Abstract

Positioning 3R manipulators may have two or four inverse kinematic solutions (IKS). This paper derives a necessary and sufficient condition for 3R positioning manipulators with orthogonal joint axes to have four distinct IKS. We show that the transition between manipulators with 2 and 4 IKS is defined by the set of manipulators with a quadruple root of their inverse kinematics. The resulting condition is explicit and states that the last link length of the manipulator must be greater than a quantity that depends on three of its remaining DH-parameters. This result is of interest for the design of new manipulators.

Cite

@article{arxiv.0709.0409,
  title  = {A DH-parameter based condition for 3R orthogonal manipulators to have 4 distinct inverse kinematic solutions},
  author = {Philippe Wenger and Damien Chablat and Maher Baili},
  journal= {arXiv preprint arXiv:0709.0409},
  year   = {2007}
}
R2 v1 2026-06-21T09:13:40.459Z