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

Philippe Wenger (1) , Damien Chablat (1) , Maher Baili (1)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

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.

Mots clés: Classification; Workspace; Singularity; Cusp; node; orthogonal manipulator; binary and quaternary manipulators.; binary and quaternary manipulators

Domaines: Robotique [cs.RO]

Philippe Wenger, Damien Chablat, Maher Baili. A DH-parameter based condition for 3R orthogonal manipulators to have 4 distinct inverse kinematic solutions. Journal of Mechanical Design, 2005, 127, pp.150-155. ⟨hal-00169594⟩