The Isoconditioning Loci of A Class of Closed-Chain Manipulators

Damien Chablat (1) , Philippe Wenger (1) , Jorge Angeles (2)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 CIM - Centre for Intelligent Machines

The subject of this paper is a special class of closed-chain manipulators. First, we analyze a family of two-degree-of-freedom (dof) five-bar planar linkages. Two Jacobian matrices appear in the kinematic relations between the joint-rate and the Cartesian-velocity vectors, which are called the ``inverse kinematics" and the ``direct kinematics" matrices. It is shown that the loci of points of the workspace where the condition number of the direct-kinematics matrix remains constant, i.e., the isoconditioning loci, are the coupler points of the four-bar linkage obtained upon locking the middle joint of the linkage. Furthermore, if the line of centers of the two actuated revolutes is used as the axis of a third actuated revolute, then a three-dof hybrid manipulator is obtained. The isoconditioning loci of this manipulator are surfaces of revolution generated by the isoconditioning curves of the two-dof manipulator, whose axis of symmetry is that of the third actuated revolute.

Mots clés: Kinematics; Closed-Loop Manipulator; Hybrid manipulator; Isoconditioning surfaces; Singularity; Working Modes

Domaines: Robotique [cs.RO]

Damien Chablat, Philippe Wenger, Jorge Angeles. The Isoconditioning Loci of A Class of Closed-Chain Manipulators. May 1998, Bruxelle, Belgium. pp.1970-1976. ⟨hal-00162274⟩