The isoconditioning loci of a class of closed-chain manipulators

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 activated revolutes is used as the axis of a third actuated revolute, then a 3-DOF hybrid manipulator is obtained. The isoconditioning loci of this manipulator are surfaces of revolution generated by the isoconditioning curves of the 2-DOF manipulator, whose axis of symmetry is that of the third actuated revolute