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Various performance indices are used for the design of serial manipulators.One method of optimization relies on the condition number of the Jacobianmatrix. The minimization of the condition number leads, under certainconditions, to isotropic configurations, for which the roundoff-erroramplification is lowest. In this paper, the isotropy conditions, introducedelsewhere, are the motivation behind the introduction of isotropic sets ofpoints. By connecting together these points, we define families of isotropicmanipulators. This paper is devoted to planar manipulators, the concepts beingcurrently extended to their spatial counterparts. Furthermore, onlymanipulators with revolute joints are considered here.

On Isotropic Sets of Points in the Plane. Application to the Design of Robot Archirectures