Robotic isotropy and optimal robot design of planar manipulators

Robot operation near isotropic configurations, where the condition number of its Jacobian matrix reaches unity, is desirable from several points of view. However, determination of all such configurations, given an arbitrary robot geometry is rather a complex problem. In this paper all the isotropic configurations of planar manipulators with 2 and 3 degrees of freedom are determined. The solutions are obtained in the form of a 4th order polynomial for the 3-DOF robot, yielding maximally 8 sets of solutions. The condition numbers are obtained as explicit analytical functions of joint coordinates and link lengths´ ratios. The optimal lengths of the links are determined by minimizing the criterion that the condition number increases most slowly with joint angles in the vicinity of isotropic configurations.