A new global isotropy index (GII) is proposed to quantify the configuration independent isotropy of a robot’s Jacobian or mass matrix. The matrix is scaled to homogenize the physical units, to tailor it to the demands of the application and to choose optimum actuator parameters. A new discrete global optimization algorithm is also proposed to optimize the GII without placing any conditions on the objective function. The algorithm is used to establish design guidelines and a globally optimum architecture for a planar haptic interface from both a kinematic and dynamic perspective and to compare three robots for use as a 5-DOF haptic pen. The algorithm demonstrates consistent effort reductions of up to six orders of magnitude over global searching with low sensitivity to initial conditions.