Isotropy in any RR planar dyad under active joint stiffness regulation

The present investigation is dedicated to the study of the static balance at the tip of a planar RR robot. For this case, a configuration can be interpreted, in the static sense, as an isotropic one when any force applied to the robot wrist yields a small displacement which is theoretically parallel to the applied force (no matter how the force is directed on the plane). This characteristic offers many advantages and it is considered as an optimal design goal. Unfortunately, the conditions to achieve such property in RR manipulators are very restrictive, and until now, only one solution is adopted, with a fixed lengths ratio. The present paper reveals how any RR planar robot can achieve isotropy at the tip by using a feedback action at the joints to gain arbitrary elastic coefficients. The new approach of design brings to less restrictive conditions than the previous ones.