A novel methodology is presented for a practical problem of balancing a round object about its contact point posing pure rolling constraint at the tip of a redundant manipulator. Two-layer controller, the objective of the first of which is to balance the object as long as the manipulator stays in a singularity-free predefined task-space, is designed. We call that a "static balance." At the second layer, the contact point of the balanced object is aimed at repositioning at a close neighborhood of an, also predefined, conceptual center or task space where the dynamic manipulability is the greatest. We call this transition a "dynamic balance." In order to achieve the dynamic balance, one needs to disturb the static balance in a controlled manner. We, then, introduce the concept of an "equilibria cone" formed by the collection of static and dynamic equilibria.