The skill of pivoting an object with a robotic system is challenging for the external forces that act on the system, mainly given by contact interaction. The complexity increases when the same skills are required to generalize across different objects. This paper proposes a framework for learning robust and generalizable pivoting skills, which consists of three steps. First, we learn a pivoting policy on an ``unitary'' object using Reinforcement Learning (RL). Then, we obtain the object's feature space by supervised learning to encode the kinematic properties of arbitrary objects. Finally, to adapt the unitary policy to multiple objects, we learn data-driven projections based on the object features to adjust the state and action space of the new pivoting task. The proposed approach is entirely trained in simulation. It requires only one depth image of the object and can zero-shot transfer to real-world objects. We demonstrate robustness to sim-to-real transfer and generalization to multiple objects.