The Cellulo robots are small tangible robots that are designed to represent virtual interactive point-like objects that reside on a plane within carefully designed learning activities. In the context of these activities, our robots not only display autonomous motion and act as tangible interfaces, but are also usable as haptic devices in order to exploit, for instance, kinesthetic learning. In this article, we present the design and analysis of the haptic interaction module of the Cellulo robots. We first detail our hardware and controller design that is low-cost and versatile. Then, we describe the task-based experimental procedure to evaluate the robot's haptic abilities. We show that our robot is usable in most of the tested tasks and extract perceptive and manipulative guidelines for the design of haptic elements to be integrated in future learning activities. We conclude with limitations of the system and future work.