Haptic interfaces can recreate the experience of touch and are necessary to improve human-robot interactions. However, at present, haptic interfaces are either electromechanical devices eliciting very limited touch sensations or devices that may provide more comprehensive kinesthetic cues but at the cost of their large volume: there is a clear trade-off between the richness of feedback and the device size. The design and manufacturing challenges in creating complex touch sensations from compact platforms still need to be solved. To overcome the physical limitation of miniaturizing force feedback robots, we adapted origami design principles to achieve portability, accuracy and scalable manufacturing. The result is Foldaway, a foldable origami robot that can render three-degrees-of-freedom force feedback in a compact platform that can fit in a pocket. This robotic platform can track the movement of the user's fingers, apply a force of up to 2 newtons and render stiffness up to 1.2newtons per millimetre. We experimented with different human-machine interactions to demonstrate the broad applicability of Foldaway prototypes: a portable interface for the haptic exploration of an anatomy atlas; a handheld joystick for interacting with virtual objects; and a bimanual controller for intuitive and safe teleoperation of drones. Haptic interfaces are important for the development of immersive human-machine interactions. To create a compact design with rich touch-sensitive functions, a robotic device called Foldaway, which folds flat, has been designed that can render three-degrees-of-freedom force feedback.