Abstract: Standard haptic rendering algorithms are not well suited for underactuated haptic devices. They compute forces oblivious of underactuation, and then they simply project the resulting forces to the actuated subspace. We propose instead a proxy-based haptic rendering method that computes displacements in the actuated subspace only, and then translates these displacements into force commands using regular controllers. Our method is well behaved in two important ways: it is locally passive w.r.t. the motion of the haptic device, and the displayed impedance can be easily controlled regardless of the mapping between device and virtual configuration spaces.