The operational workspace of parallel robots is often reduced by the presence of singularities. Recently, it has been proven that Type 2 singularities can be crossed in a way such that the dynamic model of the robot never degenerates. This discovery has been the starting point of several works on multi-model Computed Torque Control (CTC) that allow crossing of Type 2 singularities. In this paper, we propose a further improvement thanks to adaptive control. The major contribution of the paper is in the control law synthesis, which uses only linear methods, in contrast to usual approaches based on Lyapunov theory. This theoretical development will be validated both in simulation and experimentally.