Earlier quoted context omitted.
From a related video: the reaction wheels spin up while keeping total angular momentum at zero, then apply a rapid (magnetic) brake to transfer the momentum to the body (from the wheels). I'm assuming if you do that precisely enough (and in three dimensions), you can generate linear movement. EDIT: I'm probably very wrong about the movement. EDIT: The video: https://youtu.be/n_6p-1J551Y
how does conservation of linear momentum apply? edit: this question was asked when the parent comment claimed that this machine could "generate linear momentum" from the wheels.
Conservation of momentum applies when there are "no external forces", which wouldn't be the case here when you apply the brake.
EDIT: Yeah, my apologies. I didn't mean to write "momentum".