I have been taught that higher pair joints (e.g. Gears, cams, rollers) deduct 1 d.o.f. Due to the fact that they still allow 2 motions
translation along the tangent surface
rotation around the instantaneous Contact point
However, from my reasonings, the higher pair does constrain 2 motions
as it is non-slipping (like gears and rollers) it gives a relationship between the angle and the location (such as x=theta * r)
as it rotates on a surface it gives a relationship between x and y that it household be on the surface (such as x = y+2)
