Tere is nothing inherently wrong with using direct modeling, but it sounds like you are using it because you are missing some key concepts when modeling with the timeline.
Your assembly cannot work at the moment, because a base requirement in assembly is that at least one component has to be grounded. In this case the pinion for the small gear is, but one of the rials for the sliding table should also be grounded.
In general, however, attempting to simulate toothed gears by using a contact set is not going to work in practice. Contact sets at the moment work only in simple cases with simple geometry.
A gear geometry with 150 teeth is too complicated to evaluate for contact sets.
For this kind of Cam motion you might be able to use a motion link between the small gear and the slider joint and another motion link between the small and the big gear.