I think that building an as built joint would not have been an easy task and exact alignment would have also been tricky.
I recorded a screencast for you which hopefully will give you an absolute way of aligning. It is a bit complicated but it really does the job properly (I am no expert).
First thing I did was turn on capture design history (right click top component). I then made the carriage a rigid group and did the same for the rest of the model, extrusion, rails etc. This makes everything move together.
I clicked on an straight edge on the carriage and (shift) clicked on an similar straight edge on the extrusion to select both, then right clicked and selected align components. This was important to get things lined up from the start because the carriage was slightly out in rotation also. If you capture position at this point things will stay lined up and you can carry on moving the groups around.
I basically then activated the red rod component, created an axis through a cylinder/cone/tourous, on the red component, added a plane at angle to that axis, created a sketch on that plane and projected the intersection of the red component on that sketch. It is probably important to put that sketch inside that component so that the sketch moves around with the component.
I did the similar for the blue wheel; activated the component, placed a midplane between the outer edges, created a sketch on that plane and then projected the intersection of the blue component onto that sketch.
This gave me a centreline for the inside edge of the blue wheel that we want to line up exactly with the outer edge of the red cylinder component. I sketched a line (badly), pulled it longer and placed a tangent constraint between that line and the blue wheel intersect projection. I added a parallel constraint between that line and the projection from the red component.
Doing all this meant that I now had two parallel sketch lines that I could then (shift) click (to select both), right click and use align components. From here you can use an as built joint. Don't forget to ground a component in the 'red' group.
I really hope this helps you get a better understanding of aligning. It is really useful but needs a little input sometimes.