@sakura13 I think I have a good approach for rigging the chain motion. Please see the attached file.
My strategy was to control the the shape of a spline via the position of 6 points. Position Scripts are used to position these points. The mechanism is considered to have 3 rollers (A,B, and C) which the chain must pass over. The 6 points indicated in the image below.
Point 1 - is part of the Scoop object and is linked to it.
Point 2 - a point on the A roller that is at the point of tangency of a line tangent to roller A and roller B.
Point 3 - midpoint between points 2 and 3. This point is helpful for ensuring a straight spline segment between point 2 and 4 but does cause some problems when the scoop rolls far back.
Point 4 - tangent of line reference by point 2. Technically there should be 2 tangent point for roller b. This on and one for the line tangent to rollers B and C. The difference is so small that I ignored this detail.
Point 5 - a point to control the shape of the spline as it passes over roller C. Again, 2 tangent points could be used here but one provides satisfactory results if the spline's vertex is "smoothed".
Point 6 - a point to control the path of the spline after passing over roller C. Technically the chain should wrap around roller C but this is very difficult to model and may not be visible in a final animation. I decided to just have the chain disappear into the floor of the cart and hope no one would notice!
The position and rotation of the scoop is controlled by the position of Dummy001 via a Wire Parameter.
The geometry of the cart and scoop do not seem to be correct as the scoop is beyond the cart body when the bottom of the scoop is parallel to the ground. There also seems to be some interference between the scoop and the internal mechanism (blue). The model should be corrected and then the rigging adjusted.
The calculation of the tangent points 2 and 4 was a bit challenging. I prefer to work in World coordinates so local positions are converted to world then the intersection point of a line passing through the center of rollers A and B with a line tangent to the two circles is determined. From there, with a little algebra and vector math, the tangent point is determined.
Here's a Screencast of the animated results.
https://knowledge.autodesk.com/community/screencast/7f8f9e9e-969e-4f38-b902-9a8e023b1c21
lee.minardi