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I struggling with assembling the scroll shape to the shaft shape. I get this strange message that "one body does not cut across the other one"
I attach error message and the model. Maybe somebody can help?
I'm not sure I understand what you need help with (and I'm not able to download your assembly).
If you need help with assembly constraints; try constraining to other things instead of the surfaces or faces. For example, constrain the center line of the shaft to the centerline of the scroll. Add some planes to both parts and constrain them Coincident to each other (or Offset). Use an Angle constraint to "clock" the scroll with the shaft.
I think the biggest problem is that the last ellipse is too low (meaning that if you do the multi-section, the profile will be interconnected). What I propose you, is to put the last ellipse a bit higher or do it in 2 loft.
Also, when using the multi-section, be careful that all the direction of the points are going in the same direction, otherwise you get a cusp (twisted).
Last thing, you do not need all these curves, just one is enough.
I made a video and corrected the file on this dropbox link: https://www.dropbox.com/sh/dnmnzoa2a0ox7ld/AAD3TDSDqduaG6JH5RgPiFdSa?dl=0