Now I want to project the newly made side surface (without the two original circles) into 2D so I can make it with sheet metal. By projecting the side surface to 2D I mean something similar as when you project the side surface of a cone into a part of a circle.
This is the long winded manual drafting way to roll out your oblique cone onto a plane.
- Draw the top view of your cone and align the circle center points horizontally.
- Divide the circle B into equal segments. The more segments you do the more accurate your results, but the more work you need to do. For this example I have used 12 segments.
- Project the line work down and draw the front view of the cone. Place line QR (circle A diameter) at the appropriate height of your cone from line CJ (Base and diameter of circle B)
- Find the point of intersection of lines CQ and JR. This point S is the apex of your oblique cone. Project it upward to the top view. Extend line BA to intersect with projection line. This is the location of point S in top view.
5a) The following step is for illustrative purposes only. At this point you can project the points from the circle B down and it will give you their position in the front view.
5b) If you then connect these point back to point S in the front view you wind up with a bunch of lines that look like nice slopes, but only two of them are true lengths. Only the edge lines CS and JS are true length. the remainder in between have a hidden depth component to them.
- In order to get the true length, we need to get the hypotenuse of the triangle formed by the line (shown in front view) for the height of the triangle and the length of the line shown in top view for the base of the triangle. For this exercise I drew a vertical reference line to the right of the front view. I then projected the base line over, and put the apex point S on the reference line. To maintain precision and reduce potential errors I opted to use the offset command instead of copy in order to get the horizontal distance from point S to all the points around the base circle. after initiating the offset command, pick the end point of the line you are working with in the top view to set the offset distance. Below you can see the first point I chose, point H.
- Once you get one point done, repeat the process for the remaining points on circle B. Technically you do not need to do points C and J as they are already true in the front view, but you can verify your process this way by comparing the length in the true length view and the front view.
- Connect the base points in the true length view to point S and delete the vertical construction lines. Each of the sloped lines in the true length view are the true 3D lengths of those lines.
- Create a circle centered on any point on circle B and give it a radius of the next adjacent point on the perimeter. In this case I chose point L for my center and selected point K when entering the radius in AutoCAD.
- Draw a circle centered on point S in the true length sketch. make the radius equal to a point on the horizontal axis. For the first point I chose because I wanted this line vertical for aesthetics. Copy this circle to an open part of your drawing where you want your pattern to be. In the pattern location draw a vertical line from the center to the bottom quadrant. This line is line SJ.
- Repeat step 10 basically, but this time pick the adjacent point on the true length sketch. I've started to colour code these to help avoid potential confusion. In this step I chose point H.
- Copy circle L (yellow) which was created earlier and place the copy's center point on point J in your pattern layout. Then in the pattern layout, draw a line from S to the intersection of the circle you copied for point H and the circle L.
- Repeat steps 11 and 12 but with the next adjacent point. In this case point G. And this time when circle L is copied, place its center point on point H in the pattern layout.
- Repeat this process until all true length lines have had their circles copied to the pattern and their intersection points are connected to point S.
- Now because I was lazy, I only did half the points because I knew the other half would be symmetrical about the line SJ. Erase the circles to clean up your pattern and then select the points and mirror them about line SJ. Note there are two line SC in the patter. This is the line, when folded, where the sheet metal will meet.
- I used the spline function. I started at point C and worked my way around counterclockwise to point J. At point J I used a horizontal end tangency. I then went back to the start of my spline at point C and made it have a tangency perpendicular to line SC.
NOTE: Radial lines removed for clarity. You will want to keep them for later steps
- Mirror the spline about line SJ.
- Clean up the line work and you are left with the FULL cone for the base outline.
- The top of the cone now needs to be removed from the pattern. Basically its the same steps as for the base circle but we will reuse some line work. For circle A use the points where the circle A intersects the lines from S to circle B.
- Create the true length sketch associated with point S and the circle A. Because the apex and circle A are so close, you will note the true length sketch is rather busy. The important thing to remember (I forgot the first time) is your base line is now line QR not line CJ
Here is a close up of Circle A true length sketch
- Instead of copying circle L over, you can use the line in the pattern from point S to circle B. Where these line intersect circle A's colour line place a point.
Here is a close up
- Connect the points like before with a spline. Remember to make sure the start/end points tangencies are perpendicular to the radial lines from point S.
- Mirror circle A's spline
- Remove all the radial lines except for both line SC. Trim line SC to the pattern outline for circle A and you should wind up with a flat pattern that looks like the following. Pattern may vary depending on height of cone, circle diameters and their offset from each other.