The Shifted Cone is the flat pattern (development) of a truncated cone whose top circle is moved sideways from the bottom circle – an oblique or eccentric cone. The top and bottom circles stay parallel and horizontal; only the centre of the top circle is offset. Cut the pattern from thin plate and roll or brake it along the bend lines to make offset reducers, hoppers and transition pieces between two parallel round openings that are not on the same centre line.
It appears in the shapes library under Thin Walled Developments. The shape is defined in 3D; the property page shows the 3D cone, and the part that is cut is the 2D flat pattern built from it.
Shifted Cone in PrimeShape: the property page (left) and the shape as a wireframe with its dimensions (right).
How the cone is defined and developed
The bottom circle (Bottom D) is centred on the shape origin in the XY plane. The top circle (Top D) is parallel to it, Center H above it, with its centre moved by Top Offset X and Top Offset Y. The surface between the two circles is divided into Dev. Segs flat strips, each joining matching points on the top and bottom circles, and the strips are unrolled one after another into a single flat outline.
The pattern has one seam, the straight line where the rolled part closes. The seam joins a point on the bottom circle to the point at the same angle on the top circle, each angle measured from +X round that circle's own centre. That angle is Start Angle plus one segment (360° / Dev. Segs), not Start Angle itself: with the defaults (Start Angle 0, 24 segments) the seam is at 15°. In the flat pattern the first seam is laid along the X axis with its top-circle end on the insert point (0, 0) and its bottom-circle end along +X; the strips are unrolled from there. The outline is: one seam, the developed top edge, the other seam, and the developed bottom edge, as one closed path.
Moving the seam with Start Angle changes the shape of the flat pattern (the seam can be put on the shortest side, the longest side, or anywhere between) but not the finished part.
Bend lines
With Show Bends on, a bend line is added on every fold between two strips – Dev. Segs minus 1 lines. They are marking entities, not cuts, and alternate lines run in opposite directions so the marking tool zig-zags across the pattern instead of returning to the same side each time. If Bend Length is more than 0, each bend line longer than 2.1 x Bend Length is shortened to two marks of that length, one at each end, instead of a full line across the plate; shorter bend lines stay full length.
Properties
The property page lists the cone properties first, then the development properties, then the Transform group.
Property |
Description |
Default |
Top D |
Diameter of the top (smaller) circle. Length units, 0 or more; the property page rejects negative values. See Notes and limits. |
50 mm (2 in) |
Bottom D |
Diameter of the bottom (larger) circle, centred on the shape origin. Length units, 0 or more; the property page rejects negative values. If Bottom D is entered smaller than Top D the two values are swapped when the shape is built, so the larger circle is always at the bottom. |
100 mm (4 in) |
Center H |
Vertical height from the centre of the bottom circle to the centre of the top circle (the height of the part, not the slant length). Length units, 0 or more; the property page rejects negative values, so the top circle is always above the bottom circle. |
100 mm (4 in) |
Top Offset Y |
Distance the centre of the top circle is moved along Y from the centre of the bottom circle. Length units; negative values move it the other way. |
50 mm (2 in) |
Top Offset X |
Distance the centre of the top circle is moved along X from the centre of the bottom circle. Length units; negative values move it the other way. With both offsets 0 the part is a plain right (concentric) truncated cone. |
-50 mm (-2 in) |
Start Angle |
Rotates the seam round the two circles, measured from +X. The seam ends up one segment (360° / Dev. Segs) further round than the value entered. Angle units; any value, including negative, is accepted. |
0° |
Dev. Segs |
Number of flat strips the cone is divided into for the development. More segments give a smoother top and bottom edge and more bend lines. Whole number, minimum 3. |
24 |
Show Bends |
On: add the bend lines between strips to the pattern as marking. Off: the pattern is the outline only. |
On |
Bend Length (0 for Full) |
Length of the bend marks at each end of a bend line. 0 marks the full bend line from edge to edge. A bend line no longer than 2.1 x this value is marked full length. Length units, 0 or more. Used only when Show Bends is on. |
12.5 mm (0.5 in) |
The dimensions drawn on the 3D view are Center H, Bottom D, Top D, Top Offset X and Top Offset Y.
Notes and limits
•The pattern is built on the surface defined by the diameters entered; there is no plate thickness or neutral-axis allowance. Enter the diameters you want the pattern laid out on (for example the mean diameters for a part rolled from thick plate).
•The top and bottom edges of the pattern are made of straight segments, one per strip, so a low Dev. Segs value gives a visibly faceted edge.
•If the shape cannot be built from the values entered, the 3D view is cleared and the property page shows Warning: Cannot build shape from these parameters. Top D, Bottom D and Center H accept 0 but not negative values on the property page. A combination that fails inside the build is reported this way even though each value is inside its range. Change the values until the warning goes away.
•The shape has no aliases (no former names).
The Shifted Cone also has the Transform properties (Base X, Base Y, Rotation, Scale, Mirroring X), listed after its own properties. Like the other Thin Walled Developments it has no Polar Array properties.