The Arbitrary Cylinder is the flat pattern (development) of a round cylinder whose two ends are cut by planes. Each end plane can be tilted away from square, in any direction round the axis, so the two ends do not have to be parallel. Cut the pattern from thin plate and roll it along the bend lines to make a tube or duct section with angled ends. Unlike the Cylinder and Truncated Cylinder shapes, both ends can be tilted, and in different directions.
It appears in the shapes library under Thin Walled Developments. The shape is defined in 3D: the 3D view shows the cylinder, and the part that is cut is the 2D flat pattern developed from it.
Arbitrary Cylinder in PrimeShape: the property page (left) and the shape as a wireframe with its dimensions (right).
Insert point and how the cylinder is defined
The insert point is the origin of the shape. The cylinder axis is the Z axis through the origin, and D is its diameter. Each end is cut by a plane:
•The bottom plane passes through the origin, where it crosses the axis.
•The top plane crosses the axis at Height above the origin.
Each plane starts square to the axis (horizontal) and is then tilted. Angle Y is the tilt of the plane away from square. Angle Z is the direction of that tilt, measured round the axis from the X axis. With Angle Y at 0 the end is square and its Angle Z has no effect. Because Height is measured along the axis between the two crossing points, the long and short sides of the finished part are longer and shorter than Height by an amount that depends on D and the tilts.
The surface between the two end cuts is divided into Dev. Segs flat strips round the circumference, 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 lies on the cylinder at Start Angle, measured round the axis from the X axis. In the flat pattern the seam starts with its top end on the insert point (0, 0) and its bottom end along the +X axis, and the strips are unrolled from there. The outline is the seam, the developed top edge, the other seam and the developed bottom edge, as one closed path.
Changing Start Angle moves the seam round the cylinder. This changes where the seam falls in the flat pattern (on the shortest side, on the longest side, or between) but not the finished part.
Bend lines
With Show Bends on, a bend line is added on each fold between two strips, which gives Dev. Segs minus 1 bend lines. Bend lines are marking entities, not cuts. Alternate bend 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 is reduced to two marks of that length, one at each end. A bend line no longer than 2.1 times Bend Length is left as a full line.
Properties
The property page lists the cylinder properties first, then the development properties (Dev. Segs, Show Bends and Bend Length), then the Transform group.
Property |
Description |
Default |
D |
Diameter of the cylinder. Length units. Minimum 1 mm (0.04 in); a smaller value is refused with Value is out of range. |
100 mm (4 in) |
Height |
Distance along the cylinder axis from the point where the bottom plane crosses the axis (the origin) to the point where the top plane crosses it. Length units. Minimum 0; a negative value is refused with Value is out of range. |
50 mm (2 in) |
Top Angle Z |
Direction of the tilt of the top end, measured round the axis from the X axis. No effect while Top Angle Y is 0. Angle units. |
30° |
Top Angle Y |
Tilt of the top end from square to the axis. 0 gives a square end; a negative value tilts the plane the other way. Angle units. The property page sets no range. |
0° |
Bot Angle Z |
Direction of the tilt of the bottom end, measured round the axis from the X axis. No effect while Bot Angle Y is 0. Angle units. |
0° |
Bot Angle Y |
Tilt of the bottom end from square to the axis. 0 gives a square end; a negative value tilts the plane the other way. Angle units. The property page sets no range. |
-30° |
Start Angle |
Position of the seam round the cylinder axis, measured from the X axis. Angle units. Any value is accepted. |
0° |
Dev. Segs |
Number of flat strips the cylinder 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. Length units. Minimum 0. Used only when Show Bends is on. |
12.5 mm (0.5 in) |
The dimensions drawn on the 3D view are Height, D, Top Angle Z, Top Angle Y, Bot Angle Z and Bot Angle Y.
Notes and limits
•The pattern is built on the surface of diameter D. There is no plate thickness or neutral-axis allowance. Enter the diameter the pattern should be laid out on, for example the mean diameter 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.
•An Angle Y of 90° (or -90°) makes that end plane parallel to the cylinder axis, so it does not form an end of the part. The shape does not check for this, so keep the Angle Y values short of ±90°.
•The shape does not check that the two end planes stay apart inside the cylinder. If Height is small for the diameter and the tilts entered, the planes cross within the part and the pattern is not meaningful. Check the 3D view before cutting.
•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. Do not cut the pattern until the warning goes away.
•The shape has no aliases (no former names).
The Arbitrary Cylinder also has the Transform properties (Base X, Base Y, Rotation, Scale, Mirroring X), listed after its own properties. Thin Walled Developments are 3D shapes and have no Polar Array properties.