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The Arbitrary Filleted Rect To Ellipse Transition is the flat pattern (development) of a transition piece that joins a rectangular opening with rounded (filleted) corners at the bottom to an elliptical opening at the top. The ellipse can be turned in its own plane, moved off the centre of the rectangle and tilted, so the part can connect a rectangular duct or hopper outlet to an oval or angled round outlet. Cut the pattern from thin plate and fold or roll it along the bend lines.

It appears in the shapes library under Thin Walled Developments. The shape is defined in 3D; the property page shows the 3D part, and the part that is cut is the 2D flat pattern built from it. To get a round top, set Ellipse Axis 1 and Ellipse Axis 2 to the same value. To get sharp base corners, set Fillet R to 0.

How the part is defined and developed

The base rectangle lies in the XY plane with one corner on the shape origin: Base Width along +X and Base Height along +Y. Each of its four corners is rounded with a radius of Fillet R.

The top ellipse is placed as follows:

•Its centre is Center H above the base, directly over the centre of the rectangle, then moved by Top Offset X and Top Offset Y.

•Ellipse Axis 1 is the full length of one axis of the ellipse and Ellipse Axis 2 the full length of the other. Ellipse Angle turns the ellipse in its own plane: at 0 Axis 1 lies along X and Axis 2 along Y.

•Top Angle Y tilts the plane of the ellipse away from horizontal by that angle. Top Angle Z sets the direction, seen from above, in which the tilt is applied. With Top Angle Y at 0 the ellipse is horizontal and Top Angle Z has no effect.

The surface is made of two kinds of face:

•Flat sides – one flat triangle on each of the –X, –Y and +Y sides of the rectangle, and two on the +X side, one for each half of it (the seam splits that side at its middle). Each triangle runs from the straight part of its side (between the fillets) up to one point on the ellipse. That point is the point of the ellipse straight out from its centre towards that side (+X, –Y, –X or +Y of the top plane). Ellipse Angle turns the ellipse but does not move these directions.

•Corner fans – at each corner, a quarter of the ellipse is joined to the corner fillet by a fan of narrow faces, each one treated as flat. Each corner takes a quarter of the development segments. With Fillet R above 0 each face runs from a short piece of the fillet arc to a short piece of the ellipse; with Fillet R at 0 the faces are triangles that all meet at the sharp corner.

The faces are unrolled one after another into a single flat outline. The pattern has one seam, the straight line where the folded part closes. The seam runs from the middle of the rectangle side at +X (one of the Base Height sides) up to the ellipse, so that flat side is split in two halves, one at each end of the pattern. In the flat pattern the seam is laid along the X axis with its ellipse end on the insert point (0, 0) and its base end along +X. The outline is one closed path made of four parts in this order: the seam at one end of the pattern, the developed top edge, the seam at the other end, and the developed base edge. The seam is one edge of the folded part, so it appears twice in the outline.

Bend lines

With Show Bends on, a bend line is added on every fold between two faces – where a flat side meets a corner fan, and between the faces of each corner fan. With the segment count used (see Dev. Segs below) that is that count plus 4 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 is shortened to two marks of that length, one at each end, instead of a full line across the plate; a line shorter than 2.1 times Bend Length is left at full length.

With Fillet R above 0 the bend lines of a corner fan are spread along the developed fillet on the base edge; with Fillet R at 0 they all meet at the corner point.

Properties

The property page lists the transition properties first, then the development properties, then the Transform group.

The dimensions drawn on the 3D view are Center H, Base Width, Base Height, Top Angle Z, Top Angle Y, Top Offset X, Top Offset Y, Ellipse Axis 1, Ellipse Axis 2, Ellipse Angle and Fillet R.

Notes and limits

•The pattern is built on the surface defined by the sizes entered; there is no plate thickness or neutral-axis allowance. Enter the sizes you want the pattern laid out on (for example mean sizes for a part made from thick plate).

•The shape does not check Fillet R against the base size. If Fillet R is more than half of Base Width or Base Height the fillets overlap and the pattern is not a valid part. The shape does not report this unless the build itself fails. Check the 3D view.

•The shape does not check the size, offset or tilt of the ellipse against the base either. Large offsets or tilts can give a very steep or folded-back part without any warning; check the 3D view before cutting.

•The top edge and the fillets of the pattern are made of straight segments, one per corner-fan face, so a low Dev. Segs value gives a visibly faceted top edge and fillets.

•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. Change the values until the warning goes away.

The Arbitrary Filleted Rect To Ellipse Transition also has the Transform properties (Base X, Base Y, Rotation, Scale, Mirroring X), listed after the Bend Length property. It has no Polar Array properties: the Polar Array group is added only to 2D shapes, and this is a 3D development shape.