The Rect To Circle Transition is the flat pattern (development) of a square-to-round transition piece: a rectangular opening at the bottom joined to a parallel, horizontal round opening at the top, with the top circle centred directly over the centre of the rectangle. Cut the pattern from thin plate and fold or roll it along the bend lines to make duct transitions, hoppers and chutes that join a rectangular opening to a round one.
It appears in the shapes library under Thin Walled Developments. The shape is defined in 3D; the 3D view shows the formed part, and the part that is cut is the 2D flat pattern built from it. For a top circle that is moved off the centre of the rectangle use the Shifted Rect To Circle Transition, and for one that is also tilted use the Arbitrary Rect To Circle Transition.
Rect To Circle Transition in PrimeShape: the property page (left) and the shape as a wireframe with its dimensions (right).
How the part is defined and developed
The rectangle lies in the XY plane with one corner on the shape origin: Base Width along +X and Base Height along +Y. The top circle (Top D) is horizontal, Center H above the base, and centred over the middle of the rectangle.
The surface is made of two kinds of face:
•Flat sides – one flat triangle on each side of the rectangle, from that side up to one point on the top circle. The +X side is the exception: the seam divides it into two triangles, one at each end of the pattern.
•Corner fans – at each corner of the rectangle, a quarter of the top circle is joined to the corner point by a fan of narrow triangles. Each corner takes a quarter of the development segments.
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 top circle, 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 top-circle end on the insert point (0, 0) and its base end along +X. The outline is: one seam, the developed top edge, the other seam, and the developed base edge (half side, three full sides, half side), as one closed path.
Bend lines
With Show Bends on, a bend line is added on every fold between two faces – the corner lines, where a flat side meets a corner fan, and the lines between the triangles of each corner fan. With N segments (N is the segment count used, see Dev. Segs below) there are N + 4 bend 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.
The bend lines of a corner fan all meet at the corner point on the base edge. The lines at the ends of the flat sides are sharp folds; the lines inside a fan are the gentle bends that form the rounded corner.
Properties
The property page lists the transition properties first, then the development properties, then the Transform group.
Property |
Description |
Default |
Top D |
Diameter of the round top opening. Length units, minimum 1. |
50 mm (2 in) |
Base Width |
Size of the rectangular base along X. Length units, minimum 1. |
100 mm (4 in) |
Base Height |
Size of the rectangular base along Y. Length units, minimum 1. The seam is on the middle of one of the sides of this length. |
150 mm (6 in) |
Center H |
Vertical height from the base to the centre of the top circle (the height of the part, not a slant length). Length units; the property page sets no minimum, so check the 3D view if you enter a very small or negative value. |
100 mm (4 in) |
Dev. Segs |
Number of segments the top circle is divided into for the development, shared equally between the four corner fans. The value used is rounded down to a multiple of 4, with a minimum of 4 (for example 26 is used as 24, and 3 as 4). More segments give a smoother top edge and more bend lines. Whole number, minimum 3. |
24 |
Show Bends |
On: add the bend lines between faces 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, 0 or more. Used only when Show Bends is on. |
12.5 mm (shown as about 0.49 in in inch units) |
The dimensions drawn on the 3D view are Center H, Base Width, Base Height and Top D.
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 top edge of the pattern is made of straight segments, one per corner-fan triangle, so a low Dev. Segs value gives a visibly faceted top 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. Change the values until the warning goes away.
•The shape has no aliases (no former names).
The Rect To Circle Transition 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.