The Filleted Rect To Filleted Rect Transition is the flat pattern (development) of a transition piece between two rectangular openings with rounded corners: a filleted rectangle at the bottom joined to a smaller or larger, parallel, horizontal filleted rectangle at the top, with the top centred directly over the centre of the base. Cut the pattern from thin plate and fold or roll it along the bend lines to make duct reducers, hoppers and chutes between two rounded-rectangle (or obround) openings. With both fillet radii at 0 it is a plain rectangle-to-rectangle transition.
It appears in the shapes library under Thin Walled Developments. The shape is defined in 3D; the 3D view shows the part, and the part that is cut is the 2D flat pattern built from it. For a top that is moved off the centre of the base use the Shifted Filleted Rect To Filleted Rect Transition, and for one that is also tilted use the Arbitrary Filleted Rect To Filleted Rect Transition.
Filleted Rect To Filleted Rect 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 base rectangle lies in the XY plane with one corner on the shape origin: Base Width along +X and Base Height along +Y, with its corners rounded to Bot. Fillet R. The top rectangle (Top Width along X, Top Height along Y, corners rounded to Top Fillet R) is horizontal, Center H above the base, and its centre is directly over the centre of the base.
The surface is made of two kinds of face:
•Flat sides – one flat face on each side, joining the straight part of a base side to the straight part of the matching top side. A side whose straight part is zero length at both the base and the top (the fillets use the whole side) has no flat face.
•Corner segments – at each corner, the base fillet is joined to the top fillet by a row of narrow faces. Each corner takes a quarter of the development segments, and each fillet is divided into that many equal parts. If one of the two fillet radii is 0, the segments of that end all meet at the sharp corner point, making a fan. If both fillet radii are 0 there are no corner segments and the corners are single sharp folds.
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 base side at +X (one of the Base Height sides) up to the middle of the top side at +X, 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 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, as one closed path.
Bend lines
With Show Bends on, a bend line is added on every fold between two faces – where a flat side meets a corner, and between the faces of each corner. They are marking entities, not cuts. Alternate lines are reversed in direction, so consecutive bend lines run in opposite directions. 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 folds between the faces inside a rounded corner form its curve. Where one fillet radius is 0, the faces of that end of the corner meet at the sharp corner point, so the folds there fan out from that point.
Properties
The property page lists the transition properties first, then the development properties, then the Transform group.
Property |
Description |
Default |
Top Width |
Size of the top rectangle along X. Length units, minimum 1. |
50 mm (2 in) |
Top Height |
Size of the top rectangle along Y. Length units, minimum 1. |
100 mm (4 in) |
Top Fillet R |
Corner radius of the top rectangle. 0 gives sharp corners. Length units. The shape rejects a value above half the smaller of Top Width and Top Height. The property page sets no minimum, and negative values are not checked. |
25 mm (1 in) |
Center H |
Vertical height from the base to the top rectangle (the height of the part, not a slant length). Length units. The property page sets no minimum and the shape does not check the value against any limit. |
175 mm (7 in) |
Base Width |
Size of the base rectangle along X. Length units, minimum 1. |
100 mm (4 in) |
Base Height |
Size of the base rectangle along Y. Length units, minimum 1. The seam is on the middle of one of the sides of this length. |
200 mm (8 in) |
Bot. Fillet R |
Corner radius of the base rectangle. 0 gives sharp corners. Length units. The shape rejects a value above half the smaller of Base Width and Base Height. The property page sets no minimum, and negative values are not checked. |
50 mm (2 in) |
Dev. Segs |
Number of segments used to develop the rounded corners, shared equally between the four corners. The value used is rounded down to a multiple of 4, with a minimum of 8 (for example 26 is used as 24, and 3 to 11 as 8). More segments give smoother curved edges and more bend lines. Has no effect when both fillet radii are 0. 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 (0.5 in in imperial) |
The dimensions drawn on the 3D view are Center H, Base Width, Base Height, Top Width, Top Height, Bottom Fillet R and Top Fillet R.
Notes and limits
•A fillet radius equal to half the shorter side of its rectangle is allowed and makes that end a full obround (semicircular ends, as with the default values). A larger radius cannot be built: the property page shows the warning described below (the reason is not shown, so check both fillet radii against their rectangles first).
•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 curved parts of the top and base edges of the pattern are made of straight segments, one per corner face, so a low Dev. Segs value gives visibly faceted edges.
•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 Filleted Rect To Filleted Rect Transition also has the Transform properties (Base X, Base Y, Rotation, Scale, Mirroring X), listed after its own properties. Polar Array properties are offered only on 2D shapes, so this shape has none.