Fillets, Convex and Concave Arcs

≈ 36 min

Fillets, Convex and Concave Arcs

A fillet is a rounded corner blending two lines or curves. Real parts are full of them — sharp internal corners concentrate stress and crack, so castings and machined parts are filleted.

The construction is always the same idea: find the centre first, by offsetting.

Fillet between two straight lines, radius R. Draw a line parallel to each given line, R away, on the inside. Where the two parallels cross is the centre. Drop perpendiculars from that centre to each line to find the two tangent points, then draw the arc between them.

Arc tangent to a circle, radius R. The centre must be R from the line and R from the circle's circumference — so it lies on a parallel line and on a circle of radius (bigger ± R) around the original centre. Use plus for an external (convex) blend, minus for an internal (concave) one.

Worked example. For a 10 mm fillet in a corner, the centre sits 10 mm from both lines — it is not on the corner itself, and it is not 10 mm along each line from the corner either.

Core checkpoint: Locate the arc's centre by offsetting, then find the tangent points. Never start by drawing the arc.

To construct a fillet of radius R between two straight lines, where is the centre of the arc?

Where two lines drawn parallel to the given lines, each R away on the inside, cross each other.

At the corner where the two given lines meet.

At a distance R along each line from the corner.

Halfway between the two tangent points.

Once the centre is found, how are the tangent points located?

By dropping a perpendicular from the centre to each given line.

By measuring R along each line from the corner.

By bisecting the angle at the corner.

By eye, where the arc appears to touch.

Why are internal corners of cast and machined parts filleted rather than left sharp?

A sharp internal corner concentrates stress and is where cracks start.

Purely so the drawing looks more finished.

Because sharp corners cannot be dimensioned.

To reduce the mass of the part.

When constructing an arc of radius R tangent to an existing circle of radius r, what radius circle do you draw around the original centre to find the new arc's centre?

r + R for an external blend, or r − R for an internal one.

Always r + R, whichever kind of blend is required.

Always R, regardless of r.

Half of r + R.