Hexagonal flange setting-out for a laser-cut template
A machine guard has a regular hexagonal flange, 72 mm across flats, with a central Ø50 mm hole and six M6 clearance holes on a 56 mm pitch circle. The flange corners are chamfered 8 mm × 45°. The candidate has set out the hexagon by marking 36 mm from the centre with a steel rule and stepping 60° angles with a protractor. The first and last corners do not close by about 0.8 mm, and the pitch circle is 0.4 mm off centre. The drawing is to be used to laser-cut a template, so even small errors matter. The workshop has a pair of 30°/60° set squares, compasses, dividers and a drafting machine, but no CNC setting-out software.
1. Explain why the protractor-and-rule method is likely to produce a closing error and describe a more reliable construction for a hexagon across flats 72 mm using the available equipment.
Read the worked answer
The candidate has confused the across-flats dimension with the radius. Marking 36 mm from the centre gives the inradius, not the vertex radius. For a regular hexagon, across flats = 72 mm means the apothem is 36 mm, but the circumradius is R = 36 / cos 30° = 41.57 mm. Stepping 60° with a protractor also accumulates angular error around six settings; a 0.1° error per step can produce a visible closing error.
A reliable construction is:
- Draw centre lines and a circle of radius 41.57 mm.
- Mark one vertex on the vertical centre line.
- Set the compass to the same radius and step chords around the circumference; for a hexagon the chord equals the radius, so six steps close exactly.
- Join adjacent vertices to form the hexagon.
- Check opposite vertices and opposite flats before adding the pitch circle and holes. The set squares can be used to draw the 30°/60° construction lines, but the compass construction is the primary control.
2. Calculate the across-corners dimension and the side length, and state two checks that would confirm the setting-out before cutting.
Read the worked answer
For a regular hexagon, across flats AF = √3 × side, so side s = 72 / √3 = 41.57 mm. Across corners AC = 2s = 83.14 mm. Equivalently, AC = AF / cos 30° = 72 / 0.866 = 83.14 mm.
Two useful checks are:
- Measure three alternate sides; all six should be 41.57 mm within the drawing tolerance.
- Measure the distance between opposite vertices; it should be 83.14 mm, and the distance between opposite flats should be 72 mm. The centre should be 36 mm from every flat.
A further check is to draw the three long diagonals through opposite vertices; they must all pass through the same centre point. If they do not, the error is in the setting-out, not in the measuring.
3. The note '8 mm × 45°' is geometrically inconsistent at a regular hexagon corner. Explain why, and recommend a clear specification and construction order.
Read the worked answer
A regular hexagon has an interior angle of 120° at each corner. A chamfer line cannot make 45° with both sides of a 120° corner. If it makes 45° with one side, the triangle angles are 120°, 45° and 15°; with an 8 mm intercept on the 45° side, the intercept on the other side is 8 × sin 15° / sin 45° = 2.93 mm, not 8 mm. If equal 8 mm legs are intended, the chamfer makes (180° − 120°)/2 = 30° with each side.
A clear note would be '8 mm × 8 mm chamfer' or '8 mm × 30°' with a stated reference side, or a linear chamfer dimension plus one angle. Construct the hexagon first, then mark the chosen leg distances from each vertex and join them. Add the pitch circle and hole centres last, because chamfering removes the corner setting-out point and can destroy the datum.