Students will often experience difficulty in handling problems involving two and three dimensional geometrical constructions. The examples in Chapters 9 to 13 are included in order to provide a background in solving engineering problems connected with lines, planes and space. The separate chapters are grouped around applications having similar principles.
Copying a selection of these examples on the drawing board or on CAD equipment will certainly enable the reader to gain confidence. It will assist them to visualize and position the lines in space which form each part of a view, or the boundary, of a three dimensional object. It is a necessary part of draughtsmanship to be able to justify every line and dimension which appears on a drawing correctly.
Many software programs will offer facilities to perform a range of constructions, for example tangents, ellipses and irregular curves. Use these features where possible in the examples which follow.
Assume all basic dimensions where applicable.
To bisect a given angle AOB (Fig. 9.1)
1 With centre O, draw an arc to cut OA at C and OB at D.
2 With centres C and D, draw equal radii to intersect at E.
3 Line OE bisects angle AOB.
To bisect a given straight line AB (Fig. 9.2)
1 With centre A and radius greater than half AB, describe an arc.
2 Repeat with the same radius from B, the arcs intersecting at C and D.
3 Join C to D and this line will be perpendicular to and bisect AB.
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1 With centre A and radius greater than half AB, describe an arc. 2 Repeat with the same radius from B, the arcs intersecting at C and D. 3 Join C to D to bisect the arc AB. To find the centre of a given arc AB (Fig. 9.4) 1 Draw two chords, AC and BD. 2 Bisect AC and BD as shown; the bisectors will intersect at E. 3 The centre of the arc is point E. Circle radius To inscribe a circle in a given triangle ABC (Fig. 9.5) 1 Bisect any two of the angles as shown so that the bisectors intersect at D. 2 The centre of the inscribed circle is point D. To circumscribe a circle around triangle ABC (Fig. 9.6) 1 Bisect any two of the sides of the triangle as shown, so that the bisectors intersect at D. 2 The centre of the circumscribing circle is point D. To draw a hexagon, given the distance across the corners 1 Draw vertical and horizontal centre lines and a circle with a diameter equal to the given distance. 2 Step off the radius around the circle to give six equally spaced points, and join the points to give the required hexagon. Circle radius 1 Draw vertical and horizontal centre lines and a circle with a diameter equal to the given distance. 2 With a 60° set-square, draw points on the circumference 60° apart. 3 Connect these six points by straight lines to give the required hexagon.
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