The blending of lines and curves

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It is usually only the very simple type of engineering detail that has an outline composed entirely of straight lines The inclusion of curves within the outline of a component may be for several reasons: to eliminate sharp edges, thereby making it safer to handle; to eliminate a stress centre, thereby making it stronger; to avoid extra machining, thereby making it cheaper; and last, but by no means least, to improve its appoarance This last reason applies particularly to those industnes which manufacture articles to sell to the general public. It is not enough these days to meke vacuum cleaners, food mixers or ball point pens functional and reliable. It is equally important that they be attractive so that they, and not the competitors' products are the ones that catch the shopper's eye. The designer uses circles end curves to smooth out and soften an outline Modern machine shop processes like cold metal forming, and the increasing use of plastics and laminates, allow complex outlines to be manufactured as cheaply as simple ones, and the blending of lines and curves plays an increasingly important role in the draughtsmen's world.

Blending is a topic that students often have difficulty in understanding and yet there are only a few ways in which lines and curves can be blended When constructing an outline which contains curves blending, do not worry about the point of contact of the curves; rather be concerned with the positions of the centres of the curves. A curve will not blend properly with another curve or line unless the centre of the curve is correctly found If the centre is found exactly, the curve is bound to blend exactly.

To find the centre of an arc. radius t. which blends with two straight lines meeting at right angles (Fig. 8/1)

With centre A. radius t. draw arcs to cut the lines of the angle in B end C.

With centres B and C. radius t, draw two arcs to intersect in 0.

0 is the required centre.

This construction applies only if the angle is a right angle. If the lines meet at any angle other than 90*. use the construction shown in Fig. 8/2.

To find the centra of an »re, radius r. which blends with two etraight lines meeting at any angle (Fig 8/2)

Construct lines, parallel with the lines of the angle end distance r away, to interseci in 0. 0 is the required centre.

To find the centre of an arc. radiua r. which passes through a point P end blends with e straight line

Construct a line, parallel with the given line, distance r away Thacentre must lie somewhere elong this line.

With centre P. redius r, draw en arc to cut the parallel line in 0.

0 is the required centre.

Motorcycle Springer Front Fork

To find the centre of en arc, radius R, which blends with a lina and a circla, cantra B, radius r

There »re two possible centres, shown m Figs 8/4 end

Construct a line, parallel with the given line, distance R away. The centre must lie somewhere along this line

With centre B. radius R -f /. draw an arc to intersect the parallel line in 0. 0 is the required centre. The alternative construction is

Construct a line, parallel with the given line, distance R away. The centre must lie somewhere along this line.

With centre B. radius R - r. draw an arc to intersect the parallel line in 0. 0 is the required centre

Drawing Blending Pictures

Fig 8/5

To find the centre of an arc. radius P. which blends with two circles. centres A and B. radii and respectively

There are two possible centres, shown in Figs. 8/6 and 8/7.

If an arc. radius R. is to blend with a circle, radius r. the centre of th* arc must be distance R from the circumference and hence R + r (Fig. 8/6) or R-r (Fig. 8/7) from the centre of the circle.

With centre A. radius R + r,. draw an arc. With centre B. radius R+r„ draw an arc to intersect the first arc in O. 0 is the required centre. The alternative construction is:

With centre A, radius R — iy draw an arc. With centre B, radiusR-rp draw an arc to intersect the first arc in 0. 0 is the required centre.

Blending Arcs And Circles
Geometrical Drawing
STAGE 2

These seven constructions will enable you to blend radii in ell the conditions that you are likely to meet Fig 8/8 shows the outline of a plane handle drawn in three stages to show how the radii are blended.

The construction lines have been left off each successive stags for clarity but if you are answering a similar question during en examination, lesve »lithe construction lines showing. If you do not the examiner may assume that you found the centres by uial and error and you will lose the majority of the marks

There are three more constructions that are included in the blending of lines and curves and these are shown below.

To join two parallel lines with two equal radii, the turn of which equals ths distance between the linee(Fig. 8/9)

Draw the centre line between the parallel lines.

From a point A, drop a perpendicular to meet the centre line in O,.

With centre 0„ radius 0,A. draw an arc to meet the centre line in B.

Produce AB to meet the other parallel line in C. From C erect a perpendicular to meet the centre line in 0,

With centre 0,. radius 0,C. draw the arc BC.

To join two parallel lines with two equal radii, r. the sum of which is greater than the distance between the lines (Fig. 8/10) Draw the centre line between the parallel lines.

From a point A. drop a perpendicular and on it mark off AO,-r.

Draw the centre line between the parallel lines.

From a point A. drop a perpendicular and on it mark off A0,-r.

With centre Oradius r. draw an arc to meet the centre line in 8.

Produce AB to meet the other parallel line in C.

From C erect a perpendicular CO, - r.

With centre Oradius t. draw the arc BC.

To join two parallel linea with two unequal radii (say in the ratio of 3:1) given the ends of the curve A and B (Fig 8/11)

Join AB and divide into the required ratio. AC: CB — 1:3.

Perpendicularly bisect AC to meet the perpendicular from A in 0,.

With centre 0,. radius O, A. draw the arc AC. Perpendicularly bisect CB to meet the perpendicular from Bin0,. With centre 0, and radius 0,B. draw the arc CB.

Blending Arcs

DIMENSIONS IN mm

DIMENSIONS IN mm

DIMENSIONS IN mm

4. Fig. 4 shows a garden hoa. Oraw this given view lull sue and show any construction lines used in making the drawing. Do not dimension the drawing. Southern Regional Examinations Board

Exercises 8 (AH questions originally set in Imperial units) 1 Fig. t shows an exhaust pipe gasket Draw the given view lull size and show any constructions used in making your drawing Do not dimension your drawing Southern Regional Examinations Board

3. Fig. 3 shows the outline of an electric lamp.

Important—Construction lines must be visible, showing clearly how you obtained the centres of the arcs and the exact positions of the junctions between arcs and straight lines Part 1. Draw the shape lull size. Part 2 Line A-B is to be increased to 28 mm. Construct a scale and using this scale draw the left half or hght half of the shape, increasing all other dimensions proportionally Southern Regional Examinations Board

DIMENSIONS IN mm

DIMENSIONS IN mm

5. Fig. 5 shows one half of a pair of pliers Draw, full size, a front elevation looking from A. Your constructions for finding the centres of the arcs must be shown. South-Eest Regional Examinations Board

2. Fig. 2 is an elevation of the turning handle of a can opener Oraw this view, twice full sure, showing clearly the method of establishing the centres of the arcs.

East Anglian Exeminetions Board

DIMENSIONS IN mm

6. Fig. 6 shows the design for the profile of a sea wall Draw the profile of the sea wall to a scale of 10 mm -2m. Measure in metres the dimensions A, B, C and D and insen these on your drawing. In order to do this you should construct an open divided scale of 10 mm « 2 m to show units of 1 m.

Constructions for obtaining the centres of the radii must be clearly shown.

Metropolitan Regional Examinations Board

7. Details of a spanner for a hexagonal nut are shown m Fig. 7. Draw this outline showing clearly all constructions. Scale: full size. Oxford Local Exammattons

I. The end of the lever for a safety valve is shown in Fig. 8. Draw this view, showing clearly all construction lines. Scale. } full size Oxford Local Examinations

SiSL

DIMENSIONS IN mm

SiSL

DIMENSIONS IN mm

9. Draw, to a scale of 2:1. the front elevation ol a rocker arm as illustrated in Fig. 9. Oxford LocalExaminations

Isometric Drawing Blending Curves
DIMENSIONS IN mm

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