Many articles such as cans, pipes, elbows, boxes, ducting, hoppers, etc. are manufactured from thin sheet materials. Generally a template is produced from an orthographic drawing when small quantities are required (larger quantities may justify the use of press tools), and the template will include allowances for bending and seams, bearing in mind the thickness of material used.
Exposed edges which may be dangerous can be wired or folded, and these processes also give added strength, e.g. cooking tins and pans. Some cooking tins are also formed by pressing hollows into a flat sheet. This type of deformation is not considered in this chapter, which deals with bending or forming in one plane only. Some common methods of finishing edges, seams, and corners are shown in Fig. 13.1.
The following examples illustrate some of the more commonly used methods of development in pattern-making, but note that, apart from in the first case, no allowance has been made for joints and seams.
Where a component has its surfaces on flat planes of projection, and all the sides and corners shown are true lengths, the pattern is obtained by parallel-line or straight-line development. A simple application is given in Fig. 13.2 for an open box.
Allowance for corner lap
Allowance for corner lap
The development of a hexagonal prism is shown in Fig. 13.3. The pattern length is obtained by plotting the distances across the flat faces. The height at each corner is projected from the front elevation, and the top of the prism is drawn from a true view in the direction of arrow X.
An elbow joint is shown developed in Fig. 13.4. The length of the circumference has been calculated and divided into twelve equal parts. A part plan, divided
Development of part B
Development of part B
into six parts, has the division lines projected up to the joint, then across to the appropriate point on the pattern. It is normal practice on a development drawing to leave the joint along the shortest edge; however, on part B the pattern can be cut more economically if the joint on this half is turned through 180°.
An elbow joint made from four parts has been completely developed in Fig. 13.5. Again, by alternating the position of the seams, the patterns can be cut with no waste. Note that the centre lines of the parts marked B and C are 30° apart, and that the inner and outer edges are tangential to the radii which position the elbow.
A thin lamina is shown in orthographic projection in Fig. 13.6. The development has been drawn in line with the plan view by taking the length along the front elevation in small increments of width C and plotting the corresponding depths from the plan.
A typical interpenetration curve is given in Fig. 13.7. The development of part of the cylindrical portion is shown viewed from the inside. The chordal distances on the inverted plan have been plotted on either side of
the centre line of the hole, and the corresponding heights have been projected from the front elevation. The method of drawing a pattern for the branch is identical to that shown for the two-piece elbow in Fig. 13.4.
An example of radial-line development is given in Fig. 13.8. The dimensions required to make the development are the circumference of the base and the slant height of the cone. The chordal distances from the plan view have been used to mark the length of arc required for the pattern; alternatively, for a higher degree of accuracy, the angle can be calculated and then subdivided. In the front elevation, lines O1 and O7 are true lengths, and distances OG and OA have been plotted directly onto the pattern. The lines O2 to O6 inclusive are not true lengths, and, where these lines cross the sloping face on the top of the conical frustum, horizontal lines have been projected to the side of the cone and been marked B, C, D, E, and F. True lengths OF, OE, OD, OC, and OB are then marked on the pattern. This procedure is repeated for the other half of the cone. The view on the sloping face will be an ellipse, and the method of projection has been described in Chapter 12.
Part of a square pyramid is illustrated in Fig. 13.9. The pattern is formed by drawing an arc of radius OA and stepping off around the curve the lengths of the base, joining the points obtained to the apex O. Distances OE and OG are true lengths from the front elevation, and distances OH and OF are true lengths from the end elevation. The true view in direction of arrow X completes the development.
The development of part of a hexagonal pyramid is shown in Fig. 13.10. The method is very similar to that given in the previous example, but note that lines OB, OC, OD, OE, and OF are true lengths obtained by projection from the elevation.
Figure 13.11 shows an oblique cone which is developed by triangulation, where the surface is assumed to be formed from a series of triangular shapes. The base of the cone is divided into a convenient number of parts (12 in this case) numbered 0-6 and projected to the front elevation with lines drawn up to the apex
A. Lines 0A and 6A are true-length lines, but the other five shown all slope at an angle to the plane of the paper. The true lengths of lines 1A, 2A, 3A, 4A, and 5A are all equal to the hypotenuse of right-angled triangles where the height is the projection of the cone height and the base is obtained from the part plan view by projecting distances B1, B2, B3, B4, and B5 as indicated.
Assuming that the join will be made along the shortest edge, the pattern is formed as follows. Start by drawing line 6A, then from A draw an arc on either side of the line equal in length to the true length 5A. From point 6 on the pattern, draw an arc equal to the chordal distance between successive points on the plan view.
B | |||
D | |||
H V | |||
E |
G \ |
View on Arrow X
View on Arrow X
This curve will intersect the first arc twice at the points marked 5. Repeat by taking the true length of line 4A and swinging another arc from point A to intersect with chordal arcs from points 5. This process is continued as shown on the solution.
Fig. 13.10
True lengths
RAD C
Fig. 13.10
True lengths
RAD C
RAD C
True lengths
RAD C
True lengths
RAD C
RAD C
Figure 13.12 shows the development of part of an oblique cone where the procedure described above is followed. The points of intersection of the top of the cone with lines 1A, 2A, 3A, 4A, and 5A are transferred to the appropriate true-length constructions, and true-length distances from the apex A are marked on the pattern drawing.
A plan and front elevation is given in Fig. 13.13 of a transition piece which is formed from two halves of oblique cylinders and two connecting triangles. The plan view of the base is divided into 12 equal divisions, the sides at the top into 6 parts each. Each division at the bottom of the front elevation is linked with a line to the similar division at the top. These lines, P1, Q2, etc., are all the same length. Commence the pattern construction by drawing line S4 parallel to the component. Project lines from points 3 and R, and let these lines intersect with arcs equal to the chordal distances C, from the plan view, taken from points 4 and S. Repeat the process and note the effect that curvature has on the distances between the lines projected from points P, Q, R, and S. After completing the pattern to line P1, the triangle is added by swinging
1P Q RS
1P Q RS
an arc equal to the length B from point P, which intersects with the arc shown, radius A. This construction for part of the pattern is continued as indicated.
Part of a triangular prism is shown in Fig. 13.14, in orthographic projection. The sides of the prism are constructed from a circular arc of true radius OC in the end elevation. Note that radius OC is the only true length of a sloping side in any of the three views. The base length CA is marked around the circumference of the arc three times, to obtain points A, B, and C.
True shape of bottom triangle
True shape of bottom triangle
True length OE can be taken from the end elevation, but a construction is required to find the true length of OD. Draw an auxiliary view in direction with arrow Y, which is square to line OA as shown. The height of the triangle, OX, can be taken from the end elevation. The projection of point D on the side of the triangle gives the true length OD. The true shape at the bottom can be drawn by taking lengths ED, DB, and BE from the pattern and constructing the triangle shown.
A transition piece connecting two rectangular ducts is given in Fig. 13.15. The development is commenced by drawing the figure CBFG, and the centre line of this part can be obtained from the front elevation which appears as line CG, the widths being taken from the plan. The next problem is to obtain the true lengths of lines CG and DH and position them on the pattern; this can be done easily by the construction of two triangles, after the insertion of line DG. The true lengths can be found by drawing right-angled triangles where the base measurements are indicated as dimensions 1, 2, and 3, and the height is equal to the height of the front elevation. The length of the hypotenuse in each case is used as the radius of an arc to form triangles CDG and GDH. The connecting seam is taken along the centre line of figure ADHE and is marked JK. The true length of line JK appears as line HD in the front elevation, and the true shape of this end panel has been drawn beside the end elevation to establish the
\ True | ||
\ lengths | ||
D |
C | |
1.1. |
- 2 _ |
- 3 J |
Fig. 13.16
true lengths of the dotted lines EK and HK, since these are used on the pattern to draw triangles fixing the exact position of points K and J.
A transition piece connecting square and circular ducts is shown in Fig. 13.16. The circle is divided into twelve equal divisions, and triangles are formed on the surface of the component as shown. A construction is required to establish the true lengths of lines A1, A2, A3, and A4. These lengths are taken from the hypotenuse of right-angled triangles whose height is equal to the height of the front elevation, and the base measurement is taken from the projected lengths in the plan view. Note that the lengths A2 and A3 are the same, as are A1 and A4, since the circle lies at the centre of the square in the plan. The constructions from the other three corners are identical to those from corner A. To form the pattern, draw a line AB, and from A describe an arc of radius A4. Repeat from end B, and join the triangle. From point 4, swing an arc equal to the chordal length between points 4 and 3 in the plan view, and let this arc intersect with the true length A3, used as a radius from point A. Mark the intersection as point 3. This process is repeated to form the pattern shown. The true length of the seam at point E can be measured from the front elevation. Note that, although chordal distances are struck between successive points around the pattern, the points are themselves joined by a curve; hence no ultimate error of any significance occurs when using this method.
Figure 13.17 shows a similar transition piece where the top and bottom surfaces are not parallel. The construction is generally very much the same as described above, but two separate true-length constructions are required for the corners marked AD and BC. Note that, in the formation of the pattern, the true length of lines AB and CD is taken from the front
elevation when triangles AB4 and DC10 are formed. The true length of the seam is also the same as line A1 in the front elevation.
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