Three dimensional illustrations using isometric and oblique projection

Isometric projection
Figure 6.1 shows three views of a cube in orthographic
projection; the phantom line indicates the original
position of the cube, and the full line indicates the
position after rotation about the diagonal AB. The cube
has been rotated so that the angle of 45° between side
AC1 and diagonal AB now appears to be 30° in the
front elevation, C1 having been rotated to position C.
It can clearly be seen in the end view that to obtain
this result the angle of rotation is greater than 30°.
Also, note that, although DF in the front elevation
appears to be vertical, a cross check with the end
elevation will confirm that the line slopes, and that
point F lies to the rear of point D. However, the front
elevation now shows a three dimensional view, and
when taken in isolation it is known as an isometric
projection.
This type of view is commonly used in pictorial
presentations, for example in car and motor-cycle service
manuals and model kits, where an assembly has been
‘exploded’ to indicate the correct order and position of
the component parts.
It will be noted that, in the isometric cube, line AC1
is drawn as line AC, and the length of the line is reduced.
Figure 6.2 shows an isometric scale which in principle
is obtained from lines at 45° and 30° to a horizontal
axis. The 45° line XY is calibrated in millimetres
commencing from point X, and the dimensions are
projected vertically on to the line XZ. By similar
triangles, all dimensions are reduced by the same
amount, and isometric lengths can be measured from
point X when required. The reduction in length is in
the ratio
isometric length
true length
= cos 45
cos 30
= 0.7071
0.8660
= 0.8165 °°
Now, to reduce the length of each line by the use of an
isometric scale is an interesting academic exercise,
but commercially an isometric projection would be
drawn using the true dimensions and would then be
enlarged or reduced to the size required.
Note that, in the isometric projection, lines AE and
DB are equal in length to line AD; hence an equal
reduction in length takes place along the apparent
vertical and the two axes at 30° to the horizontal. Note
also that the length of the diagonal AB does not change
from orthographic to isometric, but that of diagonal
C1D1 clearly does. When setting out an isometric
projection, therefore, measurements must be made only
along the isometric axes EF, DF, and GF.
Figure 6.3 shows a wedge which has been produced
from a solid cylinder, and dimensions A, B, and C
indicate typical measurements to be taken along the
principal axes when setting out the isometric projection.
Any curve can be produced by plotting a succession of
points in space after taking ordinates from the X, Y,
and Z axes.
Figure 6.4(a) shows a cross-section through an extruded
alloy bar: the views (b), (c), and (d) give alternative
isometric presentations drawn in the three principal
planes of projection. In every case, the lengths of
ordinates OP, OQ, P1, and Q2, etc. are the same, but
are positioned either vertically or inclined at 30° to
the horizontal.
Figure 6.5 shows an approximate method for the
construction of isometric circles in each of the three
major planes. Note the position of the points of
intersection of radii RA and RB.
The construction shown in Fig. 6.5 can be used
partly for producing corner radii. Fig. 6.6 shows a
small block with radiused corners together with
isometric projection which emphasises the construction
to find the centres for the corner radii; this should be
the first part of the drawing to be attempted. The
thickness of the block is obtained from projecting back
these radii a distance equal to the block thickness and
at 30°. Line in those parts of the corners visible behind
the front face, and complete the pictorial view by adding
the connecting straight lines for the outside of the profile.
In the approximate construction shown, a small
inaccuracy occurs along the major axis of the ellipse,
and Fig. 6.7 shows the extent of the error in conjunction
with a plotted circle. In the vast majority of applications
where complete but small circles are used, for example
spindles, pins, parts of nuts, bolts, and fixing holes,
this error is of little importance and can be neglected.

Manual of
Engineering Drawing
Second edition
Colin H Simmons
I.Eng, FIED, Mem ASME.
Engineering Standards Consultant
Member of BS. & ISO Committees dealing with
Technical Product Documentation specifications
Formerly Standards Engineer, Lucas CAV.
Dennis E Maguire
CEng. MIMechE, Mem ASME, R.Eng.Des, MIED
Design Consultant
Formerly Senior Lecturer, Mechanical and
Production Engineering Department, Southall College
of Technology
City & Guilds International Chief Examiner in
Engineering Drawing

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Circular & Total Runout

Geometric Tolerancing Geometric Tolerancing is used to specify the shape of features. Things like: •Straightness •Flatness •Circularity •Cylindricity •Angularity •Profiles •Perpendicularity •Parallelism •Concentricity •And More... Geometric Tolerances are shown on a drawing with a feature control frame. Runout is specified on cylindrical parts. It is measured by placing a gage on the part, and rotating the part through 360 degrees. The total variation is recorded as the runout. • Circular runout is measured at one location. • Total Runout is measured along the entire specified surface. Principles of Engineering Drawing Thayer Machine Shop

Gear Types

The most common types of gears are illustrated in Figs. 5.16 to 5.25. Other available types are generally modifications of the basic gears shown. Gear nomenclature and definitions can be found in ANSI/AGMA 1012-F90, Gear Nomenclature, Definitions of Terms with Symbols.1 Spur gears A spur gear has a cylindrical pitch surface and teeth that are parallel to the axis. Spur gears operate on parallel axes (Fig. 5.16). Spur rack A spur rack has a plane pitch surface and straight teeth that are at right angles to the direction of motion (Fig. 5.16). Helical gears A helical gear has a cylindrical pitch surface and teeth that are helical. Parallel helical gears operate on parallel axes. Mating external helical gears on parallel axes have helices of opposite hands. If one of the mating members is an internal gear, the helices are of the same hand (Fig. 5.17). Single-helical gears Gears have teeth of only one hand on each gear (Fig. 5.18). Double-helical gears Gears have both right-hand and left-hand teeth on each gear. The teeth are separated by a gap between the helices (Fig. 5.19).Where there is no gap, they are known as herringbone gears. Wormgearing Includes worms and their mating gears. The axes are usually at right angles (Fig. 5.20). Wormgear (wormwheel) The gear that is the mate to a worm. A wormgear that is completely conjugate to its worm has a line contact and is said to be enveloping. An involute spur gear or helical gear used with a cylindrical worm has point contact only and is said to be nonenveloping (Fig. 5.20). Cylindrical worm A worm that has one or more teeth in the form of screw threads on a cylinder. Enveloping worm (hourglass) A worm that has one or more teeth and increases in diameter from its middle portion toward both ends, conforming to the curvature of the gear (Fig. 5.20). Double-enveloping wormgearing This is comprised of enveloping (hourglass) worms mated with fully enveloping wormgears (Fig. 5.21). Bevel gears These are gears that have conical pitch surfaces and operate on intersecting axes that are usually at right angles (Fig. 5.22). Miter gears These are mating bevel gears with equal numbers of teeth and with axes at right angles (Fig. 5.23). Straight bevel gears These have straight tooth elements which, if extended, would pass through the point of intersection of their axes (Fig. 5.24). Spiral bevel gears These have teeth that are curved and oblique (Fig. 5.24). Hypoid gears Similar in general form to bevel gears, hypoid gears operate on nonintersecting axes (Fig. 5.25). 

Standard Handbook of Plant Engineering (3rd Edition)

By: Rosaler, Robert © 2002 McGraw-Hill
Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)

Design Procedure for Crankshaft

The following procedure may be adopted for designing a crankshaft. 1. First of all, find the magnitude of the various loads on the crankshaft. 2. Determine the distances between the supports and their position with respect to the loads. 3. For the sake of simplicity and also for safety, the shaft is considered to be supported at the centres of the bearings and all the forces and reactions to be acting at these points. The distances between the supports depend on the length of the bearings, which in turn depend on the diameter of the shaft because of the allowable bearing pressures. 4. The thickness of the cheeks or webs is assumed to be from 0.4 ds to 0.6 ds, where ds is the diameter of the shaft. It may also be taken as 0.22D to 0.32 D, where D is the bore of cylinder in mm. 5. Now calculate the distances between the supports. 6. Assuming the allowable bending and shear stresses, determine the main dimensions of the crankshaft. Notes: 1. The crankshaft must be designed or checked for at least two crank positions. Firstly, when the crankshaft is subjected to maximum bending moment and secondly when the crankshaft is subjected to maximum twisting moment or torque. 2. The additional moment due to weight of flywheel, belt tension and other forces must be considered. 3. It is assumed that the effect of bending moment does not exceed two bearings between which a force is considered. 

FIRST MULTICOLOUR EDITION

(S.I. UNITS)

[A Textbook for the Students of B.E. / B.Tech.,

U.P.S.C. (Engg. Services); Section ‘B’ of A.M.I.E. (I)]

A TEXTBOOK OF

Machine Design

R.S. KHURMI

J.K. GUPTA