Mechanical Engineers Reference Book 12 Part 5 pot

Computer graphics systems 5/31 are defined, either textual entry or schematic capture methods can be used. Experienced users will often prefer textual entry, being a faster method (especially for repetitive features) and in which error checking is simplified. This method only requires the use of a keyboard for data entry. Inexperienced users tend to prefer a direct representation where they can see what they are drawing. If a hard-copy output is required, this is often the only suitable technique. For schematic entry systems a pointer device is required to enter coordinates to the system and such devices are described below. Pointer devices are often used in conjunction with a keyboard in order to enter data by the most efficient means for greater productivity. However, they may sometimes be used alone. Mouse, tracker ball, cursor key and joystick These are devices capable of passing orthogonally related coordinates to the application. All except the cursor keys are able to enter two coordinates simultaneously. Cursor keys are usually part of the keyboard assembly and are the slowest of the above devices to use. The amount that the coordinate is incremented for each depression of the key is usually variab!e to give coarse and fine positioning of the desired point. A mouse device contains a small ball which is moved across the surface of a desk. The movement of the ball is detected optically or mechanically and is converted to digital pulses, the number and rate of which determine the distance to move and the rate of movement. The mouse often contains switches so that the terminal position can be marked. In this way, the mouse can be driven ‘single-handed’. Using a mouse requires a free area of around 300 x 300 mm. To overcome this restriction, the tracker ball inverts the mouse so that the ball is moved directly by hand. The body of the tracker ball does not move but the ball may be freely moved in any direction without limit. Again, switches may be fitted to make a self-contained input device. A joystick operates in a similar way to the tracker ball except that movement of the joystick arm is limited to a few centimetres either side of a central position. The joystick may be biased to return to the central position when pressure is removed. Because of the limitation of movement of the joystick, it is more useful where absolute positioning is required, whereas the mouse or tracker ball indicate a relative position. However, using velocity sensing for the joystick, this limitation may be overcome. Graphics tablet The graphics tablet represents a drawing area where information is transferred to the application. The tablet has sensors embedded in its surface which detect the position of a stylus. These sensors are often arranged in a matrix. When used with a stylus, data are entered free-hand in much the same way as a user would sketch a design using pencil and paper. The stylus may have a switch in the tip so that pressing the stylus indicates a selection. When existing drawings are to be digitized, these are attached to the tablet and reference points on the drawing are converted to coordinates using a cross-hair device and switch. The application can then use the reference points to recreate the drawing. When used in this way, the graphics tablet is more commonly known as a digitizer. The graphics tablet area may also have a reserved space around its perimeter which is not used for drawing, but which is divided into small areas used for the selection of parameters. Light-pen and touch screen These operate in a similar way to the graphics tablet, except that the monitor screen is used. The light-pen detects the light generated when the CRT electron beam strikes the phosphor coating and the position of the pen is determined from the timing of the electricai pulse gener- processing. A digitizing tablet is used to extract information from existing documents rather than merely to scan the whole image and so this requires a human operator. The pointer (usually a cross-hair device) selects the major features of the document and the coordinates of these points are transferred to the processing system where the image feature may be reconstructed. Drawing The drawing operation takes the image parameters and converts them into a set of pixels in the frame buffer which define the dispiay. The frame buffer contents are then a map of what is seen on the output device and this is therefore a bit-map or pixel-map of the image. Converting the image parameters into pixels is not always simple. The change from a continuous function such as a straight line to a discretized version (pixels on a screen) can create unusual effects which are discussed in Section 5.3.4.2. Graphics processors Processing graphical data requires con- siderable processing power. If this processing is performed in software then the range of processing operations is large, limited only by the ability of the programmer. The more computing-intensive the operation, the more the throughput suffers, in terms of frames processed per second. One way of alleviating the problem is to perform some processing operations using dedicated hardware. Such devices include con- volvers for filtering and masking images and SIMD or MIMD devices for post-processing images. Parallel-processing techniques are used to increase the speed of these computing- intensive operations. In addition to the architectures men- tioned above, the transputer is often used for graphics applications. Colour look-up tables (palettes) If a display were to offer a realistic range of colours then the information that would need to be stored would require a very large frame buffer. Fortu- nately, not all colours need to be available at once in a given image. ]For example, a programmer may select 64 out of 4096 possible colours. This implies that while the system is capable of representing 4096 physical colours, only 64 logical colours are used. A means of mapping the logical colours to the physical colours is provided by the Colour Look-up Table (CLUT) or Palette. Thus the programmer writes the Palette once per image and can then refer to physical colours using one of the 64 logical colour numbers. These logical numbers may be re-used for another image to represent other colours by rewriting the Palette. In a similar way, monochrome images can be given a false-colour rendering by assigning colours (using the Palette) to each intensity level. 5.3.3.3 Human-machine interface Input devices In order to define a graphical display, two main methods exist. The first describes the desired display using some form of ‘language’. This is a text-based system where each element on the screen and its position is described by a set of alphanumeric commands entered using a keyboard. To modify the display, a text file is edited or special editing commarids are issued and the screen is recompiled. The second method uses schematic entry, where the user directly manipulates the screen interactively by using a pointing device to select the position on the screen where drawing or editing operations are to take place. This is more akin to drawing with pencil and paper and thus is preferred by most users. It is also essential for computer art, where the image cannot be easily described textually. For formal graphics (e.g. electronic circuit diagrams) where the number of symbols to be drawn is limited and conventions 5/32 Computer-integrated engineering Systems ated. A touch screen may have sensors arranged around the perimeter of the screen whjch detect when a light beam is broken by the pointing finger. Other forms of touch screen exist (for example, two transparent panels with electrically conducting surfaces will make contact when light pressure is applied at a point). The disadvantage of these forms of input is that the screen is obscured. The chief advantage is that the choice of items to select is infinitely variable. However, the resolution of these systems is limited; a touch screen to the area of a finger tip and a light-pen by the problem of focusing or refraction since the CRT faceplate is quite thick and light from a number of adjacent pixels can trigger the light-pen. 5.3.4 Applications At the applications level, graphics instructions from a display list or one of the input devices are interpreted so that an image is drawn on an output device. 5.3.4.1 World, normalized and device coordinates Most graphics systems use the Cartesian coordinate system. A single coordinate system is not usually possible since the graphics representation and the image it represents differ in scale and reference frame. Thus three coordinate systems are commonly used. World coordinates are those specified by the user. If the image represents a real object, then the world coordinates might be a set of physical coordinates describing the real-world object. For convenience and ease of processing, world coordinates are usually converted into normalized coordinates which have a range of values from 0 to 1 and are real numbers. This system allows processing operations to proceed without having to worry about arithmetic overflows where numbers grow too large to be represented by 32 bits, for example. Physical devices require the normalized coordinates to be mapped to a set of device coordinates. In this way, a number of output devices can be driven from the same application but with a particular set of mappings from normalized to device coordinates for each device. If the output device has different resolutions along each axis, then the scaling factor will alter with the resolution. The use of these coordinate systems is important when the image is transformed by rotation, zooming or clipping (see Sections 5.3.4.4 and 5.3.4.5). 5.3.4.2 Output primitives Line drawing This requires converting each point along the line into a pixel coordinate which must then be written into the frame buffer for display. For example, a diagonal line is represented by a set of pixels which are in fixed positions on the pixel matrix. In most cases the result is adequate (Figure 5.24) using an algorithm which calculates the pixel position by simple integer division. However, for a line which is close to the vertical or horizontal axis, this algorithm does not give acceptable results. A better algorithm is required which calculates the nearest pixel to the ideal line so that even steps are produced (Figure 5.25). Such an algorithm was proposed by Bresenham (see Appendix) which has the advantage of only requiring addition operations in order to plot the line after a few initial calculations have been performed (Figure 5.26). Circle drawing The advantage of circle drawing is its symmetry. Once one x,y pair has been calculated, then eight points on the circle can be defined (Figure 5.27). Calculating the plotted points using equal increments along the x axis is Figure 5.24 Pixels plotting using integer division Figure 5.25 Pixels plotted using nearest-pixel algorithm unsatisfactory as shown in Figure 5.28. Better results are obtained when points are plotted at equal angular rotations. However, the calculation involves evaluating a sine and cosine function; trigonometric functions use a lot of CPU time. Some means of reducing the number of trigonometric functions which need to be evaluated is desirable. Computer graphics systems 5/33 Figure 5.26 Bresenham’s line-drawing algorithm Figure 5.27 ilsing the circle’s symmetry, eight points can be plotted for each (x,y) coordinate pair Polygon method If the circle is drawn as a polygon, then only a few calculations are required to determine the vertices after which a straight-line algorithm is used to join the vertices. sin(A + B) = sin(A)cos(B) + cos(A)sin(B) sin(A - B) = sin(A)cosfB) - cos(A)sin(B) cos(A i B) = cos(A)cos(B) - sin(A)sin(B) cos(A - B) = cos(A)cos(B) + sin(A)sin(B) For this polygon, the ‘radius’ is incremented by 2~/n radians for each of the n vertices. If the angle A represents the current vertex, then the next vertex is found at an angle of A + 2dn. Instead of calculating the sine and cosine of this new angle, the previous values of sine and cosine are incremented according to the expressions above. Thus: sin(A + 27h) = sin(A)cos(2~/n) + cos(A)sin(2~/n) cos(A i- 2dn) = cos(A)cos(2~/m) - sin(A)sin(2v/n) Use is made of the following relationships: Circle drawn using constant x increments according to: y = fl -x2 Figure 5.28 Circle plotted using equal increments along the x-axis Now sin(A) and cos(A) become the new sine and cosine values which will be updated for the next vertex. The two multiplication operations and one addition operation per function considerably reduce the computation required since cos(2.rrln) and sin(2dn) only need to be calculated once. The initial sine and cosine values can be selected to be ‘0’ and ‘1’ if a full circle is to be drawn. Only the first 2~/8 radians need to be calculated as shown above if one takes advantage of the circle’s symmetry. This method is prone to cumulative errors, but if these are less than half a pixel in total, then the method is satisfactory. Other curves Functions in which the gradient is predictable or always less than unity (e.g. a circle) can always be plotted by incrementing in unit steps along one axis and calculating the other coordinate. Complex curves may require the computation of the inverse function especially when the gradient is large, if gaps in the curve are to he avoided. This is computa- tionally expensive. Curve-fitting techniques and straight-line approximations (e.g. polygon methods) considerably reduce the computation required if the resulting accuracy is acceptable. Characters Most applications require text to be displayed. The most common form of manipulating text is to hold bit-mapped fonts in memory, individual characters of which are copied to the screen at the desired position. These characters may be rotated in increments of 90” by manipulating the matrix to allow vertical or inverted text. Different font sizes may be produced by scaling the matrix although this only gives acceptable results for a small range of font sizes. A better solution is to hold each font in a variety of font sizes. The above techniques only permit text to be aligned to one of the axes. For text to be produced at any angle or orienta- tion, matrix transformations are possible but do not give good results. Using a strokedfont where characters are represented by a small number of curves (or strokes) means that the character definitions are independent of angle and also the displayed size. Most applications allow the user to define custom characters or symbols. In this way, fonts containing other than Roman characters may be used. 5/34 Computer-integrated engineering systems Move and copy Defined areas of the image can be quickly and easily copied using BitBlt operations, thus avoiding repeti- tion of previous calculations. This method is commonly used to enter text from the font table to the display. However, not all parts of the image can be so simply copied since overlapping blocks may be present. In this case the block will have to be recalculated and redrawn at the new coordinates. Move operations require the steps above and, in addition, the original block must be erased by recalculating and subtracting from the frame buffer. Alternatively, to erase the image, a rectangular area enclosing the image could be set to the background colour (thus erasing overlapping blocks within the area) and then any blocks partly defined in the area are redrawn with windowing applied to reconstitute the image. The options available in move and copy operations are discussed in Section 5.3.4.3. Area-fill If the shape of filled area is known, then the operation employs a polygon-drawing algorithm using a plot colour or pattern. When a pre-drawn area is to be filled, the shape of the area may not be known so aflood-fill algorithm is required. To fill such an area with a colour or pattern, a closed area is essential and a seed point within that area must be supplied from which the fill will be determined. The fill operation will set the pixels one row at a time within the desired area until a boundary is reached. For example, boundary may be defined as a foreground colour or the background colour. Fill operations on areas containing pat- terns give uncertain results if the pattern contains the boundary colour. Most fill algorithms are recursive so that complex areas may be filled. In such cases, the fill routine keeps a list of start points for each line of pixels which are to be filled. When it meets a boundary, it returns to the seed point and looks in other directions where the fill might proceed. Narrow areas of one or two pixels in width might prema- turely terminate a fill operation. Since the fill proceeds one row at a time, the narrow section might become blocked and appear to be a vertex of the enclosed area, thus terminating the fill. Section 5.3.4.3 describes some of the attributes of fill operations. Aliasing Since pixels can only be drawn on a finite matrix, continuous functions, when displayed, appear to have edges which do not exist. This artifact is called aliasing and its effect is to give diagonal lines a jagged appearance. In order to reduce this effect, various means of anti-aliasing are employed. If data in the frame buffer are processed to search for edges some will be found to be true edges (Le. exist in the real image) and can be ignored. Where aliasing is found to occur the intensity of these and adjacent pixels can be modified to mask the edge. A form of Bresenham’s line algorithm may be used to detect the relative position of a pixel from the true line and the intensity is then set in inverse proportion. Hardware techniques exist to reduce the ‘jaggies’ which include pixel phasing and convolution operations. Grids A deliberate form of aliasing is used where the application demands that all points be plotted on a grid or in an orthogonal-only mode. For example, all pixel positions calculated by the application or entered by an input device which fall within predefined areas are converted to the same pixel position - that is, the centre of the defined area. The defined areas depend on the grid spacing, which may be altered. In an orthogonal-only mode, one coordinate from the previously displayed point is fixed and only the other coordinate is free to change (usually constrained to a grid). 5.3.4.3 Attributes of output primitives Attributes may be defined for drawing opeiations which affect line styles, colour and intensity. Line-style options include the line width and pattern. The pattern may be a hatching pattern in one colour or a pattern using a number of colours. The pattern will typically repeat every 8 or 16 pixels and may be considered to be ‘tiled across the whole display. Only where the line coincides with the tiled pattern are those pixels plotted as part of the image. The most common line style is solid. Note that some attributes are not relevant or possible for certain display devices. While the intensity of a line can be varied for display on a CRT monitor, the same image will lose intensity information when plotted on a monochrome laser printer, for example. Referring to attributes individually, they are called unbundled. When used in this way, the application might require modification acccording to the display device used. Similarly, colour information will not remain constant when different displays are used, even for devices capable of using colour. As an example, a CRT display normally draws in white on a black background whereas a colour plotter would draw in black on white paper; both would display a red line in red. Thus attribute tables are often used which define the foreground and background colours to be used when the image is displayed on a CRT, to give one example. A whole set of attributes may be defined for each display device, or even for similar devices by different manufacturers. When arranged in this fashion, they are given the name bundled atttributes. Similar attributes are available to control fill styles. When a block is moved or copied this may be combined with a logical operation. For example, the source block may be ANDed, ORed or Exclusive-ORed with destination and addition or subtraction operations may be set as attributes. 5.3.4.4 Two-dimensional transformations Translation This is a movement of a graphics object in a straight line (Figure 5.29). If the distance (dw. dy) is added to each point in the object then the object will be translated I I I dx ‘I v Figure 5.29 Linear translation of an object Computer graphics systems 5/35 linearly when redrawn. This is acceptable for lines or polygons (which can be represented as a set of lines). For circles and arbitrary curves, the offset is applied to the reference point (e.g. the centre of the circle) and the object redrawn. Note that when an object is complex the redrawing of translated objects can be quite slow. In an interactive mode this can be a drawoack. Hence some applications do not update the display completely except on request. This possibly leaves some extraneous pixels set in the display but which are cleared on the next display refresh operation. If BitBlt operations are not possible (due to overlapping objects, for example) then some applications calculate a bounding box and a few reference marks on its edge in order to temporarily describe the object. This outline image can be moved interactively at high speed and the object is only fully redrawn when the destination is fixcd. Scaling requires all relative distances of points within an object to be multiplied by a factor (Figure 5.30). This factor is usually the same for horizontal and vertical directions to retain the proportions of the original object. If the scaling factor differs in each direction, then the object will appear to be stretched or compressed. Figure 5.30 Scaling operation. A scale factor of 2 is applied to the object relative to the point (x,y) Rotation requires multiplication of coordinates by sin0 and cos@, where 0 is determined from the pivotal point. The new coordinate is calculated from its position relative to the pivotal point (Figure 5.31). Reflection produces an image which may be mirrored with respect to the x-axis, y-axis or a user-defined axis (Figure 5.32). Changing the sign of one or both sets of world coordinates will convert a point so that it is mirrored about one or both orthogonal axes. Shear transformations can distort images (or correct for perspective distortions) by making the transformation factor a function of the coordinate values (Figure 5.33). Thus the transformation factor varies across an object. \ rotate Figure 5.31 Rotation of an object about the pivotal point (x,y) Matrix representations All of the transformations above can be reduced to a sequence of basic operations, each of which can be represented as a 3 x 3 matrix for a two-dimensional display. For example, a linear translation of an object by a distance (dx, dy) requires the coordinate [x y I] to be multiplied by the matrix: Successive translations are additive such that two translations of (dx, dy) and (Sx, Sy) are equivalent to a translation of (dx + Sx, dy + Sy): The scaling process requires more than one operation. The first translates the object to the graphics origin. Thus the second (scaling) operation can multiply all coordinates by the same factor (Le. with respect to the origin). The final operation translates the object back to its original position. Thus one scalar and two translation operations are required in the following order: 100 mx 0 0 100 -dx -dy 1 where mx and my are the scaling factors and dx and dy are the distance of the object from the origin. These matrices may be combined to give the scaling matrix: 0 The rotation process also requires translation to the origin before the rotate operator is applied and the inverse translation (as above). The rotation matrix is: 5/36 Computer-integrated engineering systems Figure 5.32 Reflection of an object about the x-axis Figure 5.33 A y-direction shear transformation on a unit square using a shear factor of 1 Computer graphics systems 5/37 where 0 is the angle of rotation. With the two translation operations added, the overall matrix becomes: cos8 sin8 -sin8 cos8 (1 - cos@)& + dysin8 (1 - cos8)dy - &sin0 1 Since all matrices can be multiplied together, then complex transformations can be constructed by applying the matrix operations in the desired order. 5.3.4.5 Windowing and clipping Windowing A window is a rectangular display area. There is normally a single window displayed which occupies the whole screen. However, it is now common to find software which uses windows freely and there may be several windows displayed at once. An architecture which allows only a single process to run at any one time may display multiple windows, but only one can be an active window. Multi-tasking or multi-processor systems may have several windows which are active, i.e. each is controlled by a different process which is running. Where multiple windows are displayed they will often overlap so that the window which has lower precedence (or is a background window) is partially or totally obscured (Figure 5.34). Hardware techniques are available to manage such overlaps, but more commonly this is performed in software. Clipping operations are performed when the contents of a window are being displayed so that only pixels within the permitted window limits are drawn; pixels outside the window area are clipped (Figure 5.35). The window boundaries and attributes are defined in a higher layer of the software - the window manager, which is conceptually part of the operating system. The window manager may draw a border around the window itself and label the border appropriately, but this is transparent to the process using the window. It is possible to define the windowing operation in terms of world or display coordinates (see Section 5.3.4.1) and ‘window’ is often used interchangeably when referring to either coordinate system. Where a distinction needs to be made between the two, the term viewpoint refers to the rectangular area on the display device. 3 Figure 5.34 Multiple overlapping windows I I Figure 5.35 Clipped graphics The most common operations to be performed on a window are described below and are implemented by calls to the window manager. Create The dimensions and position of ?he new window are given and a handle is returned if the window is successfully created. This handle is used in future graphics calls to specify the window in which drawing operations are to take place. A newly created window will normally have the highest priority so that it may obscure parts of existing windows. Clear and delete (close) The window handle is used to specify the window to be cleared or closed. It may not be possible to close a window if ?he process which owns it is still active. Drag (move) The size and contents of the window are unchanged, but the position in the display is altered (Figure 5.36). A translation operation is used to perform this. The window position is normally constrained so that no part may be dragged off the display, otherwise further clipping may become necessary. Resize The dimensions of the window are changed by altering the clipping parameters. The contents of the window which are visible before and after this operation remain unchanged (Figure 5.37). 5/38 Computer-integrated engineering systems Figure 5.36 Dragging a window 5. Zoom The contents of the window are recalculated using a new scaling factor (Figure 5.38). 6. Pan Here, the viewport is unchanged in position and size, but the window moves ‘behind’ the viewpoint. This is a translation operation but the clipping attributes do not ‘move’ with the window (as for drag) but rather remain constant as far as the display coordinates are concerned (Figure 5.39). Priority A window can be brough to the foreground or sent to the background by assigning it the highest or lowest priority attribute. If an intermediate priority is assigned, then the window may obscure parts of some windows and may itself be partly obscured by other windows (Figure 5.40). 7. Clipping text Where the clipped object comprises text, then clipping at the window boundary can leave partial characters visible in the same way as graphics objects are clipped at the pixel level. Sometimes this is visually undesirable. Thus text may be treated differently such that if any part of a character would be clipped, then that character is not displayed (Figure 5.41). Updating the display When an operation takes place which disturbs the boundaries of the viewpoint then it is not only the 4 window itself which needs to be redrawn; any part of the display which was partially obscured by the old viewport will also need to be redrawn (Figure 5.42). If the background is now visible, the revealed areas are simply cleared to the background colour. If parts of other windows are revealed then two strategies exist. Either the whole window is redrawn and the window manager clips the pixels according to the window’s priority, or an ‘intelligent’ process will only redraw those parts of the image that had previously been obscured. The first strategy is the simplest, but has the disadvantage of redrawing even those parts of the image that are correctly displayed - which means that overall system performance suffers. The second strategy is the most efficient in that only the area which requires redrawing is changed. This requires that the process itself can determine which objects or parts of objects were obscured and then require redrawing. This is not always easy to do or to calculate. If the windowing is performed in hardware, then the display buffers do not become corrupted where windows overlap as each window has its unique, non-overlapping buffer. Thus when moving a window reveals another, no redrawing of the image buffer is required. The display hardware fetches data from the appropriate buffer as each window or part thereof is displayed on the output device. 5.3.4.6 Segments Graphics objects may sometimes be repeated within an image. it is wasteful to store the same information several times so such objects may be stored as subpictures or segments. These objects are not restricted to being identically portrayed in the output image since variations of the same object can be produced by changing the attributes of the object. A related hardware technique involves the use of sprites. In this way a graphics object can be predefined and held in memory. Whenever this object is required, it can be quickly copied into the frame buffer at the required position without requiring graphics processing operations to draw it. However, there is usually the restriction that attributes cannot be changed and so the sprite is fixed in size and colour. Figure 5.37 Resizing a window Computer graphics systems 5139 he selected win Figure 5.38 Zoom operation on a window i Figure 5.39 Pan operatlon on a window Original display s shown within 1 Window 2 to foreground Figure 5.40 Changing the priority of window 2 [...]... 250 to 3 15 (instead of -11) hot applicable to sires up to I mm 6 /12 Design standards Table 6.3 Furrdornenrol devrazion 1 Upper deviation ES Lrner Crode I 9; S7 Nommol sizrs Over r* mm rnrn - 3 3 6 6 10 10 14 14 18 18 2 1 24 30 5 30 40 2 40 50 50 65 ~ 65 80 80 100 100 120 EO 140 140 5 160 160 180 180 200 200 280 250 3 15 3 15 355 355 400 IM) 450 450 :1 280 280 5 E 2 25 228 3 p 50 0 $ /i Grade 50 0 56 0 56 0... any other interested parties 6.1.7.1 Design: Examples BS 50 70: 1974 Graphical symbols and diagrams BS 308: Part 1: 1984 Engineering drawing practice (IS0 128 ): BS 308: Part 2: 19 85 Dimensioning (IS0 129 ) (see also reference 1) BS 450 0: 1969 Limits and fits (IS0 286) BS 50 00: Part 10: 1978 Induction motors (CENELEC HD231) BS Au 154 : 1989 Hydraulic trolley jacks BS CP117: Part 1: 19 65 Simply supported... Nominal six Over s +4 - +8 - +I0 +I2 +I5 +17 - +20 - -23 - +27 +3l - +34 - +37 +40 6 to 16 r x y : zu zb zc Fits, tolerances and limits 611 1 Table 6 3 Fundamental deviations for holes (courtesy BSI) Grade Nunrind sizes i 35 1wI 1 350 680 ux) 450 150 0 760 440 450 5 0 1 650 840 4811 400 Grade 6 to I6 -26 -34 N E +I -68 250 0 3 150 - - ~ - 52 0 290 ~ 1 45 ~ 38 0 -110 -76 -1 35 "Not applicable to sizes up to 1 mm... cd d e ef f fg g h jsb i 01 to 16 Grade 50 0 630 - - - - -260 -1 15 - -16 - -22 0 630 800 - - - - -290 -160 - -80 - -24 0 800 1000 - - - - -320 -170 - -86 - -26 0 I -30 I 0 0 I 1000 1 25 0 I - 1 - 1 - 1 - 1- 350 1-1 951 - 1 -98 I 1 25 0 1600 I - I - 1 - ! - !-3901-2201 - !-1101 - - I -28 I 2000 250 0 - - - - /-480+360] - I-1301 - 1-34 250 0 3 150 - - - - -52 0 -290 - -1 45 - -38 "Not applicable to sizes up to I... assessment (IS0 468) BS 50 78: 1974 Jig and fixture components BS 57 50: 1987 Quality assurance system (IS0 9000) (see also reference 2) BS 970: 1983 Steel material composition (IS0 683) BS 6323: Parts 1-4 Steel tubes, seamless BS 4 656 : Parts 1-34 Accuracy of machine tools (IS0 various) (e.g Part 34: 19 85 Power presses = I S 0 6899) BS 4437: 1969 Hardenability test (Jominy) (IS0 642) BS 6679: 19 85 Injection moulding... first two digits of the number 123 4 (Le 12) and stating that all parts bearing the first two digits are made from flat metal sheet as distinct from, say, 13 for castings, 14 for plastics parts and so on The original part AD234 would thus be defined as belonging to a particular assembly (A) and would be seen as a part made from flat metal sheet (12) with the individual part number of 34 This can be further... drawing of a part belonging to one complete assembly may be given a prefix, either character or number (for example, A /123 4, where A defines the particular assembly and 123 4 the individual part) This means that if a spare is required, the first sort (A) in the drawing register Drawing and graphic communications 6 /5 defines a particular assembly while the number will locate the individual part This can... character which introduced the part or represents the year of manufacture and/or a part modified in shape or dimension The whole purpose of the system is to locate the part number and/or its drawing from a part in service which may be damaged or overpainted eliminating the part number Spares lists often carry exploded drawings in which a particular assembly is shown as a set of parts approximating in position... well-established standards) BS 257 3: 1983 Stresses in crane structures (IS0 4301) BS 1726: 1964 Helical coil springs BS 4687: 1984 Roller chain drives ( I S 0 127 5) BS 1134: 1972 Surface finish ( I S 0 458 ) BS 50 78: 1974 Jigs and fixtures BS 55 00: 19 85 Unfired welded pressure vessels (IS0 2694) 4.1.7 Codes of practice Methods for design, manufacture and testing are recommended in these types of standard,... 160 160 180 180 200 200 280 250 3 15 3 15 355 355 400 IM) 450 450 :1 280 280 5 E 2 25 228 3 p 50 0 $ /i Grade 50 0 56 0 56 0 630 630 710 710 800 800 900 900 loo0 1 m 1120 1120 1 25 0 1 750 1400 1400 1M 1 M 1800 1600 2WO 2 m 2240 2240 250 0 2800 2800 2800 3 150 * In determining K M,N up to Grade 8 and P to ZC up to Grade 7, add the A value appropriate to the grade as indicated e.g for P7 from 18 to 30 A = 8 therefore . springs BS 4687: 1984 Roller chain drives (IS0 127 5) BS 1134: 1972 Surface finish (IS0 458 ) BS 50 78: 1974 Jigs and fixtures BS 55 00: 19 85 Unfired welded pressure vessels (IS0 2694) 4.1.7. interested parties. 6.1.7.1 Design: Examples BS 50 70: 1974 Graphical symbols and diagrams BS 308: Part 1: 1984 Engineering drawing practice (IS0 128 ): BS 308: Part 2: 19 85 Dimensioning (IS0 129 ). (see also reference 1) BS 450 0: 1969 Limits and fits (IS0 286) BS 50 00: Part 10: 1978 Induction motors (CENELEC HD231) BS Au 154 : 1989 Hydraulic trolley jacks BS CP117: Part 1: 19 65 Simply

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