Layout Ruler Tehcnical Field to which the Invention Relates The present invention relates to an instrument to enable a metal worker to perform flat layout pat¬ terns by marking the relevant lines directly on sheet metal stock, i.e. to mark the total length of the sheet metal stock and to mark the sight line for bending the sheet metal stock, very accurately and quickly. The invention is especially useful for, but is not limited to, 90° bends. Background Art

Analogous art includes many patents for scales or charts to provide a short cut for calculation. For example, Canadian Patent 75,600 patented April 12, 1902 by J.M. Daly provided a scale-chart for graphi¬ cally computing the tonnage resistance of trains of cars, including a chart arranged with devices or signs in successive order for indicating tonnage and a supplemental scale for indicating tonnage hauled. Canadian Patent 133,733 patented June 13, 1911 by D.H. Layne provided a computing yard-measure pro¬ vided with graduations, along one of its longi- tudinal edges, and transverse columns of figures arranged in pairs.

Canadian Patent 165,067 patented September 21, 1915 by W. Zurich provided a framing tool comprising a rectangular plate having its face laid off to form reversely disposed squares, a table or scale columns disposed between the squares and having scale indicia, and markings within the area of the squares indicative of pitches.

Canadian Patent 212,135 patented May 31, 1921 by L. Smith provided a packet formed with a base plate fashioned with upturned ends and inwardly extending retaining flanges, a series of data cards pivoted on a common centre in one flange with their opposite

ends under the inwardly extending flanges, and an upturned end on the flange at the opposite end of the base plate to guide the free ends of the cards. Canadian Patent 839,933 patented September 12, 1939 by J. Palmer provided bulk band gauges for a horizontal layout, including an elongated gauge body, graduators extending transversely of the gauge body, and scale indicia associated with the gradu- ations and occupying at least two parallel zones extending longitudinally of the gauge for reading successively therealong.

U.S. Patent 2,656,099 patented October 20, 1953 by H.J. Selling provided charts for determining the proportions of three additively primarily reacting colour dye stuffs required to produce a given colour. The charts each showed a series of constant concentration curves for one dye with respect to the concentrations of the other two dyes, for different preselected X,Y and Z stimuli of the eye.

U.S. Patent 3,134,540 patented May 26, 1964 by E.M. Shiepe provided a nomographic computory device including a first panel having associated with the surface thereof a plurality of mathematically correlated reference line coordinates each related to a variable and each having indicia associated therewith setting of a fixed scale. A second panel was provided upon which the irst panel was superim¬ posed, the second panel having a plurality of groups of moduli scale quantities with the scale quantities in each group arranged in vertical and horizontal rows and mathematically related to a particular line coordinate on the first panel. A plurality of windows were provided on the irst panel , each for revealing a scale quantity and each correlated in position to a particular line coordinate and its corresponding group of moduli scale quantities on the second panel.

U.S. Patent 3,269,649 patented August 30, 1966 by L. Abel provided numerographical apparatus for the systematic determination of the relationship between a plurality of co-related variables comprising a fixed table having a plurality of fixed parallel graduated logarithmic scales of the same modulus, a light permeable screen disposed over the table and a plurality of reading windows on the screen. U.S. Patent 3,559,881 patented February 2, 1971 by

R.L. Maison provided a nomographic instrument for solving mathematical problems. It included nomograms that enabled the manipulation of a straight line to read off the value of a dependent variable when the value of an independent variable was given, thereby computing, by means of graphic representation, systematic solutions to the problems capable of numerical calculation. The scales were immovable and the calculating line was moved by manipulations to intersect the scales at read-off points where memory indicators are positioned for reference. A plurality of calculating lines and a multiplicity of memory indicators operable at each and/or both sides of the instrument. D.S. Patent 4,122,994 patented October 31, 1978 by M.B. McReynolds et al provided a computerized aid for determining the optimum cycle lengths for use in a vehicular traffic control system wherein inbound and outbound traffic flow are equally favored. The aid was a nomograph which provided a clear visual indication of candidate optimum cycle lengths for a particular group of intersections which required only prior knowledge of intersection relative locations. The graphical computational aid pro- vided, in addition to the candidate optimum cycle length information, a visual indication of the quality of the candidate solution obtained for each of the controlled intersections of the group.

U.S. Patent 4,203,542 patented May 20, 1980 by C.F. Corbett provided a calculating apparatus including a first body member having a first linear scale. The first body member had both a hori¬ zontally-elongated opening and a vertically- elongated opening. A second slidably member was provided having a second scale thereon and a third logarithmic scale. All the scales interacted to simplify the calculation of the required feeder head parameters, e.g. size, amount of antipiping com¬ pound, in casting metals. Only the size of the casting section being fed and the normalized inscribed circle relating thereto needle to be measured.

Technical Problem

Before discussing the present invention, some general discussion of terminology used by a sheet metal worker will be provided. The "radius of bend" (R) of a sheet of material is the radius of the bend as measured on the inside of the curved material . The "minimum radius of bend" of a sheet of material is the sharpest curve, or bend, to which the sheet can be bent without critically weakening the part at the bend. If the radius of bend is too small for the temper of the sheet stock, stresses and strains will weaken the metal and may result in cracking. When making a bend or fold in a sheet of metal, the metal worker must calculate the bend allowance (B.A. ) , i.e. the length of material required for the bend. Bend allowance depends on four factors, namely: (1) the degree of bend; (2) the radius of the bend; (3) the thickness of the metal; and (4) the type of metal used. The type of material is also important. If the material is soft, it can be bent very sharply but if it is hard, the radius of bend will be greater to

avoid cracking and the bend allowance will auto¬ matically be greater.

Bending metal compresses the material on the inside of the curve and stretches the material on the outside of it. However some distance between these two extremes lies a space which is not affected by either force. This is known as the "neutral line" or "neutral axis". The neutral axis occurs at a distance approximately 0.445" of the metal thickness (0.455" x T) from the inside of the radius of bend.

When bending metal to exact dimensions, the length of the neutral axis must be determined in order that sufficient material can be allowed for the bend.

When laying out a piece of sheet metal , so that it can be cut to exact dimension before bending , one must know- the starting and ending points of the bend so that the length of "flat" of stock can be determined.

Two factors are important in determining the "set back" (S.B.), namely, the radius of bend (R) and the thickness of material (T). For 90* bends, the formula is (R+T) while for more or less than 90° the formula become K(R+T), where K is a determined factor. The "set back" is the distance from the "bend tangent line" to the "mold point". The mold point is the point of intersection of the lines extending from the two outside surfaces (called "mold lines"), while the bend tangent lines are the starting and end points of the bend.

The "brake" or "sight line" is the mark on a flat layout which serves as a guide while bending. The sight line is located one bend radius back from the bend tangent line which is to be inserted under the nose of the brake, i.e. the tool used for making the bend.

In the past, it was necessary to calculate the various necessary factors to enable the sheet metal worker to produce accurate work, i.e. bends, in sheet metal stock from drawings submitted by an engineer. Formulas and tables for various angles, radii of bends, material thicknesses, and other factors where therefore established to attempt to save time in the calculation of the bend allowance. For example, the bend allowance (BA) formula for a 90" bend was derived in the past as follows:

A. To the radius of bend (R) , add one-half the thickness of the metal (1/2T) . This gives R + 1/2T, the radius of the circle at approximately (but not exactly) the neutral axis.

B. Compute the circumference of the circle by multiplying the radius of curvature of the neutral axis (R + 1/2T) fay 2 u. This gives the circumference as 2 π (R + 1/2T) .

C. Since a 90* bend is a quarter of a circle, divide the circumference by 4.

This gives the bend allowance formula for a 90" bend as: 2 ir (R + 1/2T)

4

The formula, while practically correct, is nevertheless slightly in error because the neutral axis is not exactly in the centre of the sheet being bent.

The formula for angles other than 90 ^c is slightly different. The top part of the formula must be multiplied by the number of degrees and then divided by 360.

Since it takes time to work out bend allowance using the formulas, charts were therefore developed which show the bend allowance required for a 1 bend

according to the radius of bend and thickness of metal .

In the past, to determine the bend allowance for any degree of bend by the use of the table, the bend allowance per one degree for the thickness of material and the radius of bend required is first determined, and this is then multiplied by the number of degrees of the bend. Tables have also been developed to calculate the set back. In the past, to calculate the set-back for a 90° bend, one had to add the inside radius of the bend to the thickness of the sheet stock, i.e.

SB = R + T. However, to calculate set-back for angles larger or smaller than 90° , one had to consult Set-back Tables or K-Tables for a value, called K. Then one had to substitute this value in the formula,

SB = K(R + T) . The value for K varied with the number of degrees in the bend.

In the past, the following steps were followed when doing a flat layout pattern, these steps being performed for each bend: A. Determine the set-back (SB).

B. Determine the bend allowance (BA).

C. To find the distance from the edge of the _. sheet to the first bend tangent line (called the flat), subtract one set-back from the given height. This enabled one to draw a first bend tangent line.

D. To find the distance from the first bend tangent line to the second bend tangent line, add one bend allowance (BA) thereto. E. To find the distance from the second bend tangent line to the edge of the second flange, subtract one set-back (SB) from the given length. This line is then marked in.

F. Then a sight line is drawn in. The overall length is the amount of material required to make the angle, or the shear cut size. However, these procedures were so time consuming and the calculations were so prone to error that the procedure, recommended in the past, in order to prevent waste of material and to obtain a greater degree of accuracy in the finished part, was to make a layout, or pattern, of the part on paper, then to cut that pattern to exact size, and then to transfer those measurements to the material . To insure accuracy when doing a flat layout on metal or when transferring measurements from paper to metal, it was necessary always to work from one end (side) only.

In summary, the set back (SB), which is used for one bend or when more than one bend is required, is always used to find the position of the first bend tangent line of the bend or bends of the layout. The SB is determined in conjunction with, or in relation to, the outside given height or length dimensions.

The bend allowance (BA) is always used to find "the position of the second bend tangent line of a bend or bends of the layout. It is determined in con¬ junction with the first established bend tangent line.

The material deduction (MD) is always used to find: the overall length or shear cut size of any flanged part; or, in a box flange, the size of the corner cut out or the notching at the corner of two perpendicular flanges; or the hole or any notched- out portion of a flanged part. Such MD is deter- mined in conjunction with the outside given height, length or depth dimensions of a given flange and the given outside, height, length or depth, dimensions to the hole or the portion to be cut out.

It is readily apparent from the typical examples of patents described above that the art has not addressed itself to the provision of a scale or ruler to enable a metal worker to perform flat layout patterns directly on sheet metal stock, i.e. to mark the total length, or the shear cut size, of the sheet metal stock and to mark the sight line for bending directly on the sheet metal stock. It is therefore clear that there is a need for a simple device or ruler which can be used by a metal worker to enable the metal worker to mark out directly on the sheet metal stock the total length of the metal material as well as the bend allowance (BA), the set back (SB), the sight line, and the material deduction (MD) in a fast, very accurate manner.

Such device or ruler would obviate the need for charts and calculators, and would likewise obviate the need to make a paper layout or pattern and to make test pieces. Even an inexperienced sheet metal worker can start the layout immediately and the shear cut can be determined from the beginning. This can also provide for the possibility of doing the layout from either end or from both ends at the same time, at the convenience of the sheet metal worker. Disclosure of the Invention

This invention, now provides a layout ruler to perform flat layout patterns and to mark the total length, or the shear cut size, of a sheet metal stock and to mark the sight line for bending on the sheet metal stock comprising: a body member bearing a scale component along its central longitudinal axis, and a scale blade component provided with a plurality of spaced-apart transverse lines extending from at least one side edge of the body member, the scale blade component being provided with: (i) one

pair of spaced-apart lines representative of the inside bend radius (R) ; (ii) at least one pair of spaced-apart lines representative of the set back (SB); (iii) one pair of spaced-apart lines repre¬ sentative of the bend allowance (BA) ; and (iv) at least one pair of spaced-apart lines representative of the material deduction (MD) ; whereby, upon use of the ruler, the total length of the sheet metal stock can be determined, and the sight line can be marked thereon.

This invention also provides a packet is provided to perform flat layout patterns and to mark the total length, or the shear cut size, of a sheet metal stock and to mark the sight line for bending on the sheet metal stock, the packet comprising: a plurality of layout rulers secured together at a pivot point at a round end of each such ruler, each of the layout rulers comprising: (a) a body member bearing a scale component along its central longi¬ tudinal axis, and (b) a scale blade component pro¬ vided with a plurality of spaced-apart transverse lines extending from at least one side edge of the body member, the scale blade component being pro- vided with: (i) one pair of spaced-apart lines representative of the inside bend radius (R) ; (ii) at least one pair of spaced-apart lines represen¬ tative of the set back (SB); (iii) one pair of spaced-apart lines representative of the bend allowance (BA); and (iv) at least one pair of spaced-apart lines representative of the material deduction (MD); whereby, upon use of the ruler, the total length of the sheet metal stock can be deter¬ mined, and the sight line can be marked thereon. Each ruler is designed for a preselected thickness of material (T) . Each ruler in the packet has a separate scale blade component designed for a selected one of ^" a pair of preselected bend radii.

Preferably, by one feature of this invention, the plurality of spaced-apart transverse lines of one such scale blade component extend from each side edge of the body member, each the scale blade component being designed to produce different R, SB, BA and MD for a selected radius of 90° bend. Each such scale blade component is designed for a selected metal thickness (T). For each ruler, the spaced-apart lines provided may be representative, sequentially, of one R, two SB, one BA and two MD, or the spaced-apart lines provided may be representative, sequentially, of one R, one SB, two SB, one BA, one MD and two MD. By another feature of this invention, in this packet, the plurality of spaced-apart transverse lines of such scale blade component extend from each side edge of the body member, each of the plurality of spaced-apart transverse lines of such scale blade component being designed to produce different R, SB, BA and MD for a selected radius of 90" bend.

In such packet, and for each ruler, the spaced- apart lines provided may be representative, sequen¬ tially, of one R, two SB, one BA and two MD. Alter- natively, in such packet and for each ruler, the spaced-apart lines provided may be representative, sequentially, of one R, one SB, two SB, one BA, one MD and two MD. Advantageous Effects This invention provides advantageous effects over the prior art as a layout ruler to perform flat layout patterns and to mark the total length, or the shear cut size of a sheet metal stock and to mark the sight line for bending the sheet metal directly without use of approximation tables.

Brief Description of the Figures of the Drawings In the accompanying drawings,

Figure 1-5 show one embodiment of the 90° bend layout ruler of the present invention;

Figures 6 - 10 show a second embodiment of the 90° bend layout ruler of the present invention; Figures 11 - 15 show a third embodiment of the 90° bend layout ruler of the present invention;

Figures 16 - 20 show a fourth embodiment of the 90" bend layout ruler of the present invention; Figures 21 - 25 show a fifth embodiment of the

90" bend layout ruler of the present invention; Figures 26 - 30 show a sixth embodiment of the 90° bend layout ruler of the present invention; Figures 31 - 35 show a seventh embodiment of the 90" bend layout ruler of the present invention;

Figures 36 - 40 show a eighth embodiment of the 90" bend layout ruler of the present invention;

Figures 41 - 45 show a ninth embodiment of the 90 ^β bend layout ruler of the present invention; Figures 46 - 50 show a tenth embodiment of the 90° bend layout ruler of the present invention;

Figures 51 - 55 show an eleventh embodiment of the 90" bend layout ruler of the present invention; Figures 56 - 60 show a twelfth embodiment of the 90 ^β bend layout ruler of the present invention;

Figures 61 - 65 show a thirteenth embodiment of the 90" bend layout ruler of the present invention;

. Figures 66 - 70 show a fourteenth embodiment of the 90" bend layout ruler of the present invention; Figures 71 - 75 show a fifteenth embodiment of the 90" bend layout ruler of the present invention;

Figures 76 - 80 show a sixteenth embodiment of the 90" bend layout ruler of the present invention; Figures 81 - 85 show a seventeenth embodiment of the 90" bend layout ruler of the present invention; Figure 86 shows a packet of rulers (which may be any of the first to seventeenth embodiments of the

invention) according to another embodiment of this invention;

Figure 87 is an isometric view of a bend in a piece of sheet metal defining pictorially the terms used in the present application;

Figure 88a shows one 90" bend in a piece of sheet metal; while Figures 88b-88f show steps in the lay¬ ing out of the lines to provide the bend in the piece of sheet shown in Figure 88a, using the layout ruler of an embodiment of the present invention;

Figure 88g shows the aligning of the sight line with the brake;

Figure 89a shows two 90" bends in a piece of sheet metal; while Figures 89b-89j show steps in the laying out of the lines to provide the two 90° bends in the piece of sheet metal shown in Figure 89a, using the layout ruler of an embodiment of this invention; Figure 90a shows four 90" bends in a piece of sheet metal, while Figures 90b-90o shows steps in the laying out of the lines to provide the four 90 ^c bends in the piece of sheet metal shown in Figure 90a, using the layout ruler of an embodiment of the present invention;

Figure 91a shows a notched box flange formed from a piece of sheet metal, while Figures 91b-9lj show steps in the laying out of the lines to provide the notched box flange from a piece of sheet metal shown in Figure 91a, using the layout ruler of an embodiment of the present invention;

Figure 92a is a frontal view of the envelope of a metal worker's master bend calculator for bend angles which are more or less than 90° , to be used in conjunction with the 90° bend layout ruler of an embodiment of this invention;

Figure 92b is a rear view of the envelope of a metal worker's master bend calculator for bend

angles which are more or less than 90* , (of the envelope shown in Figure 92a) to be used in conjunction with the 90" bend layout ruler of an embodiment of this invention;

Figured 92c and 92d are views of the slide chart used in association with the envelope of Figures 92a and 92b to calculate the bend allowances for material thickness of 0.010" - 0.250"; Figures 92e and 92f are views of the slide chart used in association with the envelop of Figures 92a and 92b to calculate the set backs and the material deduction for material thickness of 0.010" - 0.250"; Figure 93a shows a 45 bend in a piece of sheet metal; while Figures 93b-93f show steps in the lay¬ ing out of the lines to provide the 45 bend in the piece of sheet metal shown in Figure 93a, using the layout ruler of an embodiment of the present inven¬ tion; Figure 94a shows a 120 bend in a piece of sheet metal; while Figures 94b-94f show steps in the laying out of the lines to provide the 120 bend in the piece of sheet metal shown in Figure 94a, using the layout ruler of an embodiment of the present invention; and

Figure 95a shows a combination of a 120" bend and a 90" bend in a piece of sheet metal; while Figures 95b-95k show steps in the laying out of the lines to provide the combination of the 120" bend and the 90" bend in the piece of sheet metal shown in Figure

95a, using the layout ruler of an embodiment of the present invention.

Description of Preferred Embodiments and Best Modes (i) Description of Figure 1 Figures 1 - 85 are generally the same, and so only Figures 1 - 5 will be described in detail in respect of the spaced-apart lines. The ruler 50 is one of a set of five (shown in Figures 1-5) for a material

thickness (T) of 0.010". Each ruler 50 in Figures 1 - 5 has a central line 51 drawn therein with numbers spaced therealong, the numerals being indicative of the pitch, i.e. the distance between two adjacent lines. Along each edge 52 is a plurality of spaced-apart transverse lines (53-56) for each preselected radius (R), i.e. for radii of 1/32", 1/16", 3/32", 1/8", 5/32", 3/16", 7/32", 1/4", 9/32" and 5/16". Transverse lines 53 are representative of the length required to provide the radius (R). Transverse lines 54 are representative of the length required to provide two set backs (SB). Lines 55 are representative of the length required to provide the bend allowance (BA). Lines 56 are representative of the length required to provide two material deductions (MD). (ii) Description of Figures 6 - 10

Figures 6-10 show a set of five rulers designed for a material thickness (T) of 0.015" and for radii of 1/32" and 1/16" (Fig. 6), 3/32" and 1/8" (Fig. 7), 5/32" and 3/16" (Fig. 8), 7/32" and 1/4" (Fig. 9), and 9/32" and 5/16" (Fig. 10). The spaced-apart marginal lines shown are, respectively, one R, one SB, two SB's, one BA, one MD and two MD's. (iii) Description of Figures 11 - 15

Figures 11-15 show a set of five rulers designed for a material thickness (T) of 0.020" and for radii of 1/32" and 1/16" (Fig. 11), 3/32" and 1/8" (Fig. 12), 5/32" and 3/16" (Fig. 13), 7/32" and 1/4" (Fig. 14), and 9/32" and 5/16" (Fig. 15). The spaced- apart marginal lines shown are, respectively, one R, two SB' s, one B , and two MD' s. (iv) Description of Figures 16 - 20 Figures 16-20 show a set of five rulers designed for a material thickness (T) of 0.030" and for radii of 1/32" and 1/16" (Fig. 16), 3/32" and 1/8" (Fig. 17), 5/32" and 3/16" (Fig. 18), 7/32" and 1/4" (Fig.

19), and 9/32" and 5/16" (Fig. 20). The spaced- apart marginal lines shown are, respectively, one R, one SB, two SB's, one BA, one MD and two MD's. (v) Description of Figures 21 - 25

Figures 21-25 show a set of five rulers designed for a material thickness (T) of 0.030" and for radii of 1/32" and 1/16" (Fig. 21), 3/32" and 1/8" (Fig. 22), 5/32" and 3/16" (Fig. 23), 7/32" and 1/4" (Fig. 24), and 9/32" and 5/16" (Fig. 25). The spaced- apart marginal lines shown are, respectively, one R, two SB's, one BA, and two MD's. (vi) Description of Figures 26 - 30

Figures 26-30 show a set of five rulers designed for a material thickness (T) of 0.040" and for radii of 1/16" and 3/32" (Fig. 26), 1/8" and 5/32" (Fig. 27), 3/16" and 7/32" (Fig. 28), 1/4" and 9/32" (Fig. 29), and 5/16" and 11/32" (Fig. 30). The spaced- apart marginal lines shown are, respectively, one R, one SB, two SB's, one BA, one MD and two MD's. (vii) Description of Figures 31 - 35

Figures 31-35 show a set of five rulers designed for a material thickness (T) of 0.040" and for radii of 1/16" and 3/32" (Fig. 31), 1/8" and 5/32" (Fig. 32), 3/16" and 7/32" (Fig. 33), 1/4" and 9/32" (Fig. 34), and 5/16" and 11/32" (Fig. 35). The spaced- apart marginal lines shown are, respectively, one R, two SB's, one BA, and two MD' s. (viii) Description of Figures 36 - 40 Figures 36-40 show a set of five rulers designed for a material thickness (T) of 0.050" and for radii of 1/16" and 3/32" (Fig. 36), 1/8" and 5/32" (Fig. 37), 3/16" and 7/32" ⁽ Fig. 38), 1/4" and 9/32" (Fig. 39), and 5/16" and 11/32" (Fig. 40). The spaced- apart marginal lines shown are, respectively, one R, one SB, two SB's, one BA, one MD and two MD's.

(ix) Description of Figures 41 - 45

Figures 41-45 show a set of five rulers designed for a material thickness (T) of 0.050" and for radii of 1/16" and 3/32" (Fig. 41), 1/8" and 5/36" (Fig.

42), 3/16" and 7/32" (Fig. 43), 1/4" and 9/32" (Fig. 44), and 5/16" and 11/32" (Fig. 45). The spaced- apart marginal lines shown are, respectively, one R, two SB's, one BA, and two MD's. (x) Description of Figures 46 - 50

Figures 46-50 show a set of five rulers designed for a material thickness (T) of 0.060" and for radii of 1/16" and 3/32" (Fig. 46), 1/8" and 5/32" (Fig. 47), 3/16" and 7/32" (Fig. 48), 1/4" and 9/32" (Fig. 49), and 5/16" and 11/32" (Fig. 50). The spaced- apart marginal lines shown are, respectively, one R, two SB's, one BA, and two MD's. (xi) Description of Figures 51 - 55

Figures 51-55 show a set of five rulers designed for a material thickness (T) of 0.065" and for radii of 1/16" and 3/32" (Fig. 51), 1/8" and 5/32" (Fig. 52), 3/16" and 7/32" (Fig. 53), 1/4" and 9/32" (Fig. 54), and 5/16" and 11/32" (Fig. 55). The spaced- apart marginal lines shown are, respectively, one R, one SB, two SB's, one BA, one MD and two MD's. (xii) Description of Figures 56 - 60

Figures 56-60 show a set of five rulers designed for a material thickness (T) of 0.065" and for radii of 1/16" and 3/32" (Fig. 56), 1/8" and 5/32" (Fig. 57), 3/16" and 7/32" (Fig. 58), 1/4" and 9/32" (Fig. 59), and 5/16" and 11/32" (Fig. 60). The spaced- apart marginal lines shown are, respectively, one R, two SB' s, one BA, and two MD's. (xiii) Description of Figures 61 - 65 Figures 61-65 show a set of five rulers designed for a material thickness (T) of 0.070" and for radii of 3/32" and 1/8" (Fig. 61), 5/32" and 3/16" (Fig. 62), 7/32" and 1/4" (Fig. 63), 9/32" and 5/16" (Fig.

64), and 11/32" and 3/8" (Fig. 65). The spaced- apart marginal lines shown are, respectively, one R, two SB's, one BA, and two MD's. (xiv) Description of Figures 66 - 70

Figures 66-70 show a set of five rulers designed for a material thickness (T) of 0.080" and for radii of 3/32" and 1/8" (Fig. 66), 5/32" and 3/16" (Fig. 67), 7/32" and 1/4" (Fig. 68), 9/32" and 5/16" (Fig. 69), and 11/32" and 3/8" (Fig. 70). The spaced- apart marginal lines shown are, respectively, one R, two SB's, one BA, and two MD's. (xy) Description of Figures 71 - 75

Figures 71-75 show a set of five rulers designed for a material thickness (T) of 0.090" and for radii of 3/32" and 1/8" (Fig. 71), 5/32" and 3/16" (Fig. 72), 7/32" and 1/4" (Fig. 73), 9/32" and 5/16" (Fig. 74), and 11/32" and 3/8" (Fig. 75). The spaced- apart marginal lines shown are, respectively, one R, two SB's, one BA, and two MD's.

(xyi) Description of Figures 76 - 80

Figures 76-80 show a set of five rulers designed for a material thickness (T) of 0.100" and for radii of 1/8" and 5/32" (Fig. 76), 3/16" and 7/32" (Fig. 77), 1/4" and 9/32" (Fig. 78), 5/16" and 1/32" (Fig. 79), and 3/8" and 11/32" (Fig. 80). The spaced- apart marginal lines shown are, respectively, one R, two SB's, one BA, and two MD's. (xyii) Description of Figures 81 - 85 Figures 81-85 show a set of five rulers designed for a material thickness (T) of 0.125" and for radii of 5/32" and 3/16" (Fig. 81), 7/32" and 1/4" (Fig. 82), 9/32" and 5/16" (Fig. 83), 11/32" and 3/8" (Fig. 84), and 13/32" and 7/16" (Fig. 85). The spaced-apart marginal lines shown are, respectively, one R, two SB's, one BA, and two MD ^r s.

It is noticed from Figures 1-85, that as the thickness of material increases, the minimum bend

radius increases, in order to avoid cracking of the material.

(xyiii) Description of Figure 86 Figure 86 shows a packet 60 of a plurality, i.e.

5, of the layout rulers 50 of Figures 1 - 5. In this drawing, the curved ends 61 are each provided with an aperture 62 through which a suitable fas¬ tener, e.g. a rivet 63 is passed to provide a rela- tively movable set of rulers.

(xix) Description of Figure 87

Figure 95a shows a combination of a 120 bend and a 90° bend in a piece of sheet metal; while Figures 95b-95k show steps in the laying out of the lines to provide the combination of the 120 bend and the 90" bend in the piece of sheet metal shown in Figure 95a, using the layout ruler of an embodiment of the present invention.

Turning firstly to Figure 87, it is seen that, for a bent piece of sheet metal 10, the "neutral axis"

11 is an imaginary line at 0.445" of the thickness (T) from the inside radius of the metal. The "flat"

12 is the distance from the edge 13 of the material to the "bend tangent line" 14. The "bend tangent lines" 14 are the edges of the bend. The mold lines 15 are the lines drawn along the outside edges 16 of the sheet metal 10. The "mold point" 17 is the intersection point of the two "mold lines" 15. The "inside radius" (R) 18 is the radius of curvature between the two bend tangent lines 14. The "given height" 19 is the distance between the "mold point" 17 and one edge 13 of the material, and similarly the "given length" 20 is the distance between the mold point 17 and the outer edge 13 of the material . The "set back" (SB) 21 is the distance between the mold point 17 and the bend tangent lines 14. The "bend allowance" (BA) 22 is the length of material along the neutral axis between the bend tangent

lines 14. The material deduction (MD) 23 is the amount or area of material not being used per bend because of the outside radius. It is surrounded by the two mold lines 15 and the outside material of the curve or bend and finishes at the level of the bend tangent lines 14.

While not shown in any of Figures 1-86, it is preferred that two layout rulers be provided on each ruler blank, i.e., one on each face of the ruler blank. Then it would be desirable to provide a translucent coloured plastic protection strip to be used on one side of the layout ruler to guard against the user of the layout ruler from using the wrong side of the layout ruler should the user become distracted. (xx) Description of Figures 88a - 88f

Figure 88a shows the final 90° bend, and Figures 88b - 88f show the five steps used in the marking off of a 1/16" radius bend [R,(53) = 1/16"] in a 0.020" thickness (T) of sheet metal, with a given height (19) of 1 1/2" and a given length (20) of 3" of a piece of sheet metal (shown in Figure 88a). The five steps are: 1) The shear cut size 881 is determined by sub¬ tracting one MD (23) from the total length 882 of 1 1/2" + 3" = 4 1/2". This is determined in Figure 88b using a 90° bend ruler 812 of this invention designed for a thickness of 0.020" and a radius of 1/16".

2) The first bend tangent line 883 is determined by subtracting one SB (21) from the given height (19) of 1 1/2". This is determined in Figure 88c, using the same 90° bend ruler 812. 3) The second bend tangent line 884 is determined by adding one BA ⁽ 22) to the first bend tangent line 883. This is determined in Figure 88d, using the same 90" bend ruler 812.

4) The brake or sight line 885 is then drawn in. The brake or sight line is the mark on a flat lavout which serves as a guide while bending. The sight line 885, which is to be inserted under the nose of the brake, is located one bend radius R, (18) back from the second bend tangent line 884. The marking- off of the brake or sight line is determined in Figure 88e, using the same 90° bend layout ruler 812.

5) The left hand side of the sheet metal is then bent upward using the drawn-in brake or sight line 885 as a guide. This is drawn-in brake or sight line 885 is shown in Figure 88f. (xxi) Description of Figure 88q

Figure 88g shows the location of the brake or sight line 885 in relation to the nose 886 of the brake 887. When bending, the brake or sight line 885 is lined up to be even with the nose 886 of the brake 887.

(xxii) Description of Figures 89a - 89j

Figure 89a shows the final two 90° bends, and Figures 89b - 89j show the steps taken in the mark¬ ing off of the length required to provide the two 5/16" radii bends [R,(53) = 5/16"], one at each end of a 0.020" thickness (T) piece of sheet metal with a given height (19) of 1 1/4" and a given length (20) of 2 1/2", and also to provide the location of a 1/8" diameter hole (899a) at a predetermined dis- tance from the bend along the ^' central longitudinal axis of the piece of sheet metal 89 (shown in Figure 89a). The steps are:

1) The shear cut size 891 is determined by subtracting two MD's (23) (i.e. one MD for each bend) from the total length 892 of 1 1/4" + 2 1/2" -*- 1 1/4" = 5". This is determined in Figure 89b using 90° bend ruler 890 of this invention designed for a thickness of 0.020" and a radius of 5/16".

2) The first bend tangent line 893 is determined by subtracting one SB (21) from the given height (19). This is determined in Figure 89c using the same 90" bend ruler 890.

3) The second bend tangent line 894 is determined by adding one BA (22) to the first bend tangent line 893. This is determined in Figure 89d using the same 90° bend ruler 890. 4) The third bend tangent line 895 is determined by subtracting two SB's (21) (i.e. one for each bend) from the total length (20) 892 from the second bend tangent .line 894. This is determined in Figure 89e using the same 90° bend ruler 890. 5) The fourth bend tangent line 896 is determined by adding one BA (22) to the third bend tangent line 895. This is determined in Figure 89f using the same 90* bend ruler 890.

6) The first brake or sight line 897 is then drawn in, its position being determined by sub¬ tracting one R (18) from the second bend tangent line 894. This is determined in Figure 89g using the same 90 ^β bend ruler 890. This first brake or sight line 897 is shown in Figure 89g. 7) The second brake or sight line 898 is then drawn in by adding one R (18) to the third bend tangent line 895. This is determined in Figure 89h using the same 90* bend ruler 890. This second brake or sight line 898 is shown in Figure 89h. 8) The normal position of the 1/8" diameter hole 899a is determined by adding the given height (19) and the given length 899 to the hole, i.e. 1 1/4" + 7/8" = 2 1/8". The true position of hole 899a is determined by subtracting one MD (23) from that distance, as determined using the same 90* bend ruler 890. The position of hole 899a is shown in Figure 89i.

9) The sheet metal is then bent, using the drawn- in brake or sight lines 897 and 898. These drawn-in brake or sight lines are shown in Figure 89j. Simi- larly to the orientation shown when bending as seen in Figure 88g, the brake or sight lines 897 and 898 are up and are lined up to be even with the nose 886 of the brake 887. (xxiii) Description of Figures 90a - 90o Figure 90a shows the "hat" flange, and Figures

90b - 90o show the steps used in the marking off of the bends necessary to provide the "hat" flange 901 having a first 3/16" radius bend [R(53) = 3/16"], a second 5/16" radius bend [R(53) = 5/16"], a third 5/32" radius bend [R(53> = 5/32"], a fourth 1/4" radius bend [R(53> = 1/4"], a first 1/8" diameter hole spaced between the first and second bends at 3/4" from the outside edge of the first bend, a second 1/8" diameter hole located between the second and third bends at 1 1/16" from the outside edge of the second bend, and a third 1/8" diameter hole located between the third and fourth bends at 11/16" from the outside edge of the fourth bend, all holes being along the centre line of a 2 1/4" wide piece of sheet metal having a thickness (T) of 0.050", a given height (19) of 1 1/2" and a given length (20) of 5". The final product is shown in Figure 90a, and the steps involved are shown in Figures 90b-90o. 1) The shear cut size 902 is determined by sub- tracting one MD (23 ⁾ per bend from the total length 902a of 1 1/2" + 1 1/2" + 5" + 3/4" + 1" = 9 3/4". For sheet metal of thickness 0.050" using the selected 90° bend rulers, the MD for 3/16"R = 0.145", the MD for 5/16"R = 0.198", the MD for 5/32"R = 0.132" and the MD for 1/4"R = 0.172" for a total of 0.647". Instead of using four rulers con¬ secutive, a ruler which had a value of approximately 0.647, i.e. a value of 0.644 was selected, such

ruler 900a being one which was for a thickness (T) of 0.080" and a radius of 3/8", such value of 0.644" being found under BA. This is determined in Figure 90b using the 0.644" BA value of this 90° bend layout ruler 900a of this invention designed for a thickness of 0.080" and a radius of 3/8".

2) The first bend tangent line 903a of the first bend is determined by subtracting one SB(21) from the given length (19) of 1". This is determined as shown in Figure 90c, using a 90° bend layout ruler 900b for a thickness of 0.050" and a radius of 3/16".

3) The second bend tangent line 903b of the first bend is determined by adding one BA (22) to the first bend tangent line 903a. This is determined as shown in Figure 90d, using the same 90° bend layout ruler 900b.

4) The first bend tangent line 903c of the second bend is determined by subtracting two SB from the given height of 1 1/2" from the second bend tangent line 903b of the first bend. The SB for the 3/16" radius bend is determined as shown in Figure 90e using the same 90° bend layout ruler 900b. The SB for the 5/16" radius bend is determined also as shown in Figure 90e using a 90° bend layout ruler 900c for a thickness (T) of 0.050" and a radius (R) of 5/16". It is to be noted that the marking should be on the reverse side, since this bend is a reverse bend. The reverse marking is shown in Figure 90e as a broken line.

5) The second bend- tangent line 903d of the second bend is determined by adding one BA to the first bend tangent line 903c of the second bend. This is determined as shown in Figure 90f using the same 90° bend layout ruler 900c. This marking, as well, is for a reverse bend, and is shown in broken lines in Figure 9Of.

6) The first bend tangent line 903e of the third bend is determined by subtracting two SB's from the given length of 5" from the bend tangent line 903d. The SB for the 5/16" radius bend is determined as shown in Figure 90g using the same 90° bend layout ruler 900c. The SB for the 5/32" radius bend is determined also as shown in Figure 90g using a 90° bend layout ruler 900d for a thickness (T) of 0.050" and a radius (R) of 5/32". It ^' is to be noted that this marking should be on the reverse side, since this bend is a reverse bend. This reverse marking 903e is shown in Figure 90g in broken lines.

7) The second bend tangent line 903f of the third bend is determined by adding one BA to the first bend tangent line 903e of the third bend. This is determined as shown in Figure 90h using the same 90° bend layout ruler 900d. This marking, 903f as well, is for a reverse bend, shown in Figure 90h in broken lines.

8) The first bend tangent line 903g of the fourth bend is determined by subtracting two SB's from the given height of 1 1/2" from the second bend tangent line 903f of the third bend. The SB for the 5/32" radius bend is determined as shown in Figure 90i using the same 90° bend layout ruler 900d. The SB for the 1/4" radius bend is determined as shown in Figure 90i using a 90° bend layout ruler 900e for a thickness (T) of 0.050" and a radius (R) of 1/4". 9) The second bend tangent line 903h of the fourth bend is determined by adding one BA to the first bend tangent line 903g of the fourth bend. This is determined as shown in Figure 90j using the same 90° bend layout ruler 900e. 10) The brake or sight lines, 904a and 904d, for the first and fourth bends are then drawn in. As noted hereinbefore, the brake or sight line is the mark on a flat layout which serves as a guide while

bending. Brake or sight line 904a of the first bend which is to be inserted under the nose of the brake is located one 3/16" bend radius R, (18) back from the second bend tangent line 903b of the first bend. The marking of the brake or sight line 904a is determined as shown in -Figure 90k using the same 90° bend layout ruler 900b previously used. The brake or sight line 904d of the fourth bend which is to be inserted under the nose of the brake is located one 1/4" R (18) back from the second bend tangent line 903h of the fourth bend. The marking of this brake or sight line 904d is determined as shown in Figure 90k, using the same 90° bend layout ruler 900e previously used.

11) The reverse brake or sight lines 904b of the second bend and 904c of the third bend are then drawn in on the reverse side. The brake or sight line 904b which is to be inserted under the nose of the brake is located one 5/16" bend radius R(18) back from the second bend tangent line 903d of the second bend. The marking of the brake or sight line 904b is determined, as shown in Figure 901, using the same 90° bend layout ruler 900c used previously. The brake or sight line 904c which is to be inserted under the nose of the brake is located one 5/32" bend radius R(18) back from the second bend tangent line 903f of the third bend. The marking of the brake or sight line 904c is determined as shown in Figure 901, using the same 90° bend layout ruler 900d used previously.

12 ) The position of the left hand and right hand holes, i.e. the one between the first and second bends, and the third and forth bends are then determined. The left hand hole is positioned from two outside dimensions minus one MD, i.e. (1" + 3/4" = 1 3/4") minus one 3/16" radius MD. The location of this hole is marked on the centerline by sub-

tracting one MD from the outside dimension line. This is determined, as shown in Figure 90m, using the same 90° bend layout ruler 900b used previ- ously. The right hand hole is positioned from two outside dimensions minus one MD, i.e. (3/4" + 11/16" = 13/16") minus one 1/4" radius MD. The location of this hole is marked on the centerline by subtracting one MD from the outside dimensions line. This is determined, as shown in Figure 90m, using the same 90° bend tangent ruler 900e used previ¬ ously.

13) The position of the hole on the top of the hat section, i.e. the hole between the second and third bends is now determined. This is determined by subtracting two MD's from the outside dimensions. The outside dimension is 1" + 1 1/2" + 1 1/16" = 3 9/16" and accordingly the hole is situated 3 9/16" from the left hand side minus one MD for the 3/16" radius bend and one MD for the 5/16" radius bend. This is determined, as shown in Figure 90n, by subtracting one MD from the outside dimension line 905c using the same 90° bend layout ruler 900b previously used, and then further subtracting therefrom one MD using the same 90° bend layout ruler 900c previously used.

14) The holes 906a, 906b and 906c marked as above are to be drilled or punched before bending, since it is not always possible to drill after bending. Also a large diameter hole should be punched, since the metal may be too thin for drilling. For the bending operation, the left hand side of the sheet metal is then bent four times using the drawn-in brake or sight lines 904a, 904b, 904c and 904d as a guide as previously described. The first bend upwardly is made using brake or sight line 904a as a guide. The sheet metal 901 is then turned over. The second bend upwardly is made using brake or

sight line 904b as a guide. The third bend upwardly is made using brake or sight line 904c as a guide. The sheet metal 901 is then turned over again and the fourth bend upwardly is made using the brake or sight line 904d as a guide. (xxiv) Description of Figures 91a - 91j

Figure 91a shows the final box-type flange having a notch cut out of one end and Figures 91b - 91j show the laying out and bending of the box-type flange having a notch cut out of one end. It is seen that the final product is an open ended box of sheet metal having thickness (T) of 0.040" and dimensions of 4" x 2 1/8" and flanges 3/4" high, and a notch 3/4" wide, which extends 3/8" into the floor. The walls are all bent at a 3/16" radius. In the flanged box there is a 5/32" diameter hole located at 1 1/8" from the front and 1 3/16" from the outside left hand wall. The steps in its pro- duction are as follows:

1) To determine the overall length, it is necessary to add the length of the floor plus the height of the walls, i.e., 3/4" + 4" + 3/4" = 5 1/2" . The shear cut length 911a is determined by subtracting two MD's (23) from the total length 911b of 5 1/2". This is determined, as shown in Figure 91b _t using a 90° bend layout ruler 912a of this invention designed for a thickness of 0.040" and a radius of 3/16". To determine the overall width, it is necessary to add the width of the floor plus the height of the back wall, i.e. 2 1/8" + 3/4" = 2 7/8". The shear cut width 911c is determined by subtracting one MD (23) from the total width 911d of 2 7/8". This is determined as shown in Figure 91b using the same 90° bend layout ruler 912a of this invention designed for a thickness of 0.040" and a radius of 3/16".

2) To determine the dimensions of the two corner notches, it is necessary to subtract one MD from the total of the given height plus the thickness (T) as a given length, i.e. 3/4" + 0.040". The dimension 911e of the corner square notch is thus determined by subtracting one MD (23) from the total dimension 901f of 3/4" + 0.040". Note that the thickness of 0.040" can best be marked off by means of using the thickness of a piece of scrap metal. This measure¬ ment is determined as shown in Figure 91c using the same 90° bend layout ruler 912a of this invention designed for a thickness of 0.040" and a radius of 3/16". Because the notch at the right hand side is identical to the notch at the left hand side, once the dimensions of the left hand notch are deter¬ mined, as described above, those dimensions are merely transferred to the right hand notch.

3) To determine the width position of the back flange notch it is necessary first to determine the

"start" point. The position of the "start" point 911g is determined by subtracting one MD (23) from the given length 911h of 3/4" + 1 3/8" = 2 1/8". To this start point 911g, is added the width of the notch, 3/4", to determine, the "end point 911i.

This is determined as shown in Figure 91d, using the same 90° bend layout ruler 912a of this invention designed for a thickness of 0.040" and a radius of 3/16". 4) To determine the depth position of the back flange notch it is necessary to subtract one MD from the total of the given height plus the given depth. The position of the depth "end" point 911j is deter¬ mined by subtracting one MD (23) from the total dimension 911k of 3/4" + 3/8" = 1 1/8". This is determined as shown in Figure 91e using the same 90° bend layout ruler 912a designed for a thickness of 0.040" and a radius of 3/16".

5 ⁾ It is possible to determine the position of the hole 913a either from the left hand side or from the right hand side. Using either, the position of the centre of the hole is determined by given height plus given length minus one MD. From the left hand side, the centre point 9111 is determined by sub¬ tracting one MD from the total 911m of 3/4" + 1 3/16" = 1 15/16". From the right hand side, the centre point 9111 is determined by subtracting one

MD from the total 911n of 3/4" + 2 13/16" = 3 9/16". This is determined, as shown in Figure 91f using the same 90° bend layout ruler 912a designed for a thickness of 0.040" and a radius of 3/16". It is observed that the centre point 9111 is coincident whether determined from the right hand side or the left hand side. This is true because of the con- gruency of the formula: 2SB - 1BA = 1 MD.

6) The first bend tangent line 911o is determined by subtracting one SB(21) from the given height 901p of 3/4". This is determined as shown in Figure 91g, using the same 90° bend layout ruler 912a designed for a thickness of 0.040" and a radius of 3/16". Because all the flanges (walls) are identical, once the first bend tangent line 911o is determined as described above, the first bend tangent lines 901o for the other two sides is merely transferred.

7) One second bend tangent line 911q is deter¬ mined by adding one BA (22) to the first bend tan- gent line 911o. This is demonstrated as shown in Figure 91h, using the same 90° bend layout ruler 912a designed for a thickness of 0.040" and a radius of 3/16". Because all the flanges (sides) are identical, once one second bend tangent line 9llq is determined as described above, the other. second bend tangent lines 911q for the other two sides is merely transferred.

8) The brake or sight lines 911r are then drawn in. The brake or sight line 911r, which is to be inserted under the nose of the brake, is located one 3/16" bend radius R, (18) back from the second bend tangent line 911q. The marking-off of the brake or sight line is shown in Figure 91i, using the same 90° bend layout ruler 912a designed for a thickness of 0.040" and a radius of 3/16". 9) The finished flat layout is shown in Figure

91j. To prevent tearing or cracking of material, it is necessary to drill or punch bend relief holes 913a, 913b at the intersection of the brake or sight lines 911r. As a general rule, the diameter of the holes 913a, 913b is approximately 3 times the sheet metal thickness.

10) The left hand side of the sheet metal as shown in Figure 91 , is then bent, using the drawn- in brake or sight lines 911r consecutively as a guide. The bending is performed as was previously shown in Figure 88g. Figure 88g shows the location of the brake or sight line 885 in relation to the nose 886 of the brake 887. When bending, the brake or sight line 885 is disposed so that it is even with the nose 886 of the brake 887.

(xxy) Description of Figures 93 - 95

Figures 93-95 show the determination of the layout procedure for bends of more or less than 90° , and combinations of bends, all using 90° bend layout rulers of this invention. However, to use these

90° bend layout rulers of this invention for this purpose, references should now be given to Figures 92a - 92f, which show the slide rule-type calculator used in conjunction with the 90° bend rulers of this invention to bends of more or less than 90° . (xxyi) Description of Figures 92a - 92f

As seen in Figure 92a, the front face 922 of the envelope 921 has instructions and diagrams thereon.

More importantly, it includes a horizontal thickness indicating window 923 and vertical bend allowance indicating windows 924a and 924b. Each end of the envelope is provided with a thumb-grip cutout 925. As seen in Figure 92b, the rear face 926 of the envelope 921 also includes a pair of tables, namely a set back table or (K) chart 927 and an aluminum alloy minimum bend radius table 928. More impor- tantly, it includes a horizontal thickness indicat¬ ing window 929 and vertical windows 930a and 903b to indicate the set back in column C and the material deduction in column D.

Figures 92c and 92d are Bend Allowance (BA) values for 1 and 90° for different bend radii (vertical) and various thicknesses (T) [horizontal]. Figures 92e and 92f are Set Back (SB) and Material Deduction (MD) values for 90° for different bend radii (vertical) and various thicknesses (T) [horizontal]. The use of the slide rule type calculators in

Figures 92a and 92b, fitted with the internal slides of Figures 92c - 92f will be described in detail in respect of Figures 93-95.

The basis of the slide rule-type calculators shown in Figures 92a and 92b is an empirical formula for bend allowance which it is dependent upon material gauge or thickness, the radius of bend and the number of degrees of bend. The Empirical Formula BA = (0.01743R + 0.0078T)N may be used for aluminum al- loys and steel sheet in determining bend allowances for a given material thickness, bend radius and degrees of bend, where

BA = Bend Allowance T = Material Thickness R = Bend Radius and N = No. of Degrees of Bend.

33 (xxyii) Description of Figures 93a - 93f

Figure 93a shows the final 45 angle bend, and Figures 93b -93f show the steps used in the marking off of a 9/32" radius, 45 angle bend [R(53) =

9/32"] in a 0.080" thickness (T) of sheet metal, with a given height (19) of 1 3/8" and a given length (20) of 1 9/16". The finished piece of sheet metal is shown in Figure 93a. It is necessary to determine the SB, BA and MD, using the calculators of Figures 92a and 92b.

For 45 , these values, calculated from empirical formulae are: SB = (R + T)K = 0.361 x 0.41421 = 0.150"

BA = (1 BA x 45)

= 0.00552 x 45 = 0.248" MD = (45 SB x 2) - (45 BA) = (0.150 x 2) - (45 BA) = 0.300 - 0.248 = 0.052"

The calculators shown in Figures 92a and 92b are then scanned to locate and select 90° bend layout rulers which contains identical or nearly identical numerical spacing values thereon. Such selected 90° bend layout rulers are then used for the purpose of providing that particular numerical spacing value. The steps in the laying out are:

1) The shear cut size 931a is determined by subtracting one 45 MD (as calculated above), 0.052", from the total length- 931b, i.e. 1 3/8" + 1 9/16" = 2 15/16". This is determined, as shown in Figure 93b, using the MD of a 90° bend layout ruler 932a of this invention designed for a thickness of 0.010" and a radius of 3/32", having a spacing value of 0.052".

2) The first bend tangent line 931d is determined by subtracting one 45 SB (as calculated above), 0.150", from the given height (19) of 1 3/8", i.e. 1

3/8" - 0.150". This is determined as shown in Figure 93c, using the MD of a 90° bend layout ruler 932b, designed for a thickness of 0.085" and a radius of 3/32", having a spacing value of 0.150".

3) The second bend tangent line 931e is determined by adding one 45 BA (as calculated above), 0.248", to the first bend tangent line 931d. This is determined as shown in Figure 93d, using the SB of a 90° bend layout ruler 932c designed for a thickness of 0.030" and a radius of 7/32", having a spacing value of 0.248".

4) The brake or sight line 931f is then drawn in. The brake or sight line 931f is located one 9/32" bend radius back from the second bend tangent line 931e. The marking of the brake or sight line is shown in Figure 93e, using the R of a 90° bend layout ruler 932d designed for a thickness of 0.050" and a radius of 9/32". It is noted that this brake or sight line 931f is moved considerably forward. That is because, for a 45 bend, most of the bent area stays deep under the nose or radius finger of the brake. It is also to be observed that a 9/32" R is quite a large radius. 5) The left hand side of the sheet metal 930 is then bent, using the drawn-in brake or sight line 931f as a guide. This is shown in Figure 93f, and follows the procedure described for Figure 88g. Figure 88g shows the location of the brake or sight line in relation to the nose 886 of the brake 887.

When bending, the brake or sight line is disposed so that it is even with the nose 886 of the brake 887. (xxyiii) Description of Figures 94a - 94f

Figure 94a shows the final 120 angle bend, and Figures 94b - 94f show the steps used in the marking-off of a 5/32" radius, 120 angle bend [R(53) = 5/32"] in a 0.040" thickness (T) sheet metal, with a given height (19) of 1 5/16" and a

given length (20) of 1 5/8". The finished piece of sheet metal is shown in Figure 94a.

It is necessary to determine the SB, BA and MD, using the calculators of Figures 92a and 92b. For 120 , these values, calculated from empirical formulae, are: SB = (R + T)K

= 0.196 x 1.7320 = 0.339" BA = (1 BA x 120)

= 0.00303 x 120 = 0.364" MD = (120 SB x 2) - (120 BA) = (0.339 x 2) - (120 BA) = 0.678 - 0.364 = 0.314" The calculators shown in Figures 92a and 92b are then scanned to locate and select 90° bend layout rulers which contain identical or nearly identical numerical spacing values thereon. Such identical 90° bend layout rulers are then used for the purpose of providing that particular numerical spacing value. The steps for the laying out are as follows:

1) The shear cut size 941a is determined by subtracting one 120 MD (as calculated above), 0.314", from the total length 941b, i.e. 1 5/16" + 1 5/8" = 2 15/16" - 0.314". This is determined, as shown in Figure 94b, using the BA of a 90° bend layout ruler 942a of this invention designed for a thickness of 0.100" and a radius of 5/32", having a spacing value of approximately 0.314", i.e. 0.315".

2) The first bend tangent line 941c is determined by subtracting one 120 SB (as calculated above) from the given length (19) of 1 5/16", i.e. 1

5/16" - 0.339". This is determined, as shown in Figure 94c, using the SB of a 90" bend layout ruler 942b, designed for a thickness of 0.090°" and a radius of 1/4", having a spacing value of approxi¬ mated 0.339", i.e. 0.340".

3) The second bend tangent line 941e is deter¬ mined by adding one 120 BA (as calculated above), 0.364", to the first bend tangent line 941c. This is determined, as shown in Figure 94d, using the BA of a 90° bend layout ruler 942c designed for a thickness of 0.030" and a radius of 7/32", having a spacing value of 0.364".

4) The brake or sight line 941f is then drawn in. The brake or sight line 941f is located one 5/32" bend radius back from the second bend tangent line 941e. The marking of the brake or sight line is shown in Figure 94e, using the R of a 90° bend layout ruler 942d designed for a thickness of 0.100" and a radius of 5/32".

5 ) The left hand side of the sheet metal is then bent upwardly, using the drawn-in brake or sight line 941f as a guide. This is shown in Figure 94f, and follows the procedure described for Figure 88g. Figure 88g shows the location of the brake or sight line in relation to the nose 886 of the brake 887. When bending, the brake or sight line is disposed so that it is even with the nose 886 of the brake 887. (xxix) Description of Figures 95a - 95k Figure 95a shows the final product of a 120 bend at one end and a 90° bend at the other end, and Figures 95b - 95k show the steps used in the marking off of a 5/32" radius, 120 angle bend [RC53) = 5/32"] in a 0.040" thickness (T) sheet metal, with a given height (19) of 1 5/16" and a given length (20) of 2 3/8" at one end, and a 5/16" radius 90° angle bend (R(53) = 5/16"), with a given height (19) of 3/4". The finished piece of sheet metal is shown in Figure 95a. It is necessary to determine the SB, BA and MD, using the calculators of Figures 92a and 92b. For 120 , these values, calculated from empirical formulae, are:

SB = ( R + T ) K

= 0.196 x 1.7320 = 0.339" ^' BA = (1 BA x 120) = 0.00303 x 120 = 0.364"

MD = (120 SB x 2) - (120 BA) ( .339 x 2) - (120 BA) 0.678 - 0.364 = 0.314" The calculators shown in Figures 92a and 92b are then scanned to locate and select 90° bend layout rulers which contain identical or nearly identical numerical spacing values thereon. Such selected 90° bend layout rulers are then used for the purpose of providing that particular numerical spacing value. For the 90° bend, a 90° bend layout ruler blade designed for a thickness (T) of 0.040" and a radius of 5/16" is used. The steps in the laying out are:

1) The shear cut size 951a for the 120 bend is determined by subtracting one 120 bend MD (as calculated above), 0.314", from the total length 951b, i.e. 1 5/16" + 2 3/8" + 3/4" = 4 7/16". This is determined, as shown in Figure 95b, using the BA of a 90° bend layout ruler 952a of this invention designed for a thickness of 0.100" and a radius of 5/32", having a spacing value of approximately 0.314", i.e. 0.315".

2) To this dimension is added shear cut size 951c which is determined by subtracting one 90° bend MD (23) from the first shear cut ^' dimension above 951a. This is determined, as shown in Figure 95c, using a 90° bend layout ruler 952b of this invention designed for a thickness of 0.040" and a radius of 5/16". 3) The first bend tangent line 951d o the 120 bend is determined by subtracting one 120 SB (as calculated above), 0.339", from the given length (19) of 1 5/16" i,e, 1 5/16 - 0.339". This is

determined as shown in Figure 95d, using the SB of a 90° bend layout ruler 952c designed for a thickness of 0.090" and a radius of 1/4", having a spacing value of approximately 0.339", i.e. 0.340".

4) The second bend tangent line 951e of the 120 bend is determined by adding one 120 BA (as calculated above), 0.364", to the first bend tangent line 951d. This is determined as shown in Figure 95e, using the BA of a 90° bend layout ruler 952d designed for a thickness of 0.030" and a radius of 7/32" having a spacing value of 0.364".

5) The first bend tangent line for the 90° bend is determined by adding one given length (2 3/8") to the second bend tangent line 951e and then subtract¬ ing two SB, i.e. one for the 120 bend and one for the 90° bend, i.e. 0.339". This is determined as shown in Figure 95f, using the SB of a 90° bend layout ruler 952c designed for a thickness of 0.090" and a radius of 1/4" having a spacing of approxi¬ mately 0.339", i.e. 0.340".

6) The first bend tangent line 951g of the 90° bend finally is determined by subtracting oηe SB(21) from the first 120 MD line 951f. This is deter- mined, as shown in Figure 95g, using the SB of a

90° bend layout ruler 952b designed for a thickness of 0.040" and a radius of 5/16" previously used.

7) The second bend tangent line 951h of the 90° bend is determined by adding one BA (22) to the first bend tangent line 951g of the 90° bend. This is determined as shown in Figure 95h, using the same 90° bend layout ruler 952b designed from a thick¬ ness of 0.040" and a radius of 5/16" previously used. 8) The brake or sight line 951i from the 120 bend is then drawn-in. The brake or sight line 951i is located one 5/32" bend radius back from the second bend tangent line 951e. The marking-off of

this brake or sight line is shown in Figure 95i, using the R of a 90° bend layout ruler 952a designed for a thickness of 0.100" and a radius of 5/32". The brake or sight line 951j of the 90° bend is then drawn in. The brake or sight line 951j is located one 5/16" bend radius R (18) back from the second bend tangent line 951h. The marking-off of this brake or sight line is shown in Figure 95j, using the R of the same 90° bend layout ruler 952b designed for a thickness of 0.040" and a radius of 5/16".

9. The left hand side of the sheet metal is then bent 120 , a 5/32" radius nose and using the drawn- in brake or sight line 951i as a guide. Then the right hand side of the sheet metal is bent 90° using a 5/16" radius nose and using the drawn-in brake or sight line 951j as a guide. This is shown in Figure 95k, following the teachings of Figure 88g.

Figure 88g shows the location of the brake or sight line in relation to the nose 886 of the brake 887. When bending the brake or sight line it is designed so that it is even with the nose 886 of the brake 887.

How the Invention is Capable of Exploitation by Industry

The invention can be easily manufactured by industrial plants. The invention can be used by sheet metal workers immediately without any further specialized training to reduce the time necessary, for example, to make bends in sheet metal and to provide more accurate such bends.