An accurate straight-edge is a very useful instrument to have, and it is essential for aligning table saw and jointer tables, as well as truing planes and workbenches. Although commercial, precision straight-edges long enough for woodworking purposes can cost hundreds of dollars, it is possible to make a set of three straight-edges accurate to one or two thousandths of an inch without requiring reference to any standard. Rather, the three straight-edges are compared with each other in such a way as to average out the errors.
Precision straight-edges are typically made of hardened steel, but they can also be made of mild steel, aluminum, rigid plastic, stable wood, or other materials. Lengths of three or four feet can be easily produced, as can longer lengths, although the latter are a little more awkward to handle and tend to sag under their own weights.
I adapted the techniques for making straight-edges from those described for making accurate surfaces, as described in Wayne R. Moore's "Foundations of Mechanical Accuracy", Moore Special Tool Co., 1970. This fascinating book describes how reference tools and machines with accuracies on the order of millionths of an inch are built.
The fundamental principle used to create precision straight-edges is that the only way that three curves can match each other is if the curves are all straight lines. By repeatedly comparing the three developing straight-edges with each other and averaging their shapes where they don't match, the three developing straight-edges will become arbitrarily straight.
Begin by selecting three identical pieces of a suitable material with the desired length of finished straight-edges. If mild steel is chosen, hot-rolled steel may be preferable to cold-rolled steel, because the latter can have significant internal stresses that can become unbalanced and cause warping if material is removed asymmetrically. Cold-rolled steel is usually shiny, in contrast to the brownish-black mill scale found on hot-rolled steel.
The thickness and depth of each piece should be great enough to prevent bending significantly under its own weight. In trading off thickness for depth, bear in mind that stiffness increases linearly with the thickness perpendicular to the load, but as the cube of the depth in the direction of the load. That is, although a 1/8"x2" bar and a 1/4"x1" bar are each twice as big as a 1/8"x1" bar, the 1/8"x2" bar is eight times a stiff as the 1/8"x1" bar, but the 1/4"x1" bar is only twice as stiff.
Each piece should be as straight as possible before the refining process begins, and the straight-edges should be smooth to begin with. Wood pieces should be ripped or jointed reasonably straight and smooth, and steel should have any mill scale or rust brushed or filed off. Mark both ends of each piece so that they can be differentiated; for example, A-A', B-B', C-C'.
In a nutshell the averaging process is to:
After we finish, we have three straight-edges, each as straight as the others. Any or all of them can be used, although it may be useful to keep them all as cross-references for each other. This is especially important for less stable materials like wood or metals with unreleaved internal stresses.
Any of the three straight-edges can be used to make more straight-edges, but when this is done, material is never removed from the reference straight-edge.
One way to speed up the final averaging process for metal straight-edges is to lap the pieces together. Lapping compounds (abrasives in a grease binder) are applied to two pieces and their edges are rubbed together. This process is repeated for all pairs of pieces in both directions until the edges are sufficiently straight. That is, we lap A:B, A:C, B:A, B:C, C:A, C:B, A':B, A':C, B':A, B':C, C':A, C':B, where A' denotes A reversed. In general, this sequence of lapping is repeated one or more times. Finer abrasives can be used in later stages of the lapping process.
One useful accessory to the straight-edge is a jig to hold it in position. This can be made by cutting a slot in a block of wood, sufficiently deep to allow the entire depth of the straight-edge to fit inside, and sufficiently narrow to keep the straight-edge from slipping out. This block is pushed over one end of the straight-edge so that its bottom rests on the surface being checked, freeing the operator to look for gaps and to insert feeler gauges between the straight-edge and the surface.
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Making Accurate Straight-Edges from Scratch / firstname.lastname@example.org / revised 1996 September 29