Have you ever wished to scale something up or down, either from plans or from actual objects? Then, you looked around the shop only to realize you don’t have any convenient tool other than measuring with rulers and then trying to convert using sometimes shaky math – especially if using English measures in feet, inches and fractions?
(A quick aside here – metrics are so much more convenient to use! Although, it is ever so hard to make the initial roll-over and adjustment into metrics, especially for us older folk)
Presented here is an easy graphical way to build custom proportional dividers in five to ten minutes or so, made to whatever conversion ratio you may need – and once made will be independent of either metric or English scales. And the beauty of these is they cost almost nothing compared to the fancy ones you find online for $100.
Step 1: Grab two flat sticks 3/4” or so wide by 1/8” or so thick and 8 to12 inches long (longer sticks may be used too if desired, but are harder to handle for small dimensions);
Step 2: Point both ends of each stick, then cut them both to EXACTLY the same length, using 12” in this example;
Step 3: Now draw a circle on your shop table or on a scrap piece of plywood with a diameter the same as the lengths of your sticks, with a line drawn along the center diameter. See Fig 1;
Step 4: Decide on the ratio needed – in this case we use 2:1. This would enable you to quickly double, or halve any dimension selected within the range of the size of your dividers. This is a valuable aid when doing lots of conversions;
Step 5: Draw arcs on both sides of the diameter line at each end. One end to have arcs of radius 2” in this instance, and the other end exactly double that, or 4”. See fig 2;
(For other ratios you use suitable multiples, say 1” on one end and 3” on the other for 3:1 ratio, etc. The ratio is the multiple of the arc lengths on each end);
Step 6: Now, place the sticks one over the other on the circle, with one end on the smaller arc and the other on its corresponding other, i.e., beginning on one end on the 2” arc and the other on the 4” arc on the OTHER side of the diameter line. It will help to weight or clamp them in place. See Fig 3:
Note that the ends of the sticks on one end will now extend slightly beyond the drawn circle, since they will no longer pass through the center of the circle. A small adjustment is now made for better accuracy, by insuring the ends are equidistant from the diameter line, AND each is the proper distance from it (4”);
Step 7: Drill a small hole through both sticks in their centers where they intersect, sized to receive a small machine screw or bolt with nut (wing or knurled finger nuts are handy here). Bolt the sticks together snugly enough to hold the sticks in position, but loose enough to still move the sticks, and voilà! There’s your proportional dividers sized for whatever multiple you select.
You can make these to any ratio you need, although anything above 3:1 tends to be increasingly inaccurate. You might even make a set with several sets of holes drilled for various ratios – or even for custom ratios like 1-5/8:1 so long as you are comfortable doing the math needed. As always, the more careful and precise your measurements, the better accuracy you will get.
If you plan to use your dividers a lot, it is very helpful to drill small holes in the ends of the sticks into which cut-off nails may be set or glued. Just be sure the resulting overall lengths are equal, including nails, and they still fit your circle.
NOTE: I should add these dividers may not always be 100% accurate and precise, and may vary by 5% or so, especially when used to their maximum (widest) openings. So don’t use these kind for your space trajectory calculations, or lunar landing modules. That said, they will be pretty darned close when carefully made. These are meant for those (1) ‘near enough’ times when you need to get the job done, and it won’t actually matter if you are an eighth inch off somewhere.
(1) (I actually once heard of a ‘shade tree’ boat repairman somewhere in Florida years ago who called his operation ‘Near Enough Boatworks’. )
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