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Simple Aid for Turning Spheres without a Jig

Discussion in 'Tutorials and Tips' started by Dennis J Gooding, Jun 28, 2016.

  1. Dennis J Gooding

    Dennis J Gooding

    Joined:
    Apr 10, 2010
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    Grants Pass Oregon
    There seems to be considerable interest lately in a certain structured procedure for turning spheres by hand. Apparently, Sören Berger and Al Hockenbery independently discovered the basic concept and both have popularized it for several years. The procedure involves first turning a cylinder with a length and diameter equal to the diameter of the desired sphere. The outline of this cylinder will appear as a square. The corners of this square then are sliced off in a straight line to produce an 8-sided outline that approximates a sphere. Optionally, one can continue the process by turning off the new corners to form a 16-sided approximation, and this can be continued further into finer approximations if desired. The final result, from whichever level, can be smoothed out by eye to produce a pretty good sphere.

    The following three images illustrate the sequence for the 16-sided approximation.


    Stages.jpg

    I personally have used this method many times to turn spherical ornaments, and spheres that become the bowls of one-piece ladles and spoons, and find it fast and convenient. (I generally stop at the 8-sided stage.) Although I have never used a sphere-turning jig, I expect that this method is far faster (and certainly a lot cheaper) than using a jig, if you do not require high accuracy. Furthermore, it strikes me that this method would be a time-efficient way of roughing out a sphere before using the jig.

    The catch (no, not that kind) is that in order to make these cuts, you first need to determine where to mark the boundaries of the cuts. At each stage, you need to mark the piece at a particular distance each side of the existing corners. In the first stage, which produces an 8‑sided approximation, the required distance is 0.293 times the diameter of the sphere. In the second stage, which produces a 16-sided approximation, the required distance is 0.108 times the diameter of the sphere. Unfortunately, unless you have a calculator in the shop and a decimal ruler or calipers, this calculation and measuring can be challenging. One option is to purchase the $70.00 multi-calipers measuring tool from Sören Berger that, when set to the diameter of the sphere, provides direct indications of the offsets needed for Stage 1 and Stage 2. For those who cannot justify the cost of this tool, I would like to offer a simple, fast, no-cost, no-math alternative that anyone can use. This method makes use of a simple design graph, as shown below.

    The first graph, when printed, will let you measure the desired quantities directly using calipers or a strip of paper, for spheres up to just over 3-1/2 inches in diameter; an extension plot follows that will go up to 6 inches. Because the measurements are proportional, relative to the selected diameter, these charts are dimension free, and the figure can be printed at any size as long as it covers the largest sphere diameter desired.
    Graph1.png
    Graph2.jpg


    To use the graphs, first set your calipers to the diameter of the desired sphere. Then, hold the calipers horizontally and slide them down the graph until they exactly span the distance between the reference line R and the diameter line D. Mark this vertical position on the graph with a horizontal line parallel to the rulings. For the offset A1, that is required for the first stage, use your calipers (or a strip of paper) to measure the distance from the line R to the line A1 along the horizontal line and use it to mark cut lines on the work piece at that distance each side of each of the corners. To obtain the offset A2 for the second stage, do exactly the same, except copy the distance between line R and line A2. Similarly, for a third stage, copy the distance from line R and line A3. When performing the cuts across a corner at any stage, be sure to leave a vestige of the original guide lines showing. These mark the new corners that will be removed in the next stage. Also, to avoid confusion, it will be helpful to change marking colors between stages.

    To draw a graph for yourself that will accommodate spheres of up to 4 inches diameter, obtain a sheet of quadrille paper (I used ¼” ruled paper, but any will work) and mark a point near the top left of the sheet, as shown in the first figure, and draw a vertical line down to one of the rulings near the bottom of the sheet. This is the reference line R. Then draw a horizontal base line as shown. Measuring from the R line along the base line, mark points at 0.20” (7/32”), 0.43 (7/16”), 1.17” (1-3/16”), and 4.00 inches. Alternatively, if you prefer to span diameters up to 6 inches on a single graph, at possibly some loss of accuracy at small diameters, make the marks at 0.30” (5/16”), 0.65” (5/8”), 1.76” (1-3/4”), and 6.00”. The fractional measurements shown are close approximations to the actual decimal values for those who do not have decimal rulers. If you need to turn larger spheres you can easily extend the range of the graph. Carefully align a second sheet of quadrille paper with the original piece, offsetting it to the right if necessary, and extend the lines R, A1, A2, A3 and D onto the new sheet.

    The length of the line R is not critical; however the longer it is for a given maximum value of D, the more accurate the procedure will be (the measurements of A1, A2, and A3 will be less sensitive to small errors in vertical positioning of the calipers on the graph). I wanted to be able to handle up to 4-inch spheres with one sheet of paper, and this led to the first graph shown. (Note that the publication process has led to slight shrinkage of the figures.) As noted above, in principle, this procedure can be extended to additional stages (more sides), but unless the sphere is very large, errors in measurement and marking will tend to blur the benefits. For those interested in trying, further values of A are easily added to the graph. The A line for each new stage moves halfway in toward the R line from the preceding A line. In other words, the line for A4 will lie almost exactly halfway between the line A3 and the reference line R, and so on for further stages.

    After the publication of the original version of this article, I discovered an interesting fact that makes it even easier to continue on to a third Stage or higher. For stages three and higher, the required value of A is almost exactly one-fourth the width of the current faces. Thus by eye one easily mark the center of a current face and then by eye divide the two halves in two to obtain the positions of cut lines needed for that face. I also found that when dealing with short straight-line cuts in the final Stages of the process, a square-ended scraper provides the fine control needed better than does a gouge.

    Mathematical Basis for the Procedure

    Consider the profile of the turning as viewed from the front. The procedure begins with a square profile of height and length equal to the diameter of the eventual sphere. Stage 1 of the procedure slices off each corner of the square and replaces it with two corners a distance A1 on either side of the old corner and produces an 8-sided figure. Examination reveals that A1 is equal to half the difference between the length of a side of the old square and the length of a side of the new 8-sided figure. Furthermore, this relationship is true for all subsequent stages as well. That is, the value of A needed in a given stage is equal to half the difference between the length of a side before performing that stage and the length of a side produced by that stage. Applying a bit of elementary trigonometry, we find:

    EQuat.jpg
     
  2. Fadi Zeidan

    Fadi Zeidan

    Joined:
    Jul 5, 2016
    Messages:
    469
    Location (City & State):
    San Antonio, TX
    Dennis,

    I found your article through Pinterest. I printed your graph and turned my first sphere Today. It is a perfect sphere, amazing simplificationto sphere making. I’m going to make few of them, it was fun to make.

    I did watch Soren Berger’s youtube video and substituted his caliber for your measurements.


    View: https://youtu.be/R4s5LziiS08


    Thanks!
     
  3. John Rander

    John Rander

    Joined:
    Dec 4, 2018
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    Location (City & State):
    Milon La Chapelle France
    Dennis,
    As a new member to this forum I found your interesting article last week. It was a perfect project for my wife (a beginning woodturner) and I on a rainy Sunday afternoon. The exercise for her of gliding the bevel to make perfect cones connecting the lines was very useful. It was simple and fun, and our sphere turned out impressively good.
    Thanks!

    Fadi,
    Your video was helpful, the colored lines made the steps very clear.
     
    Fadi Zeidan likes this.
  4. hockenbery

    hockenbery AAW Advisor Staff Member

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    This is a good thread. Turning spheres is fun and a great confidence and skill builder.
    Turn a half dozen spheres and the curves on your bowls will get better.
    Dennis’s chart is a quick to use.

    In recent years I have been dropping the accuracy of the ball layout to one decimal place.
    On a 3” ball the error is about the width of pencil line so the layout is quick with vernier calipers.
    I use .4 x diameter of the cylinder for the face.

    A1D00B11-5831-4E97-BEC4-15F925E28A6C.jpeg BA68596A-8CFF-48D7-889E-F2E89E6700F6.jpeg CFDCFD06-D22E-4327-9BD8-3ED8FD20D555.jpeg

    Slides I use in demos
    http://aaw.hockenbery.net/Turning a ball basicsforweb.pdf
     
    Last edited: Dec 10, 2018
    Fadi Zeidan and John Rander like this.
  5. John Rander

    John Rander

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    Thanks for the slides. I need to refine my final stage tooling (a bit primitive for the first try). Lots of fun.
     
  6. Jon Murphy

    Jon Murphy

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    Jan 9, 2011
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    I've been using Alan Stratton's method for a few years (he of the Creative Woodturning videos). Much of his work is simplistic but some is quite inventive. Both he and I don't like having to buy jigs to make things. There are two purchases necessary for many things - the Beall spindle tap of size appropriate to your head stock spindle and a free spinning Morse taper spindle for your tail stock. For spheres I make concave blocks of scrap wood, tapped to fit the spindle. I turn the piece between centers (or could do it in a chuck). I eyeball the circular shape lengthwise (the crosswise shape must be a circle due to the spinning lathe). Once it is reasonably close I mark a line around the middle and then cut off the "ball". Now I mount my concave "pressure blocks" and orient the "ball" so the center mark is horizontal and turn the new circle (a lot to chop off where the cut off points were). Then reverse the process. One more try may be needed, but that usually makes me a "ball" that will roll straigh, and it is done without approximations approaching the infinite nature of a circle - yes, I do understand the math and appreciate Dennis's calculational approach.

    The Beall tap and the tailstock spindle mount cost a bit of money, but they also allow you to make many other special "pressure blocks". Another of Alan Statton's innovations was for off-set turnings. Make blocks with off- for set pinholes (and a center pinhole) for head stock and tail stock and drill your piece with a center hole and one, or more, off-set holes. Use little pins from rod stock to align the work piece at any angle for any part of the piece. I realize this isn't fully descriptive, I commend you to Alan's site for the details. All I will add is that I don't use my expensive Sorby "angle chuck" any more.

    I have a box of various "pressure blocks" of various shapes for finishing the bottoms of bowls (I use tail-stock pressure rather than vacuum as I don't have the space (or money) for the vacuum device. All are scrap wood tapped with the Beall tap, and I can make another in fifteen minutes if I need it.
     
  7. Mike Johnson

    Mike Johnson

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    To speed the process on the lathe I usually cut and glue wood slabs into a square block and trim it to square on a table saw. I then mark the center points on each side of the cube and draw a circle with a compass and pencil on each side that is close to the diameter of sphere I need. I then take it to the table saw and set the blade at 45 degrees and cut the corners from all sides of the cube which leaves an octagonal shaped billet with center marks on each side. This allows mounting between a spur drive and live center. I usually drill the center points with a small diameter drill bit and inch or two deep into the billet which provides reference points when turning the sphere to a different orientation to round the sphere. If you don't drill the center marks you end up having to measure the circumference of the sphere and marking a half way point around the sphere on two sides once the pencil marks have been turned away, any small mistakes in measuring at this juncture will require more rounding in opposing orientations. Drilling the center reference points maintains the same reference each time you rotate the sphere between orientations when shadow rounding.
     
  8. John Torchick

    John Torchick

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    Simple- just turn off anything that doesn't look like a sphere. Need to try that. Thanks to all.
     
    Ken Appelt likes this.
  9. Ken Appelt

    Ken Appelt

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    John, that’s how I do it,, and it seems to work just fine.
     

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