Freesteel Blog » One tapered tool diagram coming up

One tapered tool diagram coming up

Wednesday, February 14th, 2007 at 11:36 am Written by:

Well, that’s about seven hours work. I can’t operate these newfangled graphics editors (which anyway don’t have the offset ellipse as one of their types), and have resorted to writing a python program to output the raw SVG file, which you are now previewing.

I did this to make the diagram for my previous posting on the offset ellipse, but then lost the program. This time I’ve taken the precaution of copying the code into some sort of a commented

<![CDATA[ **stuff goes here** ]]>

section so I can only lose it if I lose the diagram.

Not sure this diagram is all that comprehensible, but a is the shaft radius, t is the torus radius of the tip, t – f is the corner radius. The conical section of the tool connects tangentially to the torus tip at the radius c. If we let h be the height of the torus — the vertical distance between the c line and lower a line — then I reckon:

(a – c) / h = tan(taper_angle)

There are four distinct surfaces and one touchable edge on this toolshape. The other two edges have tangential surfaces on either side, so it’s not possible for them to touch the model.

The model is made up of triangles, which themselves are points, edges, and facets. I think I’ve been through all this before. Before lunchtime I’d like to work out the contact point between an edge and the conical surface.

I don’t know whether it’s better to put everything on one diagram, or make a series of diagrams showing the different toolshapes, for example taperless, or ballnosed. Once I get something that’s good I’ll upload it onto wikipedia, which has a great SVG engine, and stick it in one of their articles.

So here’s a question: can anyone work out what the little green dotted circle in the middle is supposed to represent?


  • 1. Anders replies at 14th February 2007, 6:31 pm :

    Hi Julian,

    Thanks for a great website, I enjoy reading about your CAM algorithm endevours. I haven’t had time to work with the zslice algorithm you gave me, but I promise I will some day!

    I tried to understand your thinking in this post and to make things clearer for myself I drew a profile view of the cutter:
    This view might be useful for your website or wikipedia also.

    I’ve labeled the surfaces 1, 2, 3, and 4 (numbers just outside the tool). And I’ve labeled the edges I, II, and III (numbers inside tool).

    From your text I understand that only edge I needs to be checked against the model, since if edge II or III was toucing the model, then so would the adjecent surfaces (which apparently are checked against the model before checking edges).

    To answer your question I think the green dotted line is the ‘equator’ of the torus, i.e. the maximal torus outer diameter.

    I still fail to see what this has to do with offset ellipses 🙂 but then I’m not a professional cam programmer…



  • 2. Jeff replies at 15th February 2007, 1:52 am :

    Where is the zslice algorithm? I may have time to work on if more detailed information can be shared.

  • 3. Julian replies at 15th February 2007, 9:30 am :

    Good image. You have recognized all the salient parts. Are you able to do that in SVG? There’s a program called for editing SVG, and you could add your annotation onto the file image I have uploaded here (click on the image). I think we’ll need individual diagrams of the different cutter shapes, even though they are all specializations of this general one.

    Offset ellipse: See that silhouette curve that goes from the left arrow on ‘c’ round the bottom of the diagram to the other side where the ‘c’ disk rejoins the taper? This is the shadow of part of the torus, and it is precisely an offset ellipse.

    Jeff: What form would you like it in? We have it available as module that can be called from python (Ander’s has had a look at this), or do you write C++.

  • 4. Francis Irving replies at 15th February 2007, 9:40 am :

    (Haven’t read the comments yet, just giving my view of the diagram). It needs a clear title saying tapered cutter, and it needs a key. They key should say what the labelled radii mean.

    Can you make the ball section bigger, perhaps by reducing height of tapered bit? I can’t see that it is a torus at all. I can’t even remember why they’re a torus, has gone out of my head from years ago. It’s a very mathsy way of putting it. It’s actually probably easier to describe as a corner radius.

    Having some vertical measurements on the diagram would help, such as your “h”.

    Maybe label the three major sections of the diagram like this: shaft (cylinder), tapered part (truncated cone?), ball part (truncated torus / thing with corner radius?).

    To make it at all comprehensible to people who don’t do maths all the time, explicitly describe if something is truncated (e.g. when I hear “cone” I think of an entire cone standing on table, right up to its point, rather than a truncated one. Similarly for torus, I know what the word means, but it makes me think of doughnuts not bits of them cut up).

    There’s loads of design things you could do that would make it clearer but I don’t know what. Something to do with thicker lines, spacing, colouring to distinguish the three parts. Oh beats me.

  • 5. Anders replies at 15th February 2007, 5:24 pm :

    Hi again, I’m struggling a bit to get svg files to display correctly from my blog, but you can probably save the file to disk and view it that way:


  • 6. Neel D replies at 19th February 2007, 4:03 am :

    Julian did you recieve the svg files that I had sent you through mail. Can you please send me the zslice algorithm mentioned here.

    Also did you recieve the mail about Z map stock and voxel ?

  • 7. Julian replies at 19th February 2007, 9:35 am :

    I am a bit snowed under with little connection to the internet for two weeks.

    The diagrams were a good first start. I’m not really in the best position to do anything with them myself. What would be really nice is if you uploaded them to mediawiki (including the file on this page) and together we authored a section in about the geometry.

    Perhaps we could make a link to every major toolshape catalogue, like , and write a survey of what types of shapes there are and how popular. We don’t really know that this shape accounts for the majority of it.

    For the z-slicing algorithm, you need to tell me what form you can use it in. It can either come as a DLL for linking to your C++ application, or as a module you can run from Python. What do you code in? It’s not stand-alone, like the Adaptive Clearing exe we were letting people see, because that would just do the same thing, but without those inside passes.

  • 8. Neel D replies at 19th February 2007, 9:53 am :

    I can write a C++ , VC interface GUI, do you have a library which can be build and debugged to follow functions and classes in real time while the toolpath is calculated. So that the program flow can be understood.

  • 9. ›&hellip replies at 17th December 2011, 11:40 am :

    […] r the corner radius. The three basic shapes that can be defined this way are shown in the picture. A more elaborate model would include tapered cutters, but I think I won't bother with that now… A cutter thus consists of a cylindrical part or a […]

Leave a comment

XHTML: You can use these tags: <a href="" title=""> <abbr title=""> <acronym title=""> <blockquote cite=""> <code> <em> <strong>