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What do you call this rolling circle curve?

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  • What do you call this rolling circle curve?

    Picture a round disk rolling on a plane. there's a fixed point in space the scribes a mark in the disk as it rolls by. In this case, the fixed point is around 1/2 way between the plane and disks centre and the shape of the curve it makes is reminiscent of a horse shoe.

    What's the curve called so I can research it? I need to be able to draw it and burn it/machine it as a slot.

    Thanks
    in Toronto Ontario - where are you?

  • #2
    try 'trochoid' maybe 'cycloid', it's been a while.

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    • #3
      Thanks Tony. One more thing to add to the memory bank for future use.

      http://web.calstatela.edu/curvebank/...ds/oideg1.html

      Dan
      At the end of the project, there is a profound difference between spare parts and left over parts.

      Location: SF East Bay.

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      • #4
        Thanks for the link Dan - just bookmarked it!

        Best wishes to ya’ll.

        Sincerely,

        Jim

        "To invent you need a good imagination and a pile of junk" - Thomas Edison

        "I've always wanted to get a job as a procrastinator but I keep putting off going out to find one so I guess I'll never realize my life's dream. Frustrating!" - Me

        Location: Bustling N.E. Arizona

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        • #5
          I was a bit disappointed that the examples did not exist anymore, however I beleive that the locus of a point on a rolling circle along a plane was a trochoid, funny name-oid.
          Oddly or coincidentally a Celtic neck band was called a torc, also horseshoe like
          (Haven't found one in the garden yet)
          Mark

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          • #6
            Wikipedia has a good explanation, including diagrams, of the many forms of the trochoid...

            https://en.wikipedia.org/wiki/Trochoid

            including the equations that describe the curves, which may be of help to the OP in generating his curve.
            Regards, Marv

            Home Shop Freeware - Tools for People Who Build Things
            http://www.myvirtualnetwork.com/mklotz

            Location: LA, CA, USA

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            • #7
              Originally posted by boslab View Post
              I was a bit disappointed that the examples did not exist anymore, however I beleive that the locus of a point on a rolling circle along a plane was a trochoid, funny name-oid.
              Oddly or coincidentally a Celtic neck band was called a torc, also horseshoe like
              (Haven't found one in the garden yet)
              Mark
              Cursor further down the page for moving examples.

              Mike

              Comment


              • #8
                I'm look for the curved line a fixed point would trace on the disk as the disk rolls by - like this horse shoe slot in this self dumping hopper.

                https://images.uline.com/is/image//c.../HD09_6779.jpg
                in Toronto Ontario - where are you?

                Comment


                • #9
                  Boy, that's a new one for me. I never saw that curve described before.

                  I suspect the designers of that hopper just traced the location of points on the curve one by one and connected them with a smooth, curved line.



                  Originally posted by Mcgyver View Post
                  I'm look for the curved line a fixed point would trace on the disk as the disk rolls by - like this horse shoe slot in this self dumping hopper.

                  https://images.uline.com/is/image//c.../HD09_6779.jpg
                  Paul A.
                  SE Texas

                  And if you look REAL close at an analog signal,
                  You will find that it has discrete steps.

                  Comment


                  • #10
                    Reminds me of the Spirograph kit I had as a kid. Drew all those examples hypotrochoids,epicycloids etc.
                    West Sussex UK

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                    • #11
                      When I did Technical Drawing back in the 60s we were taught how to construct these curves. The point on the edge of the circle gave a different shape to a point set in from the edge. Also a properly formed gear tooth is shaped as part of a cycloidal curve.

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                      • #12
                        Originally posted by Normanv View Post
                        When I did Technical Drawing back in the 60s we were taught how to construct these curves. The point on the edge of the circle gave a different shape to a point set in from the edge. Also a properly formed gear tooth is shaped as part of a cycloidal curve.
                        We were really lucky at the school I went, there was technical drawing, building drawing and geometric and engineering drawing, I picked all three but was told "they are all in the same group, pick one", I did and got thrown out of music and art so I was free to swap, I did not set fire to the music teachers piano while she was playing it, but I never denied it.
                        The headmaster knew it wasn't me but let it go.
                        Tee squares and compasses, building drawing was way more interesting than I thought, ionic, Corinthian and all that, drawing acanthus leaf capitals and arches, great.
                        They don't teach much at school these days.
                        Mark

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                        • #13
                          I have heard the combustion chamber of a Wankel rotary engine described as an epitrochoid and that could be described as two horse shoes with the ends butted together so it sounds plausible that a trochoid could be just one horse shoe. Dunno.

                          Sent from my SM-G900V using Tapatalk

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                          • #14
                            Originally posted by Paul Alciatore View Post
                            Boy, that's a new one for me. I never saw that curve described before.
                            .
                            my bring bright young just graduated engineer figured it out and drew it and probably has burned a test one by now. He started to explain how but by then I was trying figure out who could fix one of the trucks and getting ready for a customer visit (its great gig for attention deficient).
                            in Toronto Ontario - where are you?

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