epicyclic curve
in [SolidWorks]
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From: Brian on 24 May 2005 11:26 Even better yet. You may be able to google a working model of a toy that was around when i was young ( may still be, not sure ). It was called a spyrograph (sp?). The correct model of it would already have all the constraints necessary to create the correct motion type. "Brian" <don'tspam(a)me> wrote in message news:429346b2$1_5(a)newsfeed.slurp.net... > I don't believe there is a way to draw this in SW with 8 place > mathematical accuracy. But here is something that "may work": > > -Two simple cylinders cooresponding to the minor and major diameters > placed into an assembly with gear mates between the two and other > constraints that only allow appropriate motion > -a point on the perimeter of the smaller which will allow you to extract > its location > -create an assembly sketch and convert the above points' location, remove > the coincident constraint and make the point fixed. > -rotate the larger cylinder > -rinse and repeat > -a spline created from the generated points should give a reasonable > representation > > Creating a macro to auto-rotate the large cylinder, extract perimeter > point data, and repeat at a given increment should allow for a reasonably > high degree of accuracy > > > -- > Brian Hokanson > Starting Line Products > > "wurz" <mjs_cadman-ccsw(a)yahoo.co.uk> wrote in message > news:1116944042.503042.314790(a)g49g2000cwa.googlegroups.com... >> >> Giorgis wrote: >>> I need to draw an epicyclic curve on a sketch. >>> Any ideas on how I can go about it ? >>> >>> Kind Thanks >>> >>> Giorgis >> >> Seems like my Tech Drawing classes at school weren't a waste after all >> ;-) >> >> An epicyclic curve is the locus of a point on the perimeter of a small >> circle rolling (without slipping) around a larger circle. I'm not sure >> that there is a single mathematical expression for it - but it's one of >> those things that's easier to draw with a pair of compasses and a rule >> than on CAD..... >> >> I think that to draw it in SW, you would have to think more like a >> draughtsman and 'construct' the circles and lines, then tie together >> key quantities using equations and linked values. >> >> Might have a go at this one when I get a minute.... >> >> Martin >> > >
From: matt on 24 May 2005 12:38 In article <5eHke.2199$oT1.794(a)newsread1.news.pas.earthlink.net>, jeff4136(a)mindspring.com says... > > I need to draw an epicyclic curve on a sketch. > > Any ideas on how I can go about it ? > > Maybe this will help in the effort... > > http://mathworld.wolfram.com/Epicycloid.html With that you've got some equations. I have a macro on my website that will draw a spline for an equation. Theoretically it should be able to accept equations with periodic terms, but I've never tried one as complex as the ones on the above site. If you want to try my macro, it's at http://mysite.verizon.net/mjlombard/ , follow the link for Macro Library. It's called "eqcurve". As I remember, polar coordinates are the best way to deal with cardioid shapes. Good luck! Matt
From: TOP on 24 May 2005 14:20 Try this. Just set a and m. a is the OD of the circle around which you want an epicycloid and m is the number of cusps. Start a part. This will draw a sketch on the Front plane. ' ****************************************************************************** ' C:\DOCUME~1\kellnerp\LOCALS~1\Temp\swx2044\Macro1.swb - macro recorded on 05/24/05 by kellnerp ' ****************************************************************************** Const pi = 3.141592654 Dim swApp As Object Dim Part As Object Dim boolstatus As Boolean Dim longstatus As Long, longwarnings As Long Dim FeatureData As Object Dim Feature As Object Dim Component As Object Dim skPts() As Double Sub EpiCycloid(ByVal N As Long, ByVal a As Double, ByVal b As Double) ReDim skPts(N + 1, 3) As Double Dim i As Long Dim x, y, z As Double Dim phi, dphi As Double dphi = 2 * pi / N For i = 0 To N - 1 x = (a + b) * Cos(i * dphi) - b * Cos((a + b) / b * i * dphi) y = (a + b) * Sin(i * dphi) - b * Sin((a + b) / b * i * dphi) z = 0# skPts(i, 0) = x skPts(i, 1) = y skPts(i, 2) = z Next i x = (a + b) * Cos(0 * dphi) - b * Cos((a + b) / b * 0 * dphi) y = (a + b) * Sin(0 * dphi) - b * Sin((a + b) / b * 0 * dphi) z = 0# skPts(N, 0) = x skPts(N, 1) = y skPts(N, 2) = z End Sub Sub main() Set swApp = Application.SldWorks Set Part = swApp.ActiveDoc boolstatus = Part.Extension.SelectByID("Front Plane", "PLANE", 0, 0, 0, False, 0, Nothing) ' a is the OD of the circle around which you want the epicycloid. m is the number of cusps. a = 20# m = 6# 'Don't change anything below here. b = a / m N = 10 * m Call EpiCycloid(N, a, b) Part.InsertSketch2 True Part.ClearSelection2 True For i = N To 0 Step -1 Part.SketchSpline i, skPts(i, 0), skPts(i, 1), skPts(i, 2) Next i End Sub
From: Bob on 24 May 2005 17:35 Isn't that the equation for a face of a gear tooth (less root and crown)? If so, there maybe accurate equation based profiles around that could be modified. Bob "Giorgis" <giorgist(a)hotmail.com> wrote in message news:1116921235.326240.91240(a)g49g2000cwa.googlegroups.com... >I need to draw an epicyclic curve on a sketch. > Any ideas on how I can go about it ? > > Kind Thanks > > Giorgis >
From: Bill Chernoff on 24 May 2005 18:31
It would be nice if SW had a "locus" function, where a point could trace out a line as it moved according to a set of rules, equations, parameters, etc. Next up in complexity a generating function could carve away at an extrusion according to rules- think gear-shaper cutter generating a gear tooth profile. Bill (big ideas for someone else to implement) Chernoff |