The drawings look really cool but to really get them looking great I think I'll need to find a firmware which does some kind of interpolation between points to avoid the stop start nature of the motion (causes bleeding from the pen) and also avoid the small straight line segments between each point (rounded would be better for drawings like this). here's a closeup so you can see what I mean.

Cool frankenmachine! Patterns like the ones I've been drawing are modeled on the mechanism shown in the video but is more fun to see the mechanism in action I suppose.
As for generating on the board itself that's definitely possible. The external software generation allows for a preview of what will be drawn though which is useful. There are a lot of less interesting patterns in guilloche space. But then again the mechanical machine doesn't offer any previews and produces great drawings. I'd love to help get a firmware guilloche method in there - the maths is all here already in my code

VB.net code for generating the curve is as below. Its based on the solution to a 4 bar linkage given here http://synthetica.eng.uci.edu/~mccarthy/mechanicaldesign101/McCarthyNotes-2.pdf

        Dim list As New PointPairList
        Dim list2 As New PointPairList
        Dim list3 As New PointPairList


        Dim i As Integer, m1x As Double, m1y As Double, m2x As Double, m2y As Double


        Dim t As Double = 0

        Dim period1 As Double = Convert.ToDouble(M1Textbox.Text)
        Dim period2 As Double = Convert.ToDouble(M2Textbox.Text)
        Dim period3 As Double = Convert.ToDouble(M3Textbox.Text)

        Dim m1center(,) As Double = New Double(,) {{Convert.ToDouble(M1XTextbox.Text), Convert.ToDouble(M1YTextbox.Text)}}
        Dim m2center(,) As Double = New Double(,) {{Convert.ToDouble(M2XTextbox.Text), Convert.ToDouble(M2YTextbox.Text)}}
        Dim m3center(,) As Double = New Double(,) {{Convert.ToDouble(M3XTextbox.Text), Convert.ToDouble(M3YTextbox.Text)}}

        Dim TimeStep As Double = Convert.ToDouble(TStepTextbox.Text)
        Iterations = Convert.ToDouble(IterationsTextBox.Text)
        For i = 0 To Iterations

            Dim theta2 As Double = 2 * PI * (t / period1)



            Dim k1 As Double, k2 As Double, k3 As Double, alength As Double, blength As Double, clength As Double, dlength As Double

            alength = Convert.ToDouble(aLengthTextbox.Text) ' M1 radius
            blength = Convert.ToDouble(bLengthTextbox.Text) 'link lengths
            clength = Convert.ToDouble(cLengthTextbox.Text)
            dlength = Sqrt((m2center(0, 0) - m1center(0, 0)) ^ 2 + (m2center(0, 1) - m1center(0, 1)) ^ 2) 'distance between motors

            Dim radius2 As Double = 80 'M2 radius
            radius2 = Convert.ToDouble(M2LengthTextbox.Text) ' M1 radius 'M2 radius

            k1 = dlength / alength
            k2 = dlength / clength
            k3 = ((alength ^ 2) + (clength ^ 2) + (dlength ^ 2) - (blength ^ 2)) / (2 * alength * clength)

            'calculate the motor positions
            m1x = alength * Cos(theta2) + m1center(0, 0)
            m1y = alength * Sin(theta2) + m1center(0, 1)
            m2x = -radius2 * Cos(2 * PI * (t / period2)) + m2center(0, 0)
            m2y = -radius2 * Sin(2 * PI * (t / period2)) + m2center(0, 1)


            'calculate the linkage position

            list.Add(m1x, m1y)
            list2.Add(m2x, m2y)

            Dim Cterm As Double = k1 - (k2 + 1) * Cos(theta2) + k3
            Dim Bterm As Double = -2 * Sin(theta2)
            Dim Aterm As Double = Cos(theta2) - k1 - k2 * Cos(theta2) + k3

            Dim Theta4 As Double = 2 * Atan(-Bterm - Sqrt(Bterm ^ 2 - 4 * Aterm * Cterm)) + PI / 4

            Dim xlink As Double = clength * Cos(Theta4) + m2x
            Dim ylink As Double = clength * Sin(Theta4) + m2y

            list3.Add(xlink, ylink)

            Dim m3radius As Double = Sqrt((xlink - m3center(0, 0)) ^ 2 + (ylink - m3center(0, 1)) ^ 2) 'find the radius of the wheel center to the linkage

            Dim wheelangle As Double = Asin((ylink - m3center(0, 1)) / m3radius)

            Dim wheelRotated As Double = wheelangle + (t / period3) * 2 * PI

            Dim xpen As Double = m3radius * Cos(wheelRotated) + m3center(0, 0)
            Dim ypen As Double = m3radius * Sin(wheelRotated) + m3center(0, 1)

            list4.Add(xpen, ypen)

            If i = 0 Then
                xmin = xpen
                ymin = ypen
            End If

            If xpen < xmin Then
                xmin = xpen
            End If
            If xpen > xmax Then
                xmax = xpen
            End If
            If ypen < ymin Then
                ymin = ypen
            End If
            If ypen > ymax Then
                ymax = ypen
            End If

            xrange = Abs(xmax - xmin)
            yrange = Abs(ymax - ymin)

            XPointList.Add(xpen) 'generate list for pinting svg with seperating , between x and y and spaces between points
            YPointList.Add(ypen)
            'save as datatable for svgC

            'PlotData.Columns.Add("x", GetType(Double))
            'PlotData.Columns.Add("y", GetType(Double))
            'PlotData.Rows.Add(xpen, ypen)

            t = t + TimeStep
        Next i

These look amazing - thanks for posting about it! Do you have to do much work to linuxcnc to get it running with this coordinates system?

sn

Nothing very clever exactly, but lots of variations on what you'd expect. Beads, magnets, conductive foil and springs. Funnily enough, I just posted this video (https://plus.google.com/108985599431112054442/posts/ispShq8BLtk) that shows my own, first ever homing routine. This uses reed switches and little magnetic beads. I'm not sure if I will stay with this, but I've got a few other options.

Just closing the loop - this needs to be a robust machine that will keep its calibration even with rough handling.

That's a rather handsome idler wheel and switch holder! Good solution. I'm constantly oscillating between thinking the beaded cord is a great idea, or a real pain... Can I ask what made you try it out again?

sn