Web Gears - Part III: The Pinwheel Cog
It is no secret that males are obsessive. Proven by Readers' Digest many years ago, by tracking the infra-red pattern of blood flow when males think about a problem, the blood pretty much stays in our frontal lobe. No so for the females.

Why mention such a scientifically proven, yet completely politically incorrect fact? -Because "being born that way" is the only way that I might possibly explain my present & personal obsession with creating bewooden counters!

Submitted for your obsession therefore (or not =), here is the latest installment to what is proving to be far, far, too much fun:

`import turtle'''We need to be slightly more careful with the parameters here than in ourother demonstrations - the entire point of this rendition is to create a3-dimensional array of points that can be used for 'zBite' calculations.For things to work properly, we must therefore be sure that zStep <> zRange,as well as that zStep < zRange. Since this is an academic demo, in orderto make things a tad cleaner to read, we removed our in-code parameterchecks.The use of Cardinal slice-values is important!(see post at http://soft9000.com/blog9000/add.php?y= ... 122-020104)'''def draw_pinwheel(zSlices=10, zRange=100, zStep=10):    zt = turtle.Turtle(shape='turtle')    angle = int(360 / zSlices)    zSegs = int(zRange / zStep) + 1    locs = [[[-1 for z in range(1)] for y in range(zSegs)] for x in range(zSlices)]    zLine = 0    zt.hideturtle()    zt.color('red')    for ref in range(1, 360, angle):        zt.pendown()        zt.left(angle)        zLineSeg = 0        for zSeg in range(1, zRange + zStep, zStep):            zt.pendown()            zt.forward(zSeg)            zt.circle(1)            print(zLine, zLineSeg)            locs[zLine][zLineSeg] = [zt.pos()]            zt.penup()            zt.goto(0, 0)            zLineSeg += 1        zLine += 1        print(locs)        zt.goto(0, 0)    zt.color('black')    for zSub in range(1, zRange + zStep, zStep):        zt.right(90)        zt.forward(zSub)        zt.right(270)        zt.pendown()        zt.circle(zSub)        zt.penup()        zt.home()    zt.color('red')    for zLine in range(zSlices):        lineA = locs[zLine]        lineB = locs[0]        if zLine < (zSlices - 1):            lineB = locs[zLine + 1]        for zSeg in range(1, zSegs):            pointA = lineA[zSeg]            pointB = lineB[zSeg - 1]            zt.penup()            zt.goto(pointA[0][0], pointA[0][1])            zt.pendown()            zt.goto(pointB[0][0], pointB[0][1])    zt.penup()    zt.home()    zt.color('black')    zLoc = zRange + zStep    zt.goto(zLoc * -1, zLoc)    zt.write("draw_pinwheel(zSlices=" + str(zSlices) + ", zRange=" + str(zRange) + ", zStep=" + str(zStep) + ")")    zt.hideturtle()turtle.hideturtle()draw_pinwheel(zSlices=10, zRange=200, zStep=100)turtle.getscreen()._root.mainloop()`

We can cut along the red lines to make our pinwheel cog:

Of course, for those of us who feel the need to try various sizes on-the-fly, we retained that distinctive variable-sized 'Web-Gear flavoring:

When working with wood, squaring off a cog often makes for a less brittle latch point:

Next, note the use of a 3-dimensional array:

`locs =    [[[-1 for z in range(1)]      for y in range(zSegs)]        for x in range(zSlices)]...    for zLine in range(zSlices):        lineA = locs[zLine]        lineB = locs[0]        if zLine < (zSlices - 1):            lineB = locs[zLine + 1]        for zSeg in range(1, zSegs):            pointA = lineA[zSeg]            pointB = lineB[zSeg - 1]            zt.penup()            zt.goto(pointA[0][0], pointA[0][1])            zt.pendown()            zt.goto(pointB[0][0], pointB[0][1])`

For those whom might not be used to working with multi-dimensional array complexity, I added the print statements to the code for your 'edutational enjoyment.

From a re-use point of view (no pun intended,) note that one can use this array of points for drawing any type of shape (circles for classic cogs, triangles for gears, etc.)

## Cardinal Cog Locations

After a little experimentation, one will discover that not all slices are created equal!

When one is interested in precise pin locations (when aren't we?) then one will have to be sure that the number of slices requested are even whole-circle multiples:

`prime_slices = set()for slices in range(1, 100):    if 360 % slices is 0:        prime_slices.add(slices)        print("Prime slice", slices)print("There are", len(prime_slices), " proper slices")`

For steam-punkers there can some joy to be seen when non-cardinal slice values are used. For the purposes of this simulation however, please note that we should confine our pinwheel cog slice-requests to one of the primary / cardinal cog values.

For example, given the above primary-slice circle-test, note that out of 99 possible slice selections:

`Prime slice 1Prime slice 2 (impeller)Prime slice 3Prime slice 4Prime slice 5Prime slice 6Prime slice 8Prime slice 9Prime slice 10Prime slice 12 (hours)Prime slice 15Prime slice 18Prime slice 20Prime slice 24Prime slice 30Prime slice 36Prime slice 40Prime slice 45Prime slice 60Prime slice 72Prime slice 90There are 21  proper slices`

Discover also - within our present obsession (counters & clocks) - that the above set of cardinal-slice values under 100 are simply perfect for our needs.

Ultimately however, for those who feel no need to allow several cogs to be cut for a single pattern, here is the simplified version:

`import turtle'''We need to be slightly more careful with the parameters here than in ourother demonstrations - the entire point of this rendition is to create a3-dimensional array of points that can be used for 'zBite' calculations.The use of Cardinal slice-values is important!(see post at http://soft9000.com/blog9000/add.php?y= ... 122-020104)For things to work properly, we must therefore be sure that zStep <> zRange,as well as that zStep < zRange. Since this is an academic demo, in orderto make things a tad cleaner to read, we removed our in-code parameterchecks.'''def draw_pin_wheel(zSlices=10, zRange=100, zBite=-1, zSmile=False):    zt = turtle.Turtle(shape='turtle')    angle = int(360 / zSlices)    locs = [[[-1 for z in range(1)] for y in range(2)] for x in range(zSlices)]    if zBite <=0:        zBite = int(zRange / 10)    zLine = 0    zt.hideturtle()    for ref in range(1, 360, angle):        zt.left(angle)        zt.forward(zRange)        zt.circle(1)        locs[zLine][1] = zt.pos()        zt.back(zBite)        locs[zLine][0] = zt.pos()        zt.circle(1)        zt.goto(0, 0)        print(locs[zLine])        zLine += 1    if zSmile:        zt.home()        zt.begin_fill()        for line in range(len(locs)):            zt.penup()            listA = locs[line][0]            zt.goto(listA[0], listA[1])            zt.pendown()            listB = locs[0][0]            if line < zSlices - 1:                listB = locs[line + 1][0]            # Hex-draw the inner 'circle'            zt.goto(listB[0], listB[1])            zt.goto(listA[0], listA[1])        zt.end_fill()    zt.home()    zt.color('red')    for line in range(len(locs)):        zt.penup()        listA = locs[line][0]        zt.goto(listA[0], listA[1])        zt.pendown()        listB = locs[0][1]        if line < zSlices - 1:            listB = locs[line + 1][1]        # Cut-draw the outer 'cut'        zt.goto(listB[0], listB[1])        zt.goto(listA[0], listA[1])    zt.penup()    zt.color('black')    zLoc = zRange + zBite    zt.goto(zLoc * -1, zLoc)    zt.write("draw_pin_wheel(zSlices=" + str(zSlices) + ", zRange=" + str(zRange) + ", zBite=" + str(zBite) + ")")    zt.hideturtle()turtle.hideturtle()draw_pin_wheel(zSlices=10, zRange=100, zBite=30, zSmile=True)turtle.getscreen()._root.mainloop()`

Surely looking allot cleaner, the need to colorize the final pattern is suddenly not-so-much:

Note that 'zBite' is also back, as well as entirely optional.