[math-fun] Somsky and Spirograph
I believe we can make a set of Somsky rigid planetary gears that work using an original Spirograph set. This set includes wheels of size 24, 30, 32, 40, and 42, and a ring of size 96. Putting this together you should be able to use a sun of size 24 and four sets of planet gears 30+42 and 32+40. I believe this is the only combination that works with the default set of gears. It's quite possible there isn't enough space to do this without the gears overlapping. But it would be fun to try. Does anyone have an original Spirograph set? -- -- http://cube20.org/ -- [Golly link suppressed; ask me why] --
Not sure what "four sets of planet gears" means here. Anyway, I compute that it is impossible to mesh 3 distinct planet radii from this set exactly with the sun and ring. WFL On 7/21/15, Tom Rokicki <rokicki@gmail.com> wrote:
I believe we can make a set of Somsky rigid planetary gears that work using an original Spirograph set.
This set includes wheels of size 24, 30, 32, 40, and 42, and a ring of size 96. Putting this together you should be able to use a sun of size 24 and four sets of planet gears 30+42 and 32+40. I believe this is the only combination that works with the default set of gears.
It's quite possible there isn't enough space to do this without the gears overlapping. But it would be fun to try.
Does anyone have an original Spirograph set?
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Retraction --- bug detected! WFL On 7/21/15, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Not sure what "four sets of planet gears" means here.
Anyway, I compute that it is impossible to mesh 3 distinct planet radii from this set exactly with the sun and ring.
WFL
On 7/21/15, Tom Rokicki <rokicki@gmail.com> wrote:
I believe we can make a set of Somsky rigid planetary gears that work using an original Spirograph set.
This set includes wheels of size 24, 30, 32, 40, and 42, and a ring of size 96. Putting this together you should be able to use a sun of size 24 and four sets of planet gears 30+42 and 32+40. I believe this is the only combination that works with the default set of gears.
It's quite possible there isn't enough space to do this without the gears overlapping. But it would be fun to try.
Does anyone have an original Spirograph set?
-- -- http://cube20.org/ -- [Golly link suppressed; ask me why] --
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This is, I believe, a perfectly meshed Spirograph/Somsky solution. I'm not positive the real plastic pieces will have gears small enough to prevent clashing, but the math seems to work. On Tue, Jul 21, 2015 at 5:00 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Retraction --- bug detected! WFL
On 7/21/15, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Not sure what "four sets of planet gears" means here.
Anyway, I compute that it is impossible to mesh 3 distinct planet radii from this set exactly with the sun and ring.
WFL
On 7/21/15, Tom Rokicki <rokicki@gmail.com> wrote:
I believe we can make a set of Somsky rigid planetary gears that work using an original Spirograph set.
This set includes wheels of size 24, 30, 32, 40, and 42, and a ring of size 96. Putting this together you should be able to use a sun of size 24 and four sets of planet gears 30+42 and 32+40. I believe this is the only combination that works with the default set of gears.
It's quite possible there isn't enough space to do this without the gears overlapping. But it would be fun to try.
Does anyone have an original Spirograph set?
-- -- http://cube20.org/ -- [Golly link suppressed; ask me why] --
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Please specify -- at least roughly -- the sun centre offset and locations of planets you have in mind. With (minimum) offset 8/2pi teeth, and planets 32, 40, 42 all (somewhat impracticably) on the same side of the axis through sun 24 and ring 96 centres, I compute belt lengths 86.99579621, 47.00420379, 100, omitting first, second, third planet resp. Note alternative values arise via subtraction from the tooth sum of those gears involved. The discrepancy of one part in 10,000 could no doubt be absorbed by slack in the gears; however, this configuration at any rate seems not quite exact. Fred Lunnon On 7/21/15, Tom Rokicki <rokicki@gmail.com> wrote:
This is, I believe, a perfectly meshed Spirograph/Somsky solution.
I'm not positive the real plastic pieces will have gears small enough to prevent clashing, but the math seems to work.
On Tue, Jul 21, 2015 at 5:00 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Retraction --- bug detected! WFL
On 7/21/15, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Not sure what "four sets of planet gears" means here.
Anyway, I compute that it is impossible to mesh 3 distinct planet radii from this set exactly with the sun and ring.
WFL
On 7/21/15, Tom Rokicki <rokicki@gmail.com> wrote:
I believe we can make a set of Somsky rigid planetary gears that work using an original Spirograph set.
This set includes wheels of size 24, 30, 32, 40, and 42, and a ring of size 96. Putting this together you should be able to use a sun of size 24 and four sets of planet gears 30+42 and 32+40. I believe this is the only combination that works with the default set of gears.
It's quite possible there isn't enough space to do this without the gears overlapping. But it would be fun to try.
Does anyone have an original Spirograph set?
-- -- http://cube20.org/ -- [Golly link suppressed; ask me why] --
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Center of outer gear is at (0,0). Information below is (x, y, r, theta). Gear 0: 0 -15.2455256731227 24 0 Gear 1: -36.7084008061191 -54.8497339123657 30 1.29754164761468 Gear 2: 50.6617258475364 -39.1074102204309 32 -1.82681164698356 Gear 3: 36.7084008061191 39.6042082392429 42 0.961032493387983 Gear 4: -50.6617258475364 23.8618845473082 40 -1.58285857438843 On Wed, Jul 22, 2015 at 8:33 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Please specify -- at least roughly -- the sun centre offset and locations of planets you have in mind.
With (minimum) offset 8/2pi teeth, and planets 32, 40, 42 all (somewhat impracticably) on the same side of the axis through sun 24 and ring 96 centres, I compute belt lengths
86.99579621, 47.00420379, 100,
omitting first, second, third planet resp. Note alternative values arise via subtraction from the tooth sum of those gears involved.
The discrepancy of one part in 10,000 could no doubt be absorbed by slack in the gears; however, this configuration at any rate seems not quite exact.
Fred Lunnon
On 7/21/15, Tom Rokicki <rokicki@gmail.com> wrote:
This is, I believe, a perfectly meshed Spirograph/Somsky solution.
I'm not positive the real plastic pieces will have gears small enough to prevent clashing, but the math seems to work.
On Tue, Jul 21, 2015 at 5:00 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Retraction --- bug detected! WFL
On 7/21/15, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Not sure what "four sets of planet gears" means here.
Anyway, I compute that it is impossible to mesh 3 distinct planet radii from this set exactly with the sun and ring.
WFL
On 7/21/15, Tom Rokicki <rokicki@gmail.com> wrote:
I believe we can make a set of Somsky rigid planetary gears that work using an original Spirograph set.
This set includes wheels of size 24, 30, 32, 40, and 42, and a ring of size 96. Putting this together you should be able to use a sun of size 24 and four sets of planet gears 30+42 and 32+40. I believe this is the only combination that works with the default set of gears.
It's quite possible there isn't enough space to do this without the gears overlapping. But it would be fun to try.
Does anyone have an original Spirograph set?
-- -- http://cube20.org/ -- [Golly link suppressed; ask me why] --
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At the conclusion (oh yeah?) of an cringingly embarrassing catalogue of blunders in numerical math., prog. logic, and software & mech. eng. I have succeeded in confirming Tom Rockiki's exact Spirograph solution; and must now grovel for having previously cast doubt on it. WFL On 7/23/15, Tom Rokicki <rokicki@gmail.com> wrote:
Center of outer gear is at (0,0).
Information below is (x, y, r, theta).
Gear 0: 0 -15.2455256731227 24 0
Gear 1: -36.7084008061191 -54.8497339123657 30 1.29754164761468
Gear 2: 50.6617258475364 -39.1074102204309 32 -1.82681164698356
Gear 3: 36.7084008061191 39.6042082392429 42 0.961032493387983
Gear 4: -50.6617258475364 23.8618845473082 40 -1.58285857438843
And here it is in spirograph. http://tomas.rokicki.com/somsky-spiro.jpg (This may not be exactly the solution I calculated but it does work in plastic).
And here it is in spirograph. http://tomas.rokicki.com/somsky-spiro.jpg (This may not be exactly the solution I calculated but it does work in plastic). On Wed, Jul 22, 2015 at 8:33 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Please specify -- at least roughly -- the sun centre offset and locations of planets you have in mind.
With (minimum) offset 8/2pi teeth, and planets 32, 40, 42 all (somewhat impracticably) on the same side of the axis through sun 24 and ring 96 centres, I compute belt lengths
86.99579621, 47.00420379, 100,
omitting first, second, third planet resp. Note alternative values arise via subtraction from the tooth sum of those gears involved.
The discrepancy of one part in 10,000 could no doubt be absorbed by slack in the gears; however, this configuration at any rate seems not quite exact.
Fred Lunnon
On 7/21/15, Tom Rokicki <rokicki@gmail.com> wrote:
This is, I believe, a perfectly meshed Spirograph/Somsky solution.
I'm not positive the real plastic pieces will have gears small enough to prevent clashing, but the math seems to work.
On Tue, Jul 21, 2015 at 5:00 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Retraction --- bug detected! WFL
On 7/21/15, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Not sure what "four sets of planet gears" means here.
Anyway, I compute that it is impossible to mesh 3 distinct planet radii from this set exactly with the sun and ring.
WFL
On 7/21/15, Tom Rokicki <rokicki@gmail.com> wrote:
I believe we can make a set of Somsky rigid planetary gears that work using an original Spirograph set.
This set includes wheels of size 24, 30, 32, 40, and 42, and a ring of size 96. Putting this together you should be able to use a sun of size 24 and four sets of planet gears 30+42 and 32+40. I believe this is the only combination that works with the default set of gears.
It's quite possible there isn't enough space to do this without the gears overlapping. But it would be fun to try.
Does anyone have an original Spirograph set?
-- -- http://cube20.org/ -- [Golly link suppressed; ask me why] --
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participants (2)
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Fred Lunnon -
Tom Rokicki