Spirograph
{{Short description|Geometric drawing device}}
{{Use dmy dates|date=October 2020}}
{{Infobox toy
|name = Spirograph
|image = Spirograph set (UK Palitoy early 1980s) (ii) (perspective fixed).jpg
|caption = Spirograph set (early 1980s UK version)
|othernames =
|type =
|inventor = Denys Fisher
|country = United Kingdom
|company = Hasbro
|from = 1965
|to = present
|materials = Plastic
|slogan =
|website = https://www.playmonster.com/brands/spirograph/
}}
Spirograph is a geometric drawing device that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids. The well-known toy version was developed by British engineer Denys Fisher and first sold in 1965.
The name has been a registered trademark of Hasbro Inc. since 1998 following purchase of the company that had acquired the Denys Fisher company. The Spirograph brand was relaunched worldwide in 2013, with its original product configurations, by Kahootz Toys.
History
File:Spirograph2 (cropped).JPG
File:Spirograph Salesman in Kochi.jpg
In 1827, Greek-born English architect and engineer Peter Hubert Desvignes developed and advertised a "Speiragraph", a device to create elaborate spiral drawings. A man named J. Jopling soon claimed to have previously invented similar methods.{{cite web|url=https://books.google.com/books?id=ZI5fAAAAcAAJ&q=speiragraph&pg=PA361|title=Mechanics Magazine|first=John I.|last=Knight|year=1828|publisher=Knight; Lacey|via=Google Books}} When working in Vienna between 1845 and 1848, Desvignes constructed a version of the machine that would help prevent banknote forgeries,{{Cite web|url=https://collection.sciencemuseum.org.uk/objects/co60094/spirograph-and-examples-of-patterns-drawn-using-it-spirograph|title=Spirograph and examples of patterns drawn using it | Science Museum Group Collection}} as any of the nearly endless variations of roulette patterns that it could produce were extremely difficult to reverse engineer. The mathematician Bruno Abakanowicz invented a new Spirograph device between 1881 and 1900. It was used for calculating an area delimited by curves.{{cite book |url= https://books.google.com/books?id=Ri46VxE7Pc0C&pg=PA293 |title=L'Europe mathématique: histoires, mythes, identités|page=293|first1= Cathérine |last1=Goldstein |first2= Jeremy |last2= Gray |first3=Jim |last3=Ritter |publisher= Editions MSH |year= 1996 |isbn=9782735106851|access-date=17 July 2011}}
Drawing toys based on gears have been around since at least 1908, when The Marvelous Wondergraph was advertised in the Sears catalog.{{cite web |url= http://digitallibrary.imcpl.org/cdm4/document.php?CISOROOT=/tcm&CISOPTR=787&REC=4 |title=CONTENTdm Collection : Compound Object Viewer |last=Kaveney | first=Wendy |work=digitallibrary.imcpl.org |access-date=17 July 2011}}{{cite web |url= http://www.artslant.com/chi/articles/show/16968 |title=ArtSlant - Spirograph? No, MAGIC PATTERN! |first=Jim |last=Linderman |work=artslant.com |access-date=17 July 2011}} An article describing how to make a Wondergraph drawing machine appeared in the Boys Mechanic publication in 1913.{{cite web |url=http://www.marcdatabase.com/~lemur/lemur.com/library-of-antiquarian-technology/philosophical-instruments/boy-mechanic-1913/index.html#introduction |title=From The Boy Mechanic (1913) - A Wondergraph |work=marcdatabase.com |year=2004 |access-date=17 July 2011 |archive-date=30 September 2011 |archive-url=https://web.archive.org/web/20110930014649/http://www.marcdatabase.com/~lemur/lemur.com/library-of-antiquarian-technology/philosophical-instruments/boy-mechanic-1913/index.html#introduction |url-status=dead }}
The definitive Spirograph toy was developed by the British engineer Denys Fisher between 1962 and 1964 by creating drawing machines with Meccano pieces. Fisher exhibited his spirograph at the 1965 Nuremberg International Toy Fair. It was subsequently produced by his company. US distribution rights were acquired by Kenner, Inc., which introduced it to the United States market in 1966 and promoted it as a creative children's toy. Kenner later introduced Spirotot, Magnetic Spirograph, Spiroman, and various refill sets.{{cite web|last1=Coopee|first1=Todd|title=Spirograph|url=https://toytales.ca/spirograph/|website=ToyTales.ca|date=17 August 2015}}
In 2013 the Spirograph brand was re-launched worldwide, with the original gears and wheels, by Kahootz Toys. The modern products use removable putty in place of pins to hold the stationary pieces in place. The Spirograph was Toy of the Year in 1967, and Toy of the Year finalist, in two categories, in 2014. Kahootz Toys was acquired by PlayMonster LLC in 2019.{{cite web |url=https://www.playmonster.com/playmonster-expands-its-kids-arts-and-crafts-line-with-the-classic-spirograph-brand-through-its-acquisition-of-kahootz-toys/ |title=PlayMonster acquires Kahootz Toys |date=14 November 2019 |access-date=26 February 2023}}
Operation
The original US-released Spirograph consisted of two differently sized plastic rings (or stators), with gear teeth on both the inside and outside of their circumferences. Once either of these rings were held in place (either by pins, with an adhesive, or by hand) any of several provided gearwheels (or rotors)—each having holes for a ballpoint pen—could be spun around the ring to draw geometric shapes. Later, the Super-Spirograph introduced additional shapes such as rings, triangles, and straight bars. All edges of each piece have teeth to engage any other piece; smaller gears fit inside the larger rings, but they also can rotate along the rings' outside edge or even around each other. Gears can be combined in many different arrangements. Sets often included variously colored pens, which could enhance a design by switching colors, as seen in the examples shown here.
File:Spiograph Animation.gif|Animation of a Spirograph
Image:Various Spirograph Designs.jpg|Several Spirograph designs drawn with a Spirograph set using several different-colored pens
Image:Spirograph wheel number 72 (UK Palitoy early 1980s).jpg|Closeup of a Spirograph wheel
Mathematical basis
Consider a fixed outer circle of radius centered at the origin. A smaller inner circle of radius is rolling inside and is continuously tangent to it. will be assumed never to slip on (in a real Spirograph, teeth on both circles prevent such slippage). Now assume that a point lying somewhere inside is located a distance
Now mark two points
Now define the new (relative) system of coordinates
:
or equivalently,
:
It is common to assume that a counterclockwise motion corresponds to a positive change of angle and a clockwise one to a negative change of angle. A minus sign in the above formula (
Let
:
x_c &= (R - r)\cos t,\\
y_c &= (R - r)\sin t.
\end{align}
As defined above,
:
x' &= \rho\cos t',\\
y' &= \rho\sin t'.
\end{align}
In order to obtain the trajectory of
:
x &= x_c + x' = (R - r)\cos t + \rho\cos t',\\
y &= y_c + y' = (R - r)\sin t + \rho\sin t',\\
\end{align}
where
Now, use the relation between
:
x &= x_c + x' = (R - r)\cos t + \rho\cos \frac{R - r}{r}t,\\
y &= y_c + y' = (R - r)\sin t - \rho\sin \frac{R - r}{r}t\\
\end{align}
(using the fact that function
It is convenient to represent the equation above in terms of the radius
parameters describing the structure of the Spirograph. Namely, let
:
and
:
The parameter
It is now observed that
:
and therefore the trajectory equations take the form
:
x(t) &= R\left[(1 - k)\cos t + lk\cos \frac{1 - k}{k}t\right],\\
y(t) &= R\left[(1 - k)\sin t - lk\sin \frac{1 - k}{k}t\right].\\
\end{align}
Parameter
The two extreme cases
The other extreme case
If
See also
- {{anl|Apsidal precession}}
- {{anl|Cardioid}}
- {{anl|Cyclograph}}
- {{anl|Geometric lathe}}
- {{anl|Guilloché}}
- {{anl|Harmonograph}}
References
{{reflist}}
External links
- {{Official website|https://www.playmonster.com/brands/spirograph/}}
- {{cite web |url= https://www.codeproject.com/Articles/1233760/Gearographic-Curves-Part |title= Gearographic Curves |last= Voevudko |first= A. E. |date= 12 March 2018 |website= Code Project }}
{{Hasbro}}