Spirograph is a
geometric
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
drawing device that produces mathematical
roulette
Roulette is a casino game named after the French word meaning ''little wheel'' which was likely developed from the Italian game Biribi''.'' In the game, a player may choose to place a bet on a single number, various groupings of numbers, the ...
curves of the variety technically known as
hypotrochoid
In geometry, a hypotrochoid is a roulette traced by a point attached to a circle of radius rolling around the inside of a fixed circle of radius , where the point is a distance from the center of the interior circle.
The parametric equations f ...
s and
epitrochoid
In geometry, an epitrochoid ( or ) is a roulette traced by a point attached to a circle of radius rolling around the outside of a fixed circle of radius , where the point is at a distance from the center of the exterior circle.
The parametric ...
s. The well-known toy version was developed by British engineer
Denys Fisher
Denys Fisher (11 May 1918 – 17 September 2002) was an English engineer who invented the spirograph toy and created the company Denys Fisher Toys.
He left Leeds University to join the family firmKingfisher (Lubrication) Ltd In 1960 he left the ...
and first sold in 1965.
The name has been a registered
trademark
A trademark (also written trade mark or trade-mark) is a type of intellectual property consisting of a recognizable sign, design, or expression that identifies products or services from a particular source and distinguishes them from others ...
of
Hasbro
Hasbro, Inc. (; a syllabic abbreviation of its original name, Hassenfeld Brothers) is an American multinational conglomerate holding company incorporated and headquartered in Pawtucket, Rhode Island. Hasbro owns the trademarks and products of ...
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
Kahootz Toys was a toy company based in Ann Arbor, Michigan, best known for the relaunch of the classic toy Spirograph.
Kahootz founded in January 2012 by Doug Cass, Colleen Loughman, Joe Yassay, and Brent Oeschger after their previous company, Gi ...
.
History
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. When working in Vienna between 1845 and 1848, Desvignes constructed a version of the machine that would help prevent banknote forgeries, as any of the nearly endless variations of roulette patterns that it could produce were extremely difficult to reverse engineer. The mathematician
Bruno Abakanowicz
Bruno Abdank-Abakanowicz (6 October 1852 – 29 August 1900) was a Polish mathematician, inventor, and electrical engineer.
Life
Abakanowicz was born in 1852 in the Russian Empire (now Lithuania). After graduating from the Riga Technical Univ ...
invented a new Spirograph device between 1881 and 1900. It was used for calculating an area delimited by curves.
Drawing toys based on gears have been around since at least 1908, when The Marvelous Wondergraph was advertised in the
Sears catalog
Sears, Roebuck and Co. ( ), commonly known as Sears, is an American chain of department stores founded in 1892 by Richard Warren Sears and Alvah Curtis Roebuck and reincorporated in 1906 by Richard Sears and Julius Rosenwald, with what began a ...
. An article describing how to make a Wondergraph drawing machine appeared in the ''Boys Mechanic'' publication in 1913.
The definitive Spirograph toy was developed by the British engineer
Denys Fisher
Denys Fisher (11 May 1918 – 17 September 2002) was an English engineer who invented the spirograph toy and created the company Denys Fisher Toys.
He left Leeds University to join the family firmKingfisher (Lubrication) Ltd In 1960 he left the ...
between 1962 and 1964 by creating drawing machines with
Meccano
Meccano is a brand of scale model, model construction system created in 1898 by Frank Hornby in Liverpool, England. The system consists of reusable metal strips, plates, Structural steel#Common structural shapes, angle girders, wheels, axles and ...
pieces. Fisher exhibited his spirograph at the 1965
Nuremberg International Toy Fair
The Nuremberg International Toy Fair ( German: ''Spielwarenmesse''), held annually since 1949, is the largest international trade fair for toys and games. Only trade visitors associated with the toy business, journalists and invited guests are ...
. It was subsequently produced by his company. US distribution rights were acquired by
Kenner
Kenner Products, known simply as Kenner, was an American toy company founded in 1946. Throughout its history, the Kenner brand produced several highly recognizable toys and merchandise lines including action figures like the original series of ' ...
, 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.
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.
Operation
The original US-released Spirograph consisted of two differently sized plastic rings (or
stator
The stator is the stationary part of a rotary system, found in electric generators, electric motors, sirens, mud motors or biological rotors. Energy flows through a stator to or from the rotating component of the system. In an electric mot ...
s), 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
A ballpoint pen, also known as a biro (British English), ball pen (Hong Kong, Indian and Philippine English), or dot pen ( Nepali) is a pen that dispenses ink (usually in paste form) over a metal ball at its point, i.e. over a "ball point". ...
—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.
Beginners often slip the gears, especially when using the holes near the edge of the larger wheels, resulting in broken or irregular lines. Experienced users may learn to move several pieces in relation to each other (say, the triangle around the ring, with a circle "climbing" from the ring onto the triangle).
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