The two extreme cases k = 0 {\displaystyle k=0} and k = 1 {\displaystyle k=1} result in degenerate trajectories of the Spirograph. In the first extreme case, when k = 0 {\displaystyle k=0} , we have a simple circle of radius R {\displaystyle R} , corresponding to the case where C i {\displaystyle C_{i}} has been shrunk into a point. (Division by k = 0 {\displaystyle k=0} in the formula is not a problem, since both sin {\displaystyle \sin } and cos {\displaystyle \cos } are bounded functions.) In your final illustration, I believe your 52- and 60-tooth patterns are swapped if the outer gear is the same throughout. Reply Please note, anything below is simply from my research online. I may have got some facts or dates wrong. If this is the case please do get in touch - I am always happy to be corrected!++ While many will have played with it and produced some interesting patterns, and presumably also had a vague sense that some maths is happening, I suspect many won’t have thought about it too hard. I certainly didn’t, until recently when someone gave me a mini-Spirograph kit as a gift. This inspired me to dig a little deeper into how this thing works, and what kind of shapes you can make with it. Looping the loop

Spirograph Deluxe Set – PlayMonster UK Spirograph Deluxe Set – PlayMonster UK

Spirographs can produce a multitude of different interesting and intricate patterns, but did you know that these patterns have a special name? The geometric drawings that a Spirograph makes are mathematical curves known as epitrochoids and hypotrochoids. The second one of these – where inside the small circle the pen-hole is – is also a bit more information than we need. Since the orientation of the small circle will change as it goes round the big circle, the only thing that matters about the position of the pen is how far away from the centre it is. That is, if you have two holes on the cog which are the same distance from the centre of the cog, they’ll both draw the same pattern, even if you start from the same place – again, it just might be rotated around, as you’ll be starting from a different point along the line. In 1827, Greek-born English architect and engineer Peter Hubert Desvignes developed and advertised a "Speiragraph", a device to create elaborate spiral drawings. 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 invented a new Spirograph device between 1881 and 1900, which 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 . An article describing how to make a Wondergraph drawing machine appeared in the Boys Mechanic publication in 1913. Every design moves in a different way with each of the rotating light effects. The design and animation possibilities are endless! Since it was first launched in 1965, Spirograph has made it possible for aspiring artists of all ages to create beautifully intricate designs.

Shaped wheels: Shaped wheels come in a wide variety of shapes, including bar, quad, triangle, and oval. Like the round wheels, shaped versions also have multiple holes to vary the design. A Spirograph is a geometric drawing toy that originates from the Victorian era. Mathematician Bruno Abdank-Abakanowicz first invented the Spirograph sometime between 1881 and 1900, as a way of drawing spirals. But the Spirograph that we know and love today, was developed by engineer Denys Fisher in the mid-sixties, and was advertised as a way to draw “a million marvellous patterns”. Which, given the number of combinations possible, isn’t far from the truth! How does a Spirograph work?

Spirograph Design Set | Smyths Toys UK Spirograph Design Set | Smyths Toys UK

The parameter 0 ≤ l ≤ 1 {\displaystyle 0\leq l\leq 1} represents how far the point A {\displaystyle A} is located from the center of C i {\displaystyle C_{i}} . At the same time, 0 ≤ k ≤ 1 {\displaystyle 0\leq k\leq 1} represents how big the inner circle C i {\displaystyle C_{i}} is with respect to the outer one C o {\displaystyle C_{o}} .The Spirograph has been around since the mid 60s, putting it firmly in the class of being a 'retro' toy, but it's never really gone out of fashion. The clever cog and ring design can help even the most art-shy user create stunning patterns just by having a steady hand. A wheel must be placed inside a stationary plate or ring for designs to be drawn. Each plate needs to be held in place with Spiro-putty, magnets, or pins. Sets come with one of these three options (except for travel sets, which have a plate built into the lid). Fisher developed various drawing machines from Meccano pieces, eventually producing a prototype Spirograph . Patented in 16 countries, it went on sale in Schofields department store in Leeds in 1965. A year later, Fisher licensed Spirograph to Kenner Products in the United States . In 1967 Spirograph was chosen as the UK Toy of the Year. Wheels create the magic. Toothed edges and strategically placed holes provide multiple design options with each wheel. Spirograph sets come with anywhere from six to 25 wheels with the following options. Depending on the relative circle sizes and the pen-hole distance, you’ll get various different types of shape – some closer to the pointy hypocycloid, and some closer to a circle; when the hole is near to, but not on the edge, the pointy ends become thin loops; when the hole is close to, but not at the centre, it’s like drawing a circle but slightly missing where you started, so you get something fairly smooth but that wiggles in and out from the centre gently. Spirograph drawings from the outside hole to the middle hole, on the same size cog

Spirograph Travel Set | The Entertainer Spirograph Travel Set | The Entertainer

They're based in convenient locations including supermarkets, newsagents and train stations. Plus they're often open late and on Sundays.As with many inventions, it’s hard to pinpoint who exactly came up with the idea for a Spirograph, but we can look to a few different people as potential inventors. The first person we can look at is Johann Samuel Eberhardt, a Swiss mathematician who published a paper in 1843 titled “New and Useful Design for a Drawing Instrument.” Now, the device in Eberhardt’s paper didn’t look anything like a Spirograph, but he was the first person to ever imagine a design for a drawing device that used a “worm” to create line patterns. The second person we can look to is Henry Philpotts, an Englishman who patented a device in 1846 that used a similar design to Eberhardt’s.

Asda Groceries Asda Groceries

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. [8] Operation [ edit ] Animation of a Spirograph Several Spirograph designs drawn with a Spirograph set using several different-colored pens Closeup of a Spirograph wheel When starting out with a new configuration, take it slow. Keep the rotations as slow as possible to allow the muscle memory in your hand to develop. Then gradually increase speed as you feel more confident with that configuration. Should it not be ‘R = 7/2 r’ in the 5th paragraph of the ‘How Many Points?’ section? Otherwise R < r His company, Denys Fisher Toys, was sold to Palitoy in 1970 which was then bought by Hasbro . Through the 1980s and 1990s, Fisher continued to work with Hasbro in developing new toys and refining Spirograph. It has since been sold by Kahootz toys, and most recently, Playmonster.Patterns can be made using both hands, though it may take some practice. If you really want to be creative, try drawing a single picture with the help of another person. You can get several wheels going around the same plate to make something truly unique. Spirograph set size and portability While I can’t pinpoint exactly who invented the Spirograph, I found out about spiral drawing devices as the inspiration behind the toy. Popular in the late 18th century, these spiral devices used a rotating pencil to create spiralling patterns. Although they don’t look like a Spirograph and weren’t as popular, they were the first device to ever use a worm to create line patterns. 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). Let ( x c , y c ) {\displaystyle (x_{c},y_{c})} be the coordinates of the center of C i {\displaystyle C_{i}} in the absolute system of coordinates. Then R − r {\displaystyle R-r} represents the radius of the trajectory of the center of C i {\displaystyle C_{i}} , which (again in the absolute system) undergoes circular motion thus: