The Original Spirograph CLC03111 Design Set,18 x 1 x 13 centimeters

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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. Now, use the relation between t {\displaystyle t} and t ′ {\displaystyle t'} as derived above to obtain equations describing the trajectory of point A {\displaystyle A} in terms of a single parameter t {\displaystyle t} : or purse and store everything you need, though you’d need to replace the paper often. These are by far the most portable sets, but even large Spirograph sets are designed with portability in mind. They come with a carrying case in which to store wheels, pens, and paper so you can make art anywhere. Spirograph set features Most Spirograph sets have plastic wheels, but there are a few out there with metal wheels. Of course, metal is more durable than plastic, but metal is heavier to carry, and sets with metal wheels usually have fewer wheels for the price.

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). 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). It is convenient to represent the equation above in terms of the radius R {\displaystyle R} of C o {\displaystyle C_{o}} and dimensionless

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If l = 1 {\displaystyle l=1} , then the point A {\displaystyle A} is on the circumference of C i {\displaystyle C_{i}} . In this case the trajectories are called hypocycloids and the equations above reduce to those for a hypocycloid. x = x c + x ′ = ( R − r ) cos ⁡ t + ρ cos ⁡ t ′ , y = y c + y ′ = ( R − r ) sin ⁡ t + ρ sin ⁡ t ′ , {\displaystyle {\begin{aligned}x&=x_{c}+x'=(R-r)\cos t+\rho \cos t',\\y&=y_{c}+y'=(R-r)\sin t+\rho \sin t',\\\end{aligned}}} 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.) x c = ( R − r ) cos ⁡ t , y c = ( R − r ) sin ⁡ t . {\displaystyle {\begin{aligned}x_{c}&=(R-r)\cos t,\\y_{c}&=(R-r)\sin t.\end{aligned}}} Drawing toys based on gears have been around since at least 1908, when The Marvelous Wondergraph was advertised in the Sears catalog. [4] [5] An article describing how to make a Wondergraph drawing machine appeared in the Boys Mechanic publication in 1913. [6]

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: Spirograph sets come with at least one pen; some sets include two or three. By using the pens included with the set, you’re assured that they will fit in the wheel holes. However, you can use any pen or pencil that fits in the wheel hole, whether it came with the set or not. 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. Parameter R {\displaystyle R} is a scaling parameter and does not affect the structure of the Spirograph. Different values of R {\displaystyle R} would yield similar Spirograph drawings.

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x = x c + x ′ = ( R − r ) cos ⁡ t + ρ cos ⁡ R − r r t , y = y c + y ′ = ( R − r ) sin ⁡ t − ρ sin ⁡ R − r r t {\displaystyle {\begin{aligned}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{aligned}}} x ′ = ρ cos ⁡ t ′ , y ′ = ρ sin ⁡ t ′ . {\displaystyle {\begin{aligned}x'&=\rho \cos t',\\y'&=\rho \sin t'.\end{aligned}}} 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. [7]