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

Product Information

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}}} 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 The other extreme case k = 1 {\displaystyle k=1} corresponds to the inner circle C i {\displaystyle C_{i}} 's radius r {\displaystyle r} matching the radius R {\displaystyle R} of the outer circle C o {\displaystyle C_{o}} , i.e. r = R {\displaystyle r=R} . In this case the trajectory is a single point. Intuitively, C i {\displaystyle C_{i}} is too large to roll inside the same-sized C o {\displaystyle C_{o}} without slipping.

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] 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 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. 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. 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]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. 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.

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. 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

Spirograph set features

x ′ = ρ cos ⁡ t ′ , y ′ = ρ sin ⁡ t ′ . {\displaystyle {\begin{aligned}x'&=\rho \cos t',\\y'&=\rho \sin t'.\end{aligned}}} 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} : 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).

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). Round wheels: These basic wheels are probably the type with which you are familiar. They may have five to 35 holes. Each hole will create a slightly different pattern using the same wheel. As defined above, t ′ {\displaystyle t'} is the angle of rotation in the new relative system. Because point A {\displaystyle A} obeys the usual law of circular motion, its coordinates in the new relative coordinate system ( x ′ , y ′ ) {\displaystyle (x',y')} areNow define the new (relative) system of coordinates ( X ′ , Y ′ ) {\displaystyle (X',Y')} with its origin at the center of C i {\displaystyle C_{i}} and its axes parallel to X {\displaystyle X} and Y {\displaystyle Y} . Let the parameter t {\displaystyle t} be the angle by which the tangent point T {\displaystyle T} rotates on C o {\displaystyle C_{o}} , and t ′ {\displaystyle t'} be the angle by which C i {\displaystyle C_{i}} rotates (i.e. by which B {\displaystyle B} travels) in the relative system of coordinates. Because there is no slipping, the distances traveled by B {\displaystyle B} and T {\displaystyle T} along their respective circles must be the same, therefore x ( t ) = R [ ( 1 − k ) cos ⁡ t + l k cos ⁡ 1 − k k t ] , y ( t ) = R [ ( 1 − k ) sin ⁡ t − l k sin ⁡ 1 − k k t ] . {\displaystyle {\begin{aligned}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{aligned}}}