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

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holes. You can use the inside or outside of the ring. Then turn the smaller cog, using the pen. This will draw a pattern

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}}} 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). We were sent these Spirograph sets for the purposes of this post. All images and opinions are our own.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. 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.

Keep your pen as vertical as possible when drawing, as this will help the gears to move around the ring as smoothly as possible. cogs then the original, but the concept looks the same - see the Original Spirograph More on SpirographWith just one cog and one ring and the pen in position 1, the patterns varied between just two points in an elipse In 1981 Denys Fisher himself developed another drawing toy called Cyclex. Cyclex was based on advanced trigonometry. On the box 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}}}