Configurable Galton Board

thingiverse

This device serves as a platform for statistical experimentation and showcases concepts in combinatorics, Pascal's triangle, probability, and the binomial distribution. In operation, balls are poured through a funnel and collide with pegs along their path, with each peg determining whether the ball will land left or right until it reaches one of several bins. The number of paths leading to each bin is indicated by C(N, x), where N represents the number of rows of pegs (ranging from 1 to 8) and x takes values from 0 to N. A Pascal's triangle overlay is provided for reference and can be placed directly on the pegs or removed as needed during experiments. The Galton board allows users to adjust the number of bins, influencing the resulting binomial distribution. The device itself was created using a MakerBot Replicator 2 with PLA material and requires no additional parts or assembly. It was scaled at 80% for optimal printing within the machine's volume. For best results, heavier balls are recommended even at full size, while smaller-sized balls may need ball bearings substitution due to their lightweight nature causing bouncing. The build process involves printing four components: the board (using rafts for minimal warping), 28 pegs (rotated flat on the build plate and printed at 0.1 mm resolution), the funnel (upside down with mouth of cone on the build platform, no rafts or supports required, 0.2 mm resolution), and as many balls as possible (using rafts, 0.1 mm resolution, and maximizing density with an infill of 75%, ideally 100%). The triangle overlay is printed using rafts at 0.15 mm resolution. Assembly consists of inserting the 28 pegs into the board's square holes to form a triangle, leaving the upper two pairs of holes empty for adjusting funnel position. Care must be taken not to tighten the funnel holes excessively to avoid breaking tabs and possible sanding for smooth insertion. To use the device, plug in the funnel and drop balls into it, watching as they fall into bins while potentially making turns along the way. Adjust the board tilt to optimize performance (additional 10 degrees suggested). The leftmost and lowest funnel position corresponds to N=1 with balls landing in two bins, while the top position signifies N=8. The Pascal's triangle overlay can remain on the board during experiments or be removed for unobstructed play. Enjoy your statistical experimentation experience!