It's not often that LEGO releases a new part that fills a significant gap in their inventory but, this year, the release of the 11x11 Circular Gear Rack has filled a gap in the Technic range of parts.
Earlier in the month, Huw outlined the new Technic parts for 2016. This article looks at the geometry of this new part, and how it can be incorporated into your Technic models.
Technic aficionados, and anyone else interested in the geometry of LEGO parts can read on to see how versatile this new part will be.
As the part name implies, this new part occupies an 11M square. Four of these parts can be joined together to make a circle rack 21M in diameter.
A second hexagon can be inscribed on the circumference, giving 12 equally spaced vertices.
Taken to the extreme, there are 24 equally spaced holes on the circumference. Any regular polygon can be made where the number of sides is a factor of 24.
The remaining 16 holes are not equally spaced: they are slightly closer to the outside holes of each group of five holes.
These remaining holes allow for one Technic 5M Beam to be connected to each group of holes.
The radius of the holes on the circumference is 10M (½M is lost at each end of the 11M beam). The diagonal of a quadrant is 14.1M (√200). While this may be considered an illegal connection, it is possible to have 15M Beams inscribing a square on the circumference. It is a tight squeeze though.
This PDF written by Jamie Berard describes illegal LEGO connections.
A better method is to use a pair of Double Angular Beams 3x7 45°. This construction method has two advantages: the 0.1M of the diagonal is absorbed by the 45° of the angled beam and the beams get a third, and stronger, connection to the circumference.
Each circular rack has 35 teeth making a 140-tooth gear when they are joined together. The 12-tooth bevelled gear meshes with the circular rack. Other gears do not easily mesh directly.
I have tried to make a roller bearing cage but this has proved to be elusive.
The 4481 Hailfire Droid wheels remain the largest circular gear rack, but these parts are rare and expensive.
There are 14 circular gear racks in 42055 Bucket Wheel Excavator. Hopefully this part will be seen in more Technic sets in different colours.