Spike Prime - Center of Inscribed Circle of Triangle

Let's begin

This activity is using the same robot as the Intersection activity.

Note: this robot requires one additional color/light sensor (two in total). Drawing...

Model:

Pictures:

Building instructions:

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Download stud.io model:

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Connections:

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go fwd until you hit an edge
turn left along the side and follow until the vertex A
turn right along the side AC, measure the angle BAC (alpha) while turning
follow side AC until the vertex C, measure side length (b)
turn right in the direction of bisector of angle ACB (gamma)
travel 1 rotation forward, then in this point U turn to be parallel with line b (gamma/2 right)
travel until hit the side c to point V, measure length of line segment UV (x)
turn right 90+alpha towards line b, travel until you hit line b (point W), then turn right along side b
travel until point C, measure the distance WC (y)
calculation: by travelling 1 rotation from C to U, the length of side AC descreased to
UV - WA = UV - (AC - WC) = UV + WC - AC = x + y - b
therefore, travelling from C the distance d = b / (2b - x - y) leads to point O
in point B, turn right in the direction of bisector of angle ACB
travel d rotations forward to arrive at destination.

Make your own recording
Perform experiments with your model and discuss in your group what has happened.

Pick one of the three versions, build it
Make your own drawing of the gear systems (i.e. on paper)
Write down the numbers of teeth on each pair of the gear wheels
Figure out the ratio of each pair of gear wheels
Make or calculate your guess about the final ratio of gear wheels
Perform measurement with the model and program and compare
Try to invent some other combinations of gears, repeat the whole procedure with them (this can be an alternative project for an advanced group instead of the above)
Could you list all the possible combinations using these 8 gear wheels that could be built?