Difference between revisions of "Spike Prime - Center of Inscribed Circle of Triangle"
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+ | <small>(''[[Spike up Prime Interest in Mathematics|back to list of projects]]'')</small> | ||
+ | |||
+ | == 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... | ||
+ | |||
+ | == Build == | ||
+ | |||
+ | Model: | ||
+ | |||
+ | [[Image:spike_intersection_model.png|model of vehicle|300px]] | ||
+ | |||
+ | Pictures: | ||
+ | |||
+ | [[Image:spike_intersection1.jpg|inscribed circle center finding robot|300px]] | ||
+ | [[Image:spike_intersection2.jpg|inscribed circle center finding robot|300px]] | ||
+ | |||
+ | |||
+ | Building instructions: | ||
+ | |||
+ | * [[Spike Prime - Intersection - Building Instructions|Inscribed circle center finding robot (PNG)]] | ||
+ | |||
+ | Download building instructions: | ||
+ | |||
+ | * [[Media:spike_intersection.pdf| whole system (pdf)]] | ||
+ | |||
+ | Download stud.io model: | ||
+ | |||
+ | * [[Media:spike_model_intersection.io|vehicle (stud.io)]] | ||
+ | |||
+ | ...description... | ||
+ | |||
+ | Connections: | ||
+ | |||
+ | * left motor - B | ||
+ | * large motor - C | ||
+ | * right motor - D | ||
+ | * closer light sensor - E | ||
+ | * front light sensor - F | ||
+ | |||
+ | == Programs == | ||
+ | |||
+ | |||
+ | [[Image:inscribed_circle_prg.png|program]] | ||
+ | |||
+ | Download: | ||
+ | * [[Media:inscribed_circle.llsp|inscribed_circle.llsp]] | ||
+ | |||
+ | ...description... | ||
+ | |||
+ | # 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<br> | ||
+ | UV - WA = UV - (AC - WC) = UV + WC - AC = x + y - b<br> | ||
+ | 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. | ||
+ | |||
+ | == Measure, analyze, think == | ||
+ | |||
<youtube>ynJiojcIbAg</youtube> | <youtube>ynJiojcIbAg</youtube> | ||
+ | |||
+ | * Make your own recording | ||
+ | * Perform experiments with your model and discuss in your group what has happened. | ||
+ | |||
+ | == Explore and modify == | ||
+ | |||
+ | * 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? | ||
+ | |||
+ | == Present == | ||
+ | |||
+ | * | ||
+ | == Additional resources == | ||
+ | |||
+ | * Download: [http://robotika.sk/spike/spike_math_9_inscribed_circle.zip Center of Inscribed Circle of Triangle - all media files] | ||
+ | |||
+ | __notoc__ |
Revision as of 19:32, 23 July 2022
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...
Build
Model:
Pictures:
Building instructions:
Download building instructions:
Download stud.io model:
...description...
Connections:
- left motor - B
- large motor - C
- right motor - D
- closer light sensor - E
- front light sensor - F
Programs
Download:
...description...
- 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.
Measure, analyze, think
- Make your own recording
- Perform experiments with your model and discuss in your group what has happened.
Explore and modify
- 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?
Present
Additional resources