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GEAR Mechanism

GEAR Mechanism
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2019-08-20 01:05
CircleAngleTransformationSlider Animation
This example demonstrates the geometric relationship of gear rotation and meshing in gear transmission; involves core math concepts like circle, angle, geometric transformation, symmetry; constructed using GeoGebra commands such as Segment, Point, Circle, Rotate, Angle; suitable for high school students learning geometric transformations and mechanical principles.

GeoGebra Commands & Parameters

  1. Segment(C, D) → g
  2. Point(g) → F
  3. Circle(F, a) → d
  4. Point(d) → H
  5. Segment(H, K) → b
  6. Rotate(H, 45°, F) → H'
  7. Segment(H', K) → q
  8. Rotate(H', 45°, F) → H''
  9. Segment(H'', K) → r
  10. Rotate(H'', 45°, F) → H'''
  11. Segment(H''', K) → s
  12. Rotate(H''', 45°, F) → J
  13. Segment(J, K) → t
  14. Rotate(J, 45°, F) → J'
  15. Segment(J', K) → f_1
  16. Rotate(J', 45°, F) → J''
  17. Segment(J'', K) → g_1
  18. Rotate(J'', 45°, F) → J'''
  19. Segment(J''', K) → e
  20. Segment(A, B) → f
  21. Point(f) → E
  22. Circle(E, a) → c
  23. Point(c) → G
  24. Segment(G, K) → h_1
  25. Rotate(G, 45°, E) → G'
  26. Segment(G', K) → i
  27. Rotate(G', 45°, E) → G''
  28. Segment(G'', K) → j
  29. Rotate(G'', 45°, E) → G'''
  30. Segment(G''', K) → k
  31. Rotate(G''', 45°, E) → I
  32. Segment(I, K) → n
  33. Rotate(I, 45°, E) → I'
  34. Segment(I', K) → p
  35. Rotate(I', 45°, E) → I''
  36. Segment(I'', K) → m
  37. Rotate(I'', 45°, E) → I'''
  38. Segment(I''', K) → l
  39. Angle(G, E, G') → α
  40. Angle(G', E, G'') → β
  41. Angle(G'', E, G''') → γ
  42. Angle(G''', E, I) → δ
  43. Angle(I, E, I') → ε
  44. Angle(I', E, I'') → ζ
  45. Angle(I'', E, I''') → η
  46. Angle(H, F, H') → θ
  47. Angle(H', F, H'') → ι
  48. Angle(H'', F, H''') → κ
  49. Angle(H''', F, J) → λ
  50. Angle(J, F, J') → μ
  51. Angle(J', F, J'') → ν
  52. Angle(J'', F, J''') → ξ

AI Drawing Prompt Reference

Draw an illustration of a gear mechanism showing the geometric relationship of gear rotation and meshing. Start with a line segment, then draw a circle centered at one of its points. Mark multiple points along the segment and rotate them around the center repeatedly to form the teeth of the gears. Label the angles of rotation to demonstrate how the gears mesh and rotate together, suitable for high school students learning geometric transformations and mechanical principles.
The prompt above was compiled from the original drawing commands and is for reference only.