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Epicyclic Gear

Epicyclic Gear
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2019-06-05 03:35
CircleVectorGeometric Construction
This example demonstrates the working principle of an epicyclic gear. It involves concepts of circular motion and rotation angles. Using GeoGebra commands such as Circle, Rotate, and Polygon, the motion trajectory of the epicyclic gear is dynamically displayed. Suitable for high school or university mechanical engineering and mathematics courses.

GeoGebra Commands & Parameters

  1. Min(abs(ncarrier), abs(nring)) → nrot_2
  2. Min(abs(nsolar), abs(ncarrier)) → nrot_1
  3. Intersect(xAxis, yAxis) → A
  4. Circle(B, (Tplanetary * 5)) → d
  5. Circle(A, (Tsolar * 5)) → c
  6. Intersect(c, d, 1) → H
  7. Rotate(I, alfa_1, A) → I'
  8. Polygon(C, B, D) → poly1, d_1, c_1, b_1
  9. Textfield(ncarrier) → Input_ncarrier
  10. Textfield(Tsolar) → Input_Tsolar
  11. Textfield(Tplanetary) → Input_Tplanetary
  12. Circle(A, ((Tsolar + Tplanetary) * 5)) → g
  13. Circle(E, (Tring * 5)) → h
  14. Circle(D, (Tplanetary * 5)) → f
  15. Circle(C, (Tplanetary * 5)) → e
  16. Intersect(c, e, 1) → F
  17. Intersect(c, f, 1) → G
  18. Polygon(G, F, H) → poly2, h_1, g_1, f_1
  19. Rotate(L, beta_1, A) → L'
  20. Angle(L, A, L') → β
  21. Angle(I, A, I') → α
  22. Textfield(nsolar) → Input_nsolar
  23. Rotate(I', (30° * nsolar / (abs(nsolar) + 1)), A) → I''
  24. Vector(I', I'') → u
  25. Rotate(L', ((30° * nring / (abs(nring) + 1)) * Tsolar / Tring), A) → L''
  26. Vector(L', L'') → v
  27. Rotate(J, gama_1, B) → J'
  28. Rotate(J', ((30° * nplanetary / (abs(nplanetary) + 1)) * Tsolar / Tplanetary), B) → J''
  29. Vector(J', J'') → w