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Articulated cube with fixed bar (II)

Articulated cube with fixed bar (II)
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2022-03-27 22:52
FunctionTrigonometrySolid GeometryCalculusGeometric Construction
In collections Linkages
This example demonstrates a linkage structure of an articulated cube with a fixed bar, focusing on geometric constructions and constraints. Key math concepts include cube properties, cosine law, quadratic equations, median and tangent lines, differential equations, and function graphing. The construction utilizes GeoGebra commands like PointIn, Sphere, Circle, Point, IntersectConic, CircumcircleArc, If, Rotate. Suitable for high school and above students to explore complex geometric relationships and equation applications in mechanical structures.

GeoGebra Commands & Parameters

  1. PointIn(Sphere[O, 1]) → A
  2. Sphere((A + U) / 2, abs((A + U) / 2)) → sB
  3. Circle(O, 1, zAxis) → cE
  4. Point(cE) → E
  5. Sphere((A + E) / 2, abs((A + E) / 2)) → sD
  6. Sphere((U + E) / 2, abs((U + E) / 2)) → sF
  7. IntersectConic(Sphere[E, 1], Sphere[U, 1]) → cF
  8. PointIn(sD) → D
  9. PointIn(sB) → B
  10. CircumcircleArc(jE(1), U, jE(2)) → arcE
  11. PointIn(sF) → F
  12. Sphere(O, 1) → sO
  13. IntersectConic(Sphere[U, 1], Sphere[A, 1]) → cB
  14. IntersectConic(Sphere[E, 1], Sphere[A, 1]) → cD
  15. Sphere(U, 1) → sU
  16. Sphere(E, 1) → sE
  17. IntersectConic(Sphere[O, 1], Sphere[D, 1]) → cJ1
  18. IntersectConic(Sphere[B, 1], Sphere[F, 1]) → cJ2
  19. If(jo ∧ (au ∨ ae) ∧ (¬(jo ∧ (eu ∧ au ∨ eu ∧ ae ∨ au ∧ ae))), 2, (eu ∧ au ∨ eu ∧ ae ∨ au ∧ ae) ∧ fo ∧ bo ∧ do, 2, 4, jo, 3, (¬eu) ∧ (¬au) ∧ (¬ae) ∧ (¬fo) ∧ (¬bo) ∧ (¬do) ∨ eu ∧ (¬au) ∧ (¬ae) ∧ (¬fo) ∧ (¬bo) ∧ (¬do) ∨ (eu ∧ au ∨ eu ∧ ae ∨ au ∧ ae) ∧ (¬fo) ∧ (¬bo) ∧ (¬do), 6, (¬eu) ∧ au ∧ (¬ae) ∧ (¬fo) ∧ (¬bo) ∧ (¬do) ∨ (¬eu) ∧ (¬au) ∧ ae ∧ (¬fo) ∧ (¬bo) ∧ (¬do) ∨ (¬eu) ∧ (¬au) ∧ (¬ae) ∧ fo ∧ (¬bo) ∧ (¬do) ∨ (¬eu) ∧ (¬au) ∧ (¬ae) ∧ (¬fo) ∧ bo ∧ (¬do) ∨ (¬eu) ∧ (¬au) ∧ (¬ae) ∧ (¬fo) ∧ (¬bo) ∧ do ∨ eu ∧ (¬au) ∧ (¬ae) ∧ (¬fo) ∧ bo ∧ (¬do) ∨ eu ∧ (¬au) ∧ (¬ae) ∧ (¬fo) ∧ (¬bo) ∧ do ∨ (¬eu) ∧ (¬au) ∧ (¬ae) ∧ fo ∧ bo ∧ (¬do) ∨ (¬eu) ∧ (¬au) ∧ (¬ae) ∧ fo ∧ (¬bo) ∧ do ∨ (¬eu) ∧ (¬au) ∧ (¬ae) ∧ (¬fo) ∧ bo ∧ do ∨ eu ∧ (¬au) ∧ (¬ae) ∧ (¬fo) ∧ bo ∧ do ∨ (¬eu) ∧ (¬au) ∧ (¬ae) ∧ fo ∧ bo ∧ do, 5, (¬eu) ∧ au ∧ (¬ae) ∧ (¬fo) ∧ bo ∧ (¬do) ∨ (¬eu) ∧ (¬au) ∧ ae ∧ (¬fo) ∧ (¬bo) ∧ do ∨ (¬eu) ∧ au ∧ (¬ae) ∧ fo ∧ bo ∧ (¬do) ∨ (¬eu) ∧ au ∧ (¬ae) ∧ (¬fo) ∧ bo ∧ do ∨ (¬eu) ∧ (¬au) ∧ ae ∧ fo ∧ (¬bo) ∧ do ∨ (¬eu) ∧ (¬au) ∧ ae ∧ (¬fo) ∧ bo ∧ do ∨ (eu ∧ au ∨ eu ∧ ae ∨ au ∧ ae) ∧ fo ∧ bo ∧ (¬do) ∨ (eu ∧ au ∨ eu ∧ ae ∨ au ∧ ae) ∧ fo ∧ (¬bo) ∧ do ∨ (eu ∧ au ∨ eu ∧ ae ∨ au ∧ ae) ∧ (¬fo) ∧ bo ∧ do ∨ (¬eu) ∧ au ∧ (¬ae) ∧ fo ∧ bo ∧ do ∨ (¬eu) ∧ (¬au) ∧ ae ∧ fo ∧ bo ∧ do, 3) → dg
  20. Rotate(Surface[(cos(u) * cos(v)), (sin(u) * cos(v)), sin(v), u, 0, π, v, (7 * π / 6), (11 * π / 6)], (3 * π / 2), xAxis) → sO3
  21. Point(arcE) → EJ
  22. Rotate(Surface[(cos(u) * cos(v)), (sin(u) * cos(v)), sin(v), u, 0, π, v, (7 * π / 6), (11 * π / 6)], (3 * π / 2), OrthogonalLine[O, Line[O, E], zAxis]) → sO3E
  23. Circle(((-E)) / 2, sqrt(3) / 2, Line[O, E]) → jE3
  24. Circle(((-U)) / 2, sqrt(3) / 2, yAxis) → jA
  25. IntersectConic(sO, sU) → cOU
  26. IntersectConic(sO, sE) → cOE

AI Drawing Prompt Reference

Draw an articulated cube with a fixed bar. Start by creating a point A inside a unit sphere, then construct a series of spheres and circles to form the cube's vertices and edges. Finally, use these vertices and edges to build the cube's framework and apply rotation to form a fixed bar, demonstrating the articulated structure of the cube.
The prompt above was compiled from the original drawing commands and is for reference only.