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Helical Slide with Square Cross Sections

Helical Slide with Square Cross Sections
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2020-01-16 20:59
Coordinate GeometrySolid GeometryParametric Equation
This example demonstrates a helical slide with square cross sections. It involves concepts of coordinate geometry, parametric equations, and solid geometry. Using GeoGebra commands such as Surface, Translate, and CurveCartesian, the helical slide can be constructed. Suitable for high school or university-level solid geometry and coordinate geometry courses.

GeoGebra Commands & Parameters

  1. Surface(((R + (r * cos(v))) * cos(u)), ((R + (r * cos(v))) * sin(u)), (k * u), u, 0, (2 * π), v, 0, (2 * π)) → a
  2. Translate(a, Vector[(0, 0, (2 * r))]) → a'
  3. Surface(((R + r) * cos(u)), ((R + r) * sin(u)), v + (u * k), u, 0, (2 * π), v, 0, (k * u) + (2 * r)) → b
  4. Surface(((R - r) * cos(u)), ((R - r) * sin(u)), v + (u * k), u, 0, (2 * π), v, 0, (k * u) + (2 * r)) → c
  5. Translate(a, Vector[(0, 0, (2 * (π * k)))]) → a'_1
  6. Translate(c, Vector[(0, 0, (2 * (π * k)))]) → c'
  7. Translate(b, Vector[(0, 0, (2 * (π * k)))]) → b'
  8. Translate(a', Vector[(0, 0, (2 * (π * k)))]) → a''
  9. Translate(a, Vector[(0, 0, ((-2 * π) * k))]) → a'_2
  10. Translate(a', Vector[(0, 0, ((-2 * π) * k))]) → a''_1
  11. Translate(b, Vector[(0, 0, ((-2 * π) * k))]) → b'_1
  12. Translate(c, Vector[(0, 0, ((-2 * π) * k))]) → c'_1
  13. CurveCartesian(((R + r) * cos(t)), ((R + r) * sin(t)), (k * t), t, 0, (2 * π)) → d
  14. CurveCartesian(((R - r) * cos(t)), ((R - r) * sin(t)), (k * t), t, 0, (2 * π)) → e
  15. Translate(e, Vector[(0, 0, ((2 * π) * k))]) → e'
  16. Translate(d, Vector[(0, 0, (2 * r))]) → d'_1
  17. Translate(e, Vector[(0, 0, (2 * r))]) → e'_1
  18. Translate(d'_1, Vector[(0, 0, (2 * (π * k)))]) → f
  19. Translate(d, Vector[(0, 0, ((2 * π) * k))]) → d'
  20. Translate(e'_1, Vector[(0, 0, ((2 * π) * k))]) → g
  21. Translate(e, Vector[(0, 0, ((-2 * π) * k))]) → e'_2
  22. Translate(d, Vector[(0, 0, ((-2 * π) * k))]) → d'_2
  23. Translate(d'_1, Vector[(0, 0, ((-2 * π) * k))]) → h
  24. Translate(e'_1, Vector[(0, 0, ((-2 * π) * k))]) → i
  25. Sequence(Segment[(R - r, 0, (((2 * π) * i) * k)), (R + r, 0, (((2 * π) * i) * k))], i, -1, 2, 1) → l1
  26. Translate(l1, Vector[(0, 0, (2 * r))]) → l1'
  27. Sequence(Segment[(R - r, 0, (((2 * π) * i) * k)), (R - r, 0, (((2 * π) * i) * k) + (2 * r))], i, -1, 2, 1) → l2
  28. Translate(l2, Vector[((2 * r), 0, 0)]) → l2'