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Spiral Gears

Spiral Gears
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2020-01-10 23:09
SequenceTransformationGeometric Construction
This example demonstrates the motion principle of spiral gears. It involves concepts such as rotation, angles, and geometric transformations. Using GeoGebra commands like Point, Sequence, CurveCartesian, and Rotate, the motion trajectories of the gears can be dynamically displayed. Suitable for high school students and educators for teaching and research.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Sequence((x(A) + (((r_0 * a) * t) * cos(t)), y(A) + (((r_0 * a) * t) * sin(t))), t, 3.141592653589793, (L * π), π / n) → liste2
  4. CurveCartesian(x(A) + ((r_0 * a^(t - α)) * cos(t)), y(A) + ((r_0 * a^(t - α)) * sin(t)), t, -12.41593, 6.283185307179586) → b_1
  5. Rotate(liste2, d, A) → liste2'
  6. Sequence(Polygon[Element[liste2', i + 1], Element[liste2', i], 3], i, 1, Length[liste2]) → liste3
  7. Midpoint(A, B) → C
  8. Sequence((x(B) - (((r_0 * a) * t) * cos(t)), y(B) - (((r_0 * a) * t) * sin(t))), t, 3.141592653589793, (L * π), π / n) → liste4
  9. Rotate(liste4, (-(d + 0.1)), B) → liste4'
  10. Polygon(A - (0.25, 0.25), B + (0.25, -0.25), B + (0.25, 0.25), A + (-0.25, 0.25)) → poly1, e, f, g, h
  11. Sequence(Polygon[Element[liste4', i + 1], Element[liste4', i], 3], i, 1, Length[liste2] - 2) → liste5
  12. Sequence(Segment[Element[liste2', i], A], i, 1, Length[liste2]) → liste6
  13. Sequence(Segment[Element[liste4', i], B], i, 1, Length[liste4'] - 1) → liste7
  14. Circle(A, 0.25) → k
  15. Circle(B, 0.25) → p
  16. Polygon(A - (0.195, 0.195), B + (0.195, -0.195), B + (0.195, 0.195), A + (-0.195, 0.195)) → poly2, i, j, l, m
  17. Sequence(CurveCartesian[x(A) + ((r_0 * a^(t - i)) * cos(t)), y(A) + ((r_0 * a^(t - i)) * sin(t)), t, -12.41593, 12.56637], i, 0, c, π / n) → liste1