MathPlotAI Logo MathPlotAI

Law of Cosines Application: Piston and Crankshaft Animation

Law of Cosines Application: Piston and Crankshaft Animation
Loading the math board and drawing, please wait…
2016-02-28 06:46
TrigonometryCoordinate Geometry
This example demonstrates the application of the Law of Cosines through an animation of a piston and crankshaft mechanism. It involves the use of commands such as Circle, Segment, and Angle. Suitable for high school mathematics education, particularly in coordinate geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Circle((0, 0), 1) → c
  2. Polygon((1.24, 0.6), (5, 0.6), (5, -0.6), (1.24, -0.6)) → Cylinder, g, i, j, l
  3. Segment(Pwheel, Pd) → L
  4. Polygon((x(Pd), -0.6), (x(Pd), 0.6), (x(Pd) + 1.3, 0.6), (x(Pd) + 1.3, -0.6)) → Piston, a, b, e, f
  5. Circle(O, 0.5) → h
  6. Arc(h, (cos(rotation - π / 2), sin(rotation - π / 2)), (cos(rotation + π / 2), sin(rotation + π / 2))) → k
  7. Segment(O, Pwheel) → Pseg1
  8. Segment(O, Pd) → Pseg2
  9. Segment(Po', Pd') → Tseg1
  10. Segment(Pwheel', Pd') → Tseg3
  11. Segment(Po', Pwheel') → Tseg2
  12. Angle(Tseg1, Tseg2) → Θ

AI Drawing Prompt Reference

Draw an animation of a piston and crankshaft mechanism, including a circle with radius 1, a polygon representing the crankshaft, and a rectangle representing the piston. There is an arc rotating around the center of the circle with an angle of rotation - π/2. Finally, draw two line segments connecting the crankshaft and the piston, and their angle.
The prompt above was compiled from the original drawing commands and is for reference only.