MathPlotAI Logo MathPlotAI

Articulated cube with fixed bar (I)

Articulated cube with fixed bar (I)
Loading the math board and drawing, please wait…
2022-05-08 03:16
TrigonometrySolid GeometryMatrixGeometric Construction
In collections Linkages
This example demonstrates a linkage structure of a cube with articulated bars, where one bar is fixed. Core math concepts include geometric construction, solid geometry, matrix operations, quadratic equations, and linear equations. Construction highlights involve commands like Sphere, PointIn, Circle, Point, IntersectConic, and CircumcircleArc. Suitable for high school and above students learning mechanical structures, spatial geometry, and mathematical modeling.

GeoGebra Commands & Parameters

  1. Sphere(O, 1) → sO
  2. PointIn(sO) → A
  3. Sphere((A + U) / 2, abs((A + U) / 2)) → sB
  4. Circle((0, 0), 1) → cE
  5. Point(cE) → E
  6. Sphere((A + E) / 2, abs((A + E) / 2)) → sD
  7. Sphere((U + E) / 2, abs((U + E) / 2)) → sF
  8. IntersectConic(Sphere[E, 1], Sphere[U, 1]) → cF
  9. PointIn(sD) → D
  10. PointIn(sB) → B
  11. CircumcircleArc(jE(1), U, jE(2)) → arcE
  12. PointIn(sF) → F
  13. Sphere(U, 1) → sU

AI Drawing Prompt Reference

Create a 3D solid-geometry diagram showing an articulated cube linkage with one fixed bar. Begin with a sphere centered at the origin with radius 1, and define a point A lying on that sphere. Construct additional spheres whose centers are midpoint expressions involving A, a given point U, and a point E; obtain E from a planar circle with center (0,0) and radius 1. Use the intersection of two unit spheres (one based on E, one based on U) to form an intersection conic, then pick the points D, B, and F by selecting their positions on the corresponding spheres. Also draw a circumcircle arc determined by E and U. Finally include the unit sphere centered at U as the fixed reference, so the overall configuration depicts a cube-like articulated linkage with a fixed bar.
The prompt above was compiled from the original drawing commands and is for reference only.