四杆机构运动学

四杆机构运动学
几何画板及绘图内容加载中,请稍等……
2020-10-26 02:33
本范例演示四杆机构的运动学,包括速度和加速度图。涉及核心数学概念有向量和几何变换。通过使用GeoGebra命令如Intersect、Circle、Rotate等构造图形。适合机械工程和数学教育领域。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → O_2
  2. Circle(O_2, r2) → circO2A
  3. Intersect(circO2A, xAxis, 2) → A_{old}
  4. Rotate(A_{old}, th2, O_2) → A
  5. Vector(O_2, A) → pO2A
  6. Vector(Ov, Ov + (((0, 0, w2) ⊗ pO2A) * scaleV)) → vA
  7. Circle(O_2, r1) → circO2O4_{1}
  8. Intersect(circO2O4_{1}, xAxis, 2) → O4_{old}
  9. Rotate(O4_{old}, th1, O_2) → O_4
  10. Circle(O_4, r4) → circO4B
  11. Circle(A, r3) → circAB
  12. Intersect(circO4B, circAB, 2) → B
  13. Vector(A, B) → pAB
  14. Segment(B, O_4) → L4
  15. OrthogonalLine(Ov, L4) → nj
  16. Segment(A, B) → L3
  17. Point({Ov + vA}) → endVA
  18. OrthogonalLine(endVA, L3, xOyPlane) → ni
  19. Intersect(ni, nj) → E
  20. Vector(endVA, E) → vBA
  21. Textfield(r1) → InputBox1
  22. Textfield(thAC) → InputBox2
  23. Textfield(r2) → InputBox3
  24. Textfield(r3) → InputBox4
  25. Textfield(r4) → InputBox5
  26. Textfield(rAC) → InputBox6
  27. Angle(A_{old}, O_2, A) → th2dep
  28. Segment(O_2, A) → L2
  29. Textfield(th1) → InputBox7
  30. Circle(A, rAC) → circAC
  31. Intersect(circAC, L3, 1) → C_{old}
  32. Rotate(C_{old}, thAC, A) → C
  33. Angle(C_{old}, A, C) → thACdep
  34. Segment(A, C) → LAC
  35. Segment(C, B) → LCB
  36. Vector(Ov, E) → vB
  37. Vector(Oa, Oa + (((0, 0, w2) ⊗ ((0, 0, w2) ⊗ pO2A)) * scaleA)) → aAn
  38. Vector(Oa + aAn, Oa + aAn + (((0, 0, dw2) ⊗ pO2A) * scaleA)) → aAt
  39. Vector(Oa + aAn + aAt, Oa + aAn + aAt + (((0, 0, w3) ⊗ ((0, 0, w3) ⊗ pAB)) * scaleA)) → aBAn
  40. Point({Oa + aAn + aAt + aBAn}) → endaBAn
  41. Vector(O_4, B) → pO4B
  42. Vector(Oa, Oa + (((0, 0, w4) ⊗ ((0, 0, w4) ⊗ pO4B)) * scaleA)) → aBn
  43. Point({Oa, Oa + (((0, 0, w4) ⊗ ((0, 0, w4) ⊗ pO4B)) * scaleA)}) → endaBn
  44. OrthogonalLine(endaBn, L4, xOyPlane) → nm
  45. OrthogonalLine(endaBAn, L3, xOyPlane) → nn
  46. Intersect(nm, nn) → F
  47. Vector(endaBn, F) → aBt
  48. Vector(endaBAn, F) → aBAt
  49. Textfield(scaleV) → InputBox8
  50. Textfield(scaleA) → InputBox9
  51. Segment(O_2, O_4) → L1
  52. Vector(A, C) → pAC
  53. Vector(endVA, endVA + (scaleV * ((0, 0, w3) ⊗ pAC))) → vCA
  54. Point({endVA + vCA}) → endVCA
  55. Vector(Ov, endVCA) → vC
  56. Vector(E, endVCA) → vCB
  57. Vector(Oa + aAn + aAt, Oa + aAn + aAt + (((0, 0, w3) ⊗ ((0, 0, w3) ⊗ pAC)) * scaleA)) → aCAn
  58. Vector(Oa + aAn + aAt + aCAn, Oa + aAn + aAt + aCAn + (((0, 0, dw3) ⊗ pAC) * scaleA)) → aCAt
  59. Point({Oa + aAn + aAt + aCAn + aCAt}) → endaCAt
  60. Vector(Oa, endaCAt) → aC
  61. Point({Oa + aAn + aAt}) → endaA
  62. Segment(F, endaA) → f
  63. Segment(endaA, endaCAt) → g
  64. Segment(F, endaCAt) → h

AI 绘图提示语参考

画一个四杆机构动力学示意图,包含速度和加速度图。首先绘制坐标轴交点,以该点为圆心画两个圆,交轴得到两个点,旋转其中一个点得到杆件。再以其他点为圆心画圆,交点确定连接点,绘制杆件和向量。最后,通过向量运算和几何变换,画出速度和加速度向量,并标注关键参数。
以上提示语为根据原始绘图命令整理而来,仅供参考。