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Four-bar Linkage Kinematics

Four-bar Linkage Kinematics
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2020-10-26 02:33
VectorTransformationGeometric Construction
This example demonstrates the kinematics of a four-bar linkage, including velocity and acceleration diagrams. Key mathematical concepts include vectors and geometric transformations. Constructed using GeoGebra commands such as Intersect, Circle, Rotate, etc. Suitable for mechanical engineering and mathematics education.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a four-bar linkage kinematics diagram with velocity and acceleration diagrams. Start by plotting the intersection of coordinate axes, draw two circles centered at the origin, intersecting the axes to find points. Rotate one point to form a link. Then, draw circles centered at other points, find intersection points to determine connection points, and draw links and vectors. Finally, perform vector operations and geometric transformations to plot velocity and acceleration vectors, and label key parameters.
The prompt above was compiled from the original drawing commands and is for reference only.