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四冲程发动机模拟

四冲程发动机模拟
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2013-06-05 03:46
函数三角函数几何作图滑块动画函数图像
所属专题 Sine and Cosine Functions
①本范例演示四冲程发动机工作循环中活塞位移与时间关系的图形模拟；②涉及核心数学概念包括函数图像、三角函数、几何作图、参数方程；③构造要点运用了Line, Circle, Intersect, Point, If, Angle, OrthogonalLine, Segment, Mirror, Polygon, Midpoint, Vector, Conic, CircleSector, Sequence等GeoGebra命令与对象；④适合高中及以上学生及工程技术人员学习发动机原理与数学建模。

GeoGebra 命令及参数

  1. Line(Crankshaft, Crankshaft + (0, 10)) → Vertical
  2. Circle(Crankpin, (scaleFactor * rodLength)) → ConnectingRodCircle
  3. Intersect(ConnectingRodCircle, Vertical, 2) → Wristpin
  4. Line(Crankpin, Crankshaft) → i
  5. Point(i) → CounterBalCenterPt
  6. If(angleNumAdj > 0 ∧ angleNumAdj < 0.1, ((-1 * 1.5) * angleNumAdj), If[angleNumAdj ≥ 0.1 ∧ angleNumAdj < 0.2, ((-1 * 1.5) * ((-angleNumAdj) + 0.2)), 0]) → valve1MotionVert
  7. Angle(CrankShaftRadius, Crankshaft, Rotate[CrankShaftRadius, α, Crankshaft]) → angle
  8. Line(Wristpin, Crankpin) → b
  9. OrthogonalLine(Crankpin, b) → c
  10. OrthogonalLine(Wristpin, b) → d
  11. Circle(Crankpin, 0.2) → rodbasecircledark
  12. Circle(Wristpin, 0.2) → f
  13. Segment(TopDeadCenter + ((-1 * 0.4), 0), TopDeadCenter + (0.4, 0)) → TDCSeg
  14. Segment(BottomDeadCenter + ((-1 * 0.4), 0), BottomDeadCenter + (0.4, 0)) → BDCSeg
  15. Circle(Crankpin, 0.4) → k
  16. OrthogonalLine(Crankpin, i) → j
  17. OrthogonalLine(Crankshaft, i) → l
  18. Circle(CounterBalCenterPt, 0.9) → q
  19. Intersect(k, j) → C, D
  20. Intersect(q, i, 2) → A
  21. OrthogonalLine(A, i) → m
  22. Circle(A, 0.4) → p
  23. Intersect(p, m, 1) → B
  24. Intersect(rodbasecircledark, c, 1) → rodImageBL
  25. Intersect(rodbasecircledark, c, 2) → rodImageBR
  26. Intersect(f, d, 1) → rodImageTR
  27. Intersect(f, d, 2) → rodImageTL
  28. Circle(CounterBalCenterPt, 0.2) → r
  29. Intersect(r, i, 1) → H
  30. OrthogonalLine(CounterBalCenterPt, i) → s
  31. Intersect(q, s, 1) → I
  32. Intersect(q, s, 2) → J
  33. Circle(H, 0.5) → t
  34. Intersect(t, i, 2) → K
  35. Circle(K, 0.4) → c_1
  36. OrthogonalLine(K, i) → a_1
  37. Intersect(c_1, a_1, 1) → L
  38. Intersect(c_1, a_1, 2) → M
  39. Segment(Crankshaft, Crankpin) → crankPinOffsetSkeleton
  40. Segment(Wristpin, Crankpin) → rodSkeleton
  41. Segment(PistonHeadTop + (0, (-1 * 0.05)), Wristpin) → CompressionHeightSeg
  42. Line(Valve1CamPt, Valve1HalfHeight) → a
  43. OrthogonalLine(Valve1HalfHeight, a) → e
  44. Circle(Valve1HalfHeight, 0.28) → g
  45. Intersect(g, e, 2) → Valve1CamTL
  46. Intersect(g, e, 1) → Valve1CamTR
  47. Mirror(Valve1HalfHeight, Valve1CamPt) → Valve1HalfHeight'
  48. Circle(Valve1HalfHeight', 0.28) → d_1
  49. OrthogonalLine(Valve1HalfHeight', a) → b_1
  50. Intersect(d_1, b_1, 2) → Valve1CamBR
  51. Intersect(d_1, b_1, 1) → Valve1CamBL
  52. Polygon(Crankshaft + (0.22, 0.01 + (scaleFactor * deckHeight) + valve1MotionVert), Crankshaft + (0.61, 0.01 + (scaleFactor * deckHeight) + valve1MotionVert), Crankshaft + (0.56, 0.08 + (scaleFactor * deckHeight) + valve1MotionVert), Crankshaft + (0.27, 0.08 + (scaleFactor * deckHeight) + valve1MotionVert)) → valve1, e_1, f_1, g_1, h_1
  53. Circle(Crankpin, 0.5) → h
  54. Circle(Crankpin, 0.5) → rodbasecirclelargelight
  55. Midpoint(TopDeadCenter, BottomDeadCenter) → StrokeCenter
  56. Polygon(displBL, displBR, displTR, displTL) → polyStroke1, e_2, f_2, g_2, n_1
  57. If(angleNum < 150, 153, If[angleNum < 165, 102, If[angleNum < 180, 51, 0]]) → polyStroke2RdNum
  58. Polygon(displBL, displBR, displTR, displTL) → polyStroke2, displbl, displbr, displtr, displtl
  59. If(angleNum < 180, 255, If[angleNum < 195, 204, If[angleNum < 210, 153, 102]]) → polyStroke2BlueNum
  60. Polygon(displBL, displBR, displTR, displTL) → polyStroke3, displbl_1, displbr_1, displtr_1, displtl_1
  61. Polygon(displBL, displBR, displTR, displTL) → polyStroke4, displbl_2, displbr_2, displtr_2, displtl_2
  62. Point(i) → E
  63. Mirror(D, i) → D'''
  64. If(angleNum < 75, 360 + angleNum, angleNum) → valve4NumAdj
  65. If(valve4NumAdj > 315 ∧ valve4NumAdj < 360, ((-1 * 0.0034) * (valve4NumAdj - 315)), If[valve4NumAdj ≥ 360 ∧ valve4NumAdj < 405, (0.0034 * (valve4NumAdj - 315 - 405)) + 1.07, 0]) → valve4MotionVert
  66. Polygon(Crankshaft + ((-1 * 0.22), 0.01 + (scaleFactor * deckHeight) + valve4MotionVert), Crankshaft + ((-1 * 0.61), 0.01 + (scaleFactor * deckHeight) + valve4MotionVert), Crankshaft + ((-1 * 0.56), 0.08 + (scaleFactor * deckHeight) + valve4MotionVert), Crankshaft + ((-1 * 0.27), 0.08 + (scaleFactor * deckHeight) + valve4MotionVert)) → valve4, i_1, j_1, k_1, l_1
  67. Mirror(Valve4HalfHeight, Valve4CamPt) → Valve4HalfHeight'
  68. Circle(Valve4HalfHeight', 0.28) → p_1
  69. Circle(Valve4HalfHeight, 0.28) → q_1
  70. Line(Valve4HalfHeight', Valve4HalfHeight) → m_1
  71. OrthogonalLine(Valve4HalfHeight', m_1) → r_1
  72. OrthogonalLine(Valve4HalfHeight, m_1) → s_1
  73. Intersect(p_1, r_1, 2) → Valve4CamBR
  74. Intersect(p_1, r_1, 1) → Valve4CamTR
  75. Intersect(q_1, s_1, 1) → Valve4CamTL
  76. Intersect(q_1, s_1, 2) → Valve4CamBL
  77. Polygon(Crankshaft + (0.38, 0.08 + (scaleFactor * deckHeight) + valve1MotionVert), Crankshaft + (0.44, 0.08 + (scaleFactor * deckHeight) + valve1MotionVert), Crankshaft + (0.94, 1.62 + (scaleFactor * deckHeight) + valve1MotionVert), Crankshaft + (0.74, 1.68 + (scaleFactor * deckHeight) + valve1MotionVert)) → valve1Rod, t_1, a_2, b_2, c_2
  78. Polygon(Crankshaft + ((-1 * 0.38), 0.08 + (scaleFactor * deckHeight) + valve4MotionVert), Crankshaft + ((-1 * 0.44), 0.08 + (scaleFactor * deckHeight) + valve4MotionVert), Crankshaft + ((-1 * 0.94), 1.62 + (scaleFactor * deckHeight) + valve4MotionVert), Crankshaft + ((-1 * 0.74), 1.68 + (scaleFactor * deckHeight) + valve4MotionVert)) → valve4Rod, d_2, h_2, i_2, j_2
  79. Vector(StrokeCenter, StrokeCenter + (0, ((-1 * scaleFactor) * crankPin))) → strokeVectorBotom
  80. Vector(StrokeCenter, StrokeCenter + (0, (scaleFactor * crankPin))) → strokeVectorTop
  81. Vector(StrokeCenter, StrokeCenter + (((0.5 * scaleFactor) * bore), 0)) → boreVectorRt
  82. Vector(StrokeCenter, StrokeCenter + ((((-1 * 0.5) * scaleFactor) * bore), 0)) → boreVectorL
  83. Vector(CylModBDC, CylModBDC + ((((-1 * 0.5) * scaleFactor) * bore), 0)) → cylModBoreVectorL
  84. Vector(CylModBDC, CylModBDC + (((0.5 * scaleFactor) * bore), 0)) → cylModBoreVectorRt
  85. Conic(F, G, N, O, P) → k_2
  86. Segment(Wristpin + ((((-1 * 0.5) * scaleFactor) * bore), (scaleFactor * compressionHeight)), Wristpin + (((0.5 * scaleFactor) * bore), (scaleFactor * compressionHeight))) → pistonTopSkeleSeg
  87. Line(Valve4CamBR, Valve4CamBL) → n
  88. Line(Valve4CamTR, Valve4CamTL) → l_2
  89. OrthogonalLine(Valve4CamPt, n) → m_2
  90. Mirror(Valve4CamBL2, m_2) → Valve4CamBL2'
  91. OrthogonalLine(Valve4CamPt, m_2) → n_2
  92. Mirror(Valve4CamBL2, n_2) → Valve4CamBL2'_1
  93. Mirror(Valve4CamBL2'_1, m_2) → Valve4CamBL2'_2
  94. Segment(CylinderTopCenter, CylinderTopCenter + (-1, 0.5)) → ImpactSeg2
  95. Segment(CylinderTopCenter, CylinderTopCenter + ((-1 * 1.75), (-1 * 0.45))) → ImpactSeg3
  96. Segment(CylinderTopCenter, CylinderTopCenter + ((-1 * 0.75), (-1 * 0.75))) → ImpactSeg4
  97. Segment(CylinderTopCenter, CylinderTopCenter + ((-1 * 0.25), (-1 * 1.5))) → ImpactSeg5
  98. Segment(CylinderTopCenter, CylinderTopCenter + (0.4, (-1 * 1.25))) → ImpactSeg1
  99. Segment(CylinderTopCenter, CylinderTopCenter + (1, -1)) → ImpactSeg6
  100. Segment(CylinderTopCenter, CylinderTopCenter + (2, (-1 * 0.75))) → ImpactSeg7
  101. Segment(CylinderTopCenter, CylinderTopCenter + (1.75, (-1 * 0.25))) → ImpactSeg8
  102. Mirror(CylinderTopCenter, CylinderTopCenter) → CylinderTopCenter'
  103. Mirror(CylinderTopCenter + ((-1 * 1.75), (-1 * 0.45)), CylinderTopCenter) → Q
  104. Segment(CylinderTopCenter', Q) → ImpactSeg3'
  105. Mirror(CylinderTopCenter, CylinderTopCenter') → CylinderTopCenter'_1
  106. Mirror(CylinderTopCenter + ((-1 * 0.75), (-1 * 0.75)), CylinderTopCenter') → R
  107. Segment(CylinderTopCenter'_1, R) → ImpactSeg4'
  108. Mirror(CylinderTopCenter, CylinderTopCenter'_1) → CylinderTopCenter'_2
  109. Mirror(CylinderTopCenter + ((-1 * 0.25), (-1 * 1.5)), CylinderTopCenter'_1) → S
  110. Segment(CylinderTopCenter'_2, S) → ImpactSeg5'
  111. Mirror(CylinderTopCenter, CylinderTopCenter'_2) → CylinderTopCenter'_3
  112. Mirror(CylinderTopCenter + (0.4, (-1 * 1.25)), CylinderTopCenter'_2) → T
  113. Segment(CylinderTopCenter'_3, T) → ImpactSeg1'
  114. Mirror(CylinderTopCenter, CylinderTopCenter'_3) → CylinderTopCenter'_4
  115. Mirror(CylinderTopCenter + (1, -1), CylinderTopCenter'_3) → U
  116. Segment(CylinderTopCenter'_4, U) → ImpactSeg6'
  117. Mirror(CylinderTopCenter, CylinderTopCenter'_4) → CylinderTopCenter'_5
  118. Mirror(CylinderTopCenter + (2, (-1 * 0.75)), CylinderTopCenter'_4) → V
  119. Segment(CylinderTopCenter'_5, V) → ImpactSeg7'
  120. Mirror(CylinderTopCenter, CylinderTopCenter'_5) → CylinderTopCenter'_6
  121. Mirror(CylinderTopCenter + (1.75, (-1 * 0.25)), CylinderTopCenter'_5) → W
  122. Segment(CylinderTopCenter'_6, W) → ImpactSeg8'
  123. Vector(Midpoint[CylModBDC, CylModDeckCntr] + ((((-1 * 0.5) * scaleFactor) * bore) - 0.1, 0), CylModBDC + ((((-1 * 0.5) * scaleFactor) * bore) - 0.1, 0)) → cylModSDeckVectorBot
  124. Vector(Midpoint[CylModBDC, CylModDeckCntr] + ((((-1 * 0.5) * scaleFactor) * bore) - 0.1, 0), CylModDeckCntr + ((((-1 * 0.5) * scaleFactor) * bore) - 0.1, 0)) → cylModDeckVectorTop
  125. CircleSector(CounterBalCenterPt, J, I) → counterBalanceBody
  126. Segment(J, I) → counterBalanceSectorSegment
  127. Intersect(counterBalanceBody, counterBalanceSectorSegment, 1) → Z
  128. OrthogonalLine(D, counterBalanceSectorSegment) → counterBalanceLine
  129. Intersect(counterBalanceBody, counterBalanceSectorSegment, 2) → A_1
  130. OrthogonalLine(D''', counterBalanceSectorSegment) → counterBalanceLine2
  131. Mirror(D''', Crankshaft) → D''
  132. Mirror(D, Crankshaft) → D'
  133. Vector(Midpoint[CylModBDC, CylModTDC] + (((0.5 * scaleFactor) * bore) + 0.1, 0), CylModBDC + (((0.5 * scaleFactor) * bore) + 0.1, 0)) → cylModStrokeVectorBottom
  134. Vector(Midpoint[CylModBDC, CylModTDC] + (((0.5 * scaleFactor) * bore) + 0.1, 0), CylModTDC + (((0.5 * scaleFactor) * bore) + 0.1, 0)) → cylModStrokeVectorTop
  135. Vector((0, 0), (10.5, 0)) → x_{Axis}
  136. Sequence(Segment[(i, -0.15), (i, 0.15)], i, 0, 10, 0.25) → x_{Axis-hash}
  137. Sequence(Segment[(i, -0), (i, 6)], i, 0, 10, 0.25) → x_{axis-grid}
  138. Angle(BetaRefPt, Crankpin, Wristpin) → β
  139. Sequence((-0.15, i), i, 0, 6, 10 / graphYaxisScale) → graphYaxisIntervalElements
  140. Sequence(Segment[(-0.15, i), (0.15, i)], i, 0, 6, 10 / graphYaxisScale) → y_{Axis-hash}
  141. Sequence(Segment[(0, i), (10.15, i)], i, 0, 6, 10 / graphYaxisScale) → y_{Axis-grid}
  142. Vector((0, 0), (0, 6.4)) → y_{axis}

AI 绘图提示语参考

画一个四冲程发动机的图形模拟，展示活塞位移与时间的关系。包含曲轴、连杆、活塞、气门等关键部件，用函数图像和三角函数表示运动规律。先画出曲轴和活塞的几何关系，再添加连杆和曲柄的连接，最后用滑块控制角度变化，展示整个发动机的工作循环。
以上提示语为根据原始绘图命令整理而来，仅供参考。