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海滩怪兽：受 Theo Jansen 启发的马形连杆机构演示

海滩怪兽：受 Theo Jansen 启发的马形连杆机构演示
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2012-09-18 15:41
变换几何作图滑块动画轨迹
所属专题 Portugal is great
① 本范例演示一个受 Theo Jansen 启发的马形“海滩怪兽”连杆机构，展示其在平面上的周期性步态运动。② 涉及核心数学概念包括几何变换（旋转、镜像、平移）、圆与线的相交、中点与垂线构造、以及参数化运动的轨迹分析。③ 作图要点：使用 Point、Segment、Midpoint、Rotate、Angle、Circle、Intersect、OrthogonalLine、Line、Mirror 等命令，创建点 a、t、b、c1‑c4、A、B、C、B'、β、d、e、D、f、g、E、h、i、j、F、k、p、q、G、l、m、n、H、r、s、b1、e1、I、t_1、d1、f1、J 等对象，通过连杆的旋转与镜像实现腿部的协同运动。④ 适合高中几何选修、大学几何建模课程，以及 STEM 创客活动中演示连杆机构与动态几何的教学演示。

GeoGebra 命令及参数

  1. Point(Circle[A, a]) → B
  2. Segment(A, B) → c
  3. Midpoint(c) → C
  4. Rotate(B, t, C) → B'
  5. Angle(B, C, B') → β
  6. Circle(C, b) → d
  7. Segment(C, B') → e
  8. Intersect(d, e, 1.0) → D
  9. Circle(D, c1) → f
  10. Circle(A, c2) → g
  11. Intersect(f, g, 2.0) → E
  12. Segment(D, E) → h
  13. Segment(A, E) → i
  14. OrthogonalLine(A, i) → j
  15. Intersect(g, j, 2.0) → F
  16. Segment(A, F) → k
  17. Circle(D, c3) → p
  18. Circle(A, c4) → q
  19. Intersect(p, q, 1.0) → G
  20. Segment(A, G) → l
  21. Line(G, k) → m
  22. Line(F, l) → n
  23. Intersect(m, n) → H
  24. OrthogonalLine(G, m) → r
  25. Segment(D, G) → s
  26. Segment(H, G) → b1
  27. OrthogonalLine(G, b1) → e1
  28. Point(e1) → I
  29. Segment(G, I) → t_1
  30. Circle(D, c1) → d1
  31. Circle(B, c2) → f1
  32. Intersect(d1, f1, 1.0) → J
  33. Segment(D, J) → a1
  34. Segment(B, J) → g1
  35. Circle(D, c3) → h1
  36. Circle(B, c4) → k1
  37. Intersect(h1, k1, 2.0) → K
  38. Circle(B, c2) → p1
  39. OrthogonalLine(B, g1) → i1
  40. Intersect(p1, i1, 1.0) → L
  41. Segment(B, L) → j1
  42. Segment(B, K) → l1
  43. Line(L, l1) → m1
  44. Line(K, j1) → n1
  45. OrthogonalLine(K, n1) → q1
  46. Point(q1) → M
  47. Intersect(m1, n1) → N
  48. Segment(K, M) → r1
  49. Segment(D, K) → s1
  50. Circle(B, c2) → d2
  51. Circle(B, c4) → h2
  52. Rotate(D, 240.0*°, C) → O
  53. Angle(O, C, D) → γ
  54. Circle(O, c1) → t1
  55. Circle(A, c2) → e2
  56. Intersect(t1, e2, 2.0) → P
  57. Segment(O, P) → a2
  58. Segment(A, P) → b2
  59. OrthogonalLine(A, b2) → f2
  60. Intersect(e2, f2, 2.0) → Q
  61. Segment(A, Q) → g2
  62. Circle(O, c3) → k2
  63. Circle(A, c4) → p2
  64. Intersect(k2, p2, 1.0) → R
  65. Segment(O, R) → i2
  66. Segment(A, R) → j2
  67. Line(R, k) → l2
  68. OrthogonalLine(R, l2) → m2
  69. Line(R, g2) → n2
  70. Line(Q, j2) → q2
  71. Intersect(n2, q2) → S
  72. OrthogonalLine(R, n2) → r2
  73. Point(r2) → T
  74. Segment(R, T) → s2
  75. Circle(O, c1) → t2
  76. Circle(B, c2) → d3
  77. Intersect(t2, d3, 1.0) → U
  78. Segment(O, U) → a3
  79. Segment(B, U) → b3
  80. OrthogonalLine(B, b3) → e3
  81. Intersect(p1, e3, 1.0) → V
  82. Circle(O, c3) → f3
  83. Circle(B, c4) → g3
  84. Intersect(f3, g3, 2.0) → W
  85. Segment(B, W) → h3
  86. Line(V, h3) → i3
  87. Segment(B, V) → j3
  88. Line(W, j3) → k3
  89. OrthogonalLine(W, k3) → l3
  90. Point(l3) → Z
  91. Intersect(i3, k3) → A1
  92. Segment(O, W) → m3
  93. Segment(W, Z) → n3
  94. Segment(V, A1) → p3
  95. Segment(A1, W) → q3
  96. Segment(A1, Z) → r3
  97. Segment(U, V) → s3
  98. Segment(J, L) → t3
  99. Segment(N, K) → a4
  100. Segment(N, L) → b4
  101. Segment(N, M) → d4
  102. Segment(E, F) → e4
  103. Segment(R, S) → f4
  104. Segment(S, T) → g4
  105. Segment(Q, S) → h4
  106. Segment(F, H) → i4
  107. Segment(H, I) → j4
  108. Segment(P, Q) → k4
  109. Segment(C, O) → l4
  110. Segment(C, D) → m4
  111. OrthogonalLine(T, s2) → n4
  112. OrthogonalLine(I, t_1) → p4
  113. OrthogonalLine(Z, n3) → q4
  114. OrthogonalLine(M, r1) → r4
  115. Line(F1, G1) → c5
  116. Line(T, c5) → s4
  117. Line(I, c5) → t4
  118. Line(Z, c5) → a5
  119. Line(M, c5) → b5
  120. Point(s4) → B1
  121. Point(t4) → C1
  122. Point(a5) → D1
  123. Point(b5) → E1
  124. Segment(T, B1) → d5
  125. Segment(I, C1) → e5
  126. Segment(M, E1) → f5
  127. Segment(Z, D1) → g5
  128. Segment(H1, I1) → h5
  129. Circle(P, 1.5) → k5
  130. Point(k5) → J1
  131. Circle(H1, 1.0) → p5
  132. Circle(I1, 1.0) → q5
  133. Segment(P, J1) → m5
  134. Circle(J1, 1.0) → r5
  135. Point(r5) → K1
  136. Segment(J1, K1) → i5
  137. Segment(H1, K1) → j5
  138. Segment(J1, H1) → a6
  139. Rotate(J1, 45.0*°, K1) → L1
  140. Angle(J1, K1, L1) → δ
  141. Circle(K1, 0.6) → s5
  142. Segment(K1, L1) → l5
  143. Intersect(s5, l5, 1.0) → M1
  144. Segment(K1, M1) → n5
  145. Segment(I1, M1) → t5
  146. Rotate(K1, 300.0*°, M1) → N1
  147. Angle(N1, M1, K1) → ε
  148. Mirror(M1, N1) → O1
  149. Segment(K1, O1) → b6
  150. Segment(O1, N1) → c6
  151. Segment(N1, M1) → d6
  152. Segment(H1, A) → e6
  153. Segment(A, B) → f6
  154. Segment(B, P1) → g6
  155. Segment(P1, I1) → h6

AI 绘图提示语参考

画一个受 Theo Jansen 启发的多腿连杆机构，展示其周期性行走步态。从一个固定基点出发，绘制一根可旋转的连杆，取其中点作为枢轴，绕该点旋转得到对称点；以枢轴为心、给定半径作圆，与连杆相交确定关节点；再以该关节点为心作两圆，分别与基点为心的圆相交得到两个新关节；连接这些关节形成三角形框架，过基点作垂线与圆相交得到支撑点；再通过垂线、连线的交点构造出腿部的伸展段，利用镜像和垂足构造出另一侧对称腿；最终所有连杆随参数滑块联动，呈现连续的步态轨迹。
以上提示语为根据原始绘图命令整理而来，仅供参考。