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Theo Jansen 机械装置

Theo Jansen 机械装置
几何画板及绘图内容加载中，请稍等……
2014-06-04 07:27
测试改名0圆多边形向量几何作图
所属专题 GeoGebra and 4D Frame: ideas collection
①本范例演示了Theo Jansen设计的机械装置，通过旋转和几何变换模拟行走机构。②涉及核心数学概念包括圆与三角形的相似性、向量变换、几何作图等。③构造过程中运用了Line（线段）、Circle（圆）、Intersect（交点）、Point（点）、Rotate（旋转）、Segment（线段）、OrthogonalLine（垂线）、Polygon（多边形）、If（条件判断）、Vector（向量）、Dilate（缩放）、Translate（平移）、Midpoint（中点）、PointIn（点在对象内）、Mirror（镜像）等GeoGebra命令和对象。④适合高中及以上学生学习和理解机械原理与几何变换。

GeoGebra 命令及参数

  1. Line(B_4, yAxis) → l_9
  2. Line(A, xAxis) → g
  3. Circle(A, 5) → f
  4. Intersect(f, g, 1) → C
  5. Circle(A, r) → c
  6. Point(c) → B
  7. Rotate(B, α, A) → B'
  8. Rotate(B', 120*°, A) → B''_1
  9. Rotate(B''_1, 120*°, A) → B'''
  10. Segment(A, B''') → a
  11. Segment(A, B''_1) → b
  12. Segment(A, B') → d
  13. Intersect(f, g, 2) → D
  14. Circle(D, r_2) → k
  15. Circle(C, r_2) → h
  16. Point(h) → E
  17. Circle(B', 6) → e
  18. Intersect(h, e, 1) → F
  19. Intersect(h, e, 2) → G
  20. Intersect(k, e, 2) → H
  21. Intersect(k, e, 1) → I
  22. Segment(B', F) → i
  23. Segment(B', G) → j
  24. Segment(B', H) → l
  25. Segment(B', I) → m
  26. Segment(C, F) → n
  27. Segment(C, G) → p
  28. Segment(D, H) → q
  29. Segment(D, I) → s
  30. OrthogonalLine(C, n) → t
  31. OrthogonalLine(D, q) → a_1
  32. Intersect(h, t, 2) → J
  33. Intersect(k, a_1, 1) → K
  34. Polygon(F, C, J) → polígono1, j_1, f_1, c_1
  35. Polygon(H, K, D) → polígono2, d_1, h_1, k_1
  36. Line(G, t) → b_1
  37. Line(I, a_1) → e_1
  38. Line(J, p) → g_1
  39. Line(K, s) → i_1
  40. Intersect(b_1, g_1) → L
  41. Intersect(e_1, i_1) → M
  42. Polygon(K, M, I, D) → polígono3, k_2, m_1, i_2, d_2
  43. Polygon(C, G, L, J) → polígono4, c_2, g_2, l_1, j_2
  44. OrthogonalLine(G, b_1) → n_1
  45. Circle(G, 4) → q_1
  46. Intersect(q_1, n_1, 2) → N
  47. Polygon(G, L, N) → polígono5, n_2, g_3, l_2
  48. Circle(N, 1) → s_1
  49. Intersect(s_1, n_1, 2) → P_4
  50. Segment(N, P_4) → a_2
  51. OrthogonalLine(I, m_1) → p_1
  52. Circle(I, 4) → r_1
  53. Intersect(r_1, p_1, 2) → O
  54. Polygon(I, O, M) → polígono6, m_2, i_3, o
  55. Circle(O, 1) → t_1
  56. Intersect(t_1, p_1) → Q_4, R
  57. Segment(O, R) → b_2
  58. Circle(B''_1, 6) → e_2
  59. Intersect(h, e_2, 1) → S
  60. Intersect(h, e_2, 2) → T
  61. Intersect(k, e_2, 2) → U
  62. Intersect(k, e_2, 1) → V
  63. Segment(S, B''_1) → f_2
  64. Segment(B''_1, T) → h_2
  65. Segment(U, B''_1) → p_2
  66. Segment(V, B''_1) → q_2
  67. Segment(D, U) → r_6
  68. Segment(V, D) → s_2
  69. Segment(S, C) → t_2
  70. Segment(C, T) → a_3
  71. OrthogonalLine(C, t_2) → b_3
  72. OrthogonalLine(D, r_6) → c_3
  73. Intersect(k, c_3, 1) → W
  74. Intersect(h, b_3, 1) → Z
  75. Polygon(S, C, Z) → polígono7, z, s_3, c_4
  76. Polygon(U, W, D) → polígono8, d_3, u_2, w
  77. Line(Z, a_3) → e_3
  78. Line(W, s_2) → f_3
  79. Line(T, s_3) → h_3
  80. Line(V, u_2) → j_3
  81. Intersect(e_3, h_3) → A_1
  82. Intersect(f_3, j_3) → B_1
  83. Polygon(Z, A_1, T, C) → polígono9, z_1, a_4, t_3, c_5
  84. Polygon(D, V, B_1, W) → polígono10, d_4, v, b_4, w_1
  85. OrthogonalLine(T, a_4) → k_3
  86. OrthogonalLine(V, v) → l_3
  87. Circle(T, 4) → p_3
  88. Circle(V, 4) → q_3
  89. Intersect(p_3, k_3, 1) → C_1
  90. Intersect(q_3, l_3, 1) → D_1
  91. Polygon(A_1, C_1, T) → polígono11, t_4, a_5, c_6
  92. Polygon(B_1, D_1, V) → polígono12, v_1, b_5, d_5
  93. Circle(C_1, 1) → r_3
  94. Circle(D_1, 1) → e_4
  95. Intersect(r_3, k_3, 1) → E_1
  96. Intersect(e_4, l_3, 1) → F_1
  97. Segment(C_1, E_1) → m_3
  98. Segment(D_1, F_1) → n_3
  99. Circle(B''', 6) → f_4
  100. Intersect(h, f_4) → G_1, H_1, ,
  101. Intersect(k, f_4) → I_1, J_1, ,
  102. Segment(G_1, B''') → g_4
  103. Segment(H_1, B''') → h_4
  104. Segment(B''', J_1) → i_4
  105. Segment(B''', I_1) → j_4
  106. Segment(D, J_1) → k_4
  107. Segment(D, I_1) → l_4
  108. Segment(H_1, C) → m_4
  109. Segment(C, G_1) → n_4
  110. OrthogonalLine(C, n_4) → p_4
  111. OrthogonalLine(D, k_4) → q_4
  112. Intersect(h, p_4, 2) → K_1
  113. Intersect(k, q_4, 1) → L_1
  114. Polygon(J_1, L_1, D) → polígono13, d_6, j_5, l_5
  115. Polygon(G_1, C, K_1) → polígono14, k_5, g_5, c_7
  116. Line(H_1, g_5) → r_4
  117. Line(I_1, j_5) → s_4
  118. Line(K_1, m_4) → e_5
  119. Line(L_1, l_4) → f_5
  120. Intersect(r_4, e_5) → M_1
  121. Intersect(s_4, f_5) → N_1
  122. Polygon(K_1, C, H_1, M_1) → polígono15, k_6, c_8, h_5, m_5
  123. Polygon(L_1, N_1, I_1, D) → polígono16, l_6, n_5, i_5, d_7
  124. Line(H_1, m_4) → p_5
  125. Line(I_1, i_5) → q_5
  126. Circle(H_1, 4) → r_5
  127. Circle(I_1, 4) → s_5
  128. OrthogonalLine(H_1, h_5) → t_5
  129. Circle(H_1, 4) → e_6
  130. Circle(I_1, 4) → f_6
  131. Intersect(e_6, t_5, 2) → O_1
  132. Polygon(H_1, O_1, M_1) → polígono17, m_6, h_6, o_1
  133. Circle(O_1, 1) → g_6
  134. Intersect(g_6, t_5, 2) → Q_1
  135. Segment(O_1, Q_1) → a_6
  136. Polygon(F, C, B') → poly1, b', f_7, c_9
  137. Polygon(H, B', D) → poly2, d_8, h_7, b'_1
  138. Polygon(G, C, B') → poly3, b'_2, g_7, c_{10}
  139. Polygon(D, I, B') → poly4, b'_3, d_9, i_7
  140. If(patas_1, 0, 1) → u
  141. If(patas_1, 0, 1) → v_2
  142. If(patas_1, 0, 1) → w_2
  143. If(patas_1, 0, 1) → o_3
  144. If(patas_1, 0, 1) → v_3
  145. If(patas_1, 0, 1) → w_3
  146. Polygon(B', F, J, L, N, G) → poly8, b'_4, f_9, j_7, l_7, n_7, g_9
  147. Polygon(B', H, K, M, O, I) → poly9, b'_5, h_9, k_7, m_7, o_2, i_8
  148. Segment(K_2, M_2) → s_6
  149. Point(s_6) → N_2
  150. Vector(M_2, N_2) → u_1
  151. Dilate(N_2, dezact1, K_2) → O_2
  152. Vector(K_2, O_2) → u_3
  153. Translate(B', u_3) → B''_2
  154. Translate(F, u_3) → F'
  155. Translate(J, u_3) → J'
  156. Translate(L, u_3) → L'
  157. Translate(N, u_3) → N'
  158. Translate(G, u_3) → G'
  159. Polygon(B''_2, F', J', L', N', G') → poly8', b'', f', j', l', n', g'
  160. Dilate(N_2, dezact1_2, K_2) → Q_2
  161. Vector(K_2, Q_2) → u_4
  162. Translate(B', u_4) → B''
  163. Translate(H, u_4) → H'
  164. Translate(K, u_4) → K'
  165. Translate(M, u_4) → M'
  166. Translate(O, u_4) → O'
  167. Translate(I, u_4) → I'
  168. Polygon(B'', H', K', M', O', I') → poly9', b''_1, h', k', m', o', i'
  169. Segment(G', I') → t_6
  170. Midpoint(t_6) → R_2
  171. OrthogonalLine(R_2, t_6) → p_7
  172. Circle(R_2, 9) → q_7
  173. Intersect(q_7, p_7, 2) → S_2
  174. Intersect(q_7, p_7, 1) → T_2
  175. Segment(T_2, S_2) → r_7
  176. Line(P_1, xAxis) → b_6
  177. Point(b_6) → R_1
  178. Segment(P_1, R_1) → i_6
  179. Segment(P_1, R_1) → j_6
  180. Midpoint(i_6) → T_1
  181. OrthogonalLine(T_1, b_6) → n_6
  182. Circle(T_1, 8) → p_6
  183. Intersect(p_6, n_6, 2) → G_2
  184. Circle(G_2, r) → q_6
  185. PointIn(q_6) → P_2
  186. Segment(G_2, P_2) → a_7
  187. Rotate(G_2, 45*°, G_2) → U_2
  188. Rotate(P_2, δ, G_2) → V_2
  189. Segment(U_2, V_2) → b_7
  190. Line(U_2, b_7) → e_7
  191. Mirror(e_7, n_6) → s_7
  192. Point(n_6) → W_2
  193. Line(W_2, b_6) → t_7
  194. Intersect(e_7, t_7) → Z_2
  195. Intersect(s_7, t_7) → A_3
  196. Segment(V_2, Z_2) → a_8
  197. Intersect(q_6, s_7, 2) → B_3
  198. Line(B_3, e_7) → e_8
  199. Line(V_2, s_7) → f_8
  200. Intersect(e_8, f_8) → C_3
  201. Circle(C_3, r) → g_8
  202. Intersect(g_8, f_8, 2) → D_3
  203. Intersect(g_8, e_8, 2) → E_3
  204. Line(D_3, e_8) → h_8
  205. Line(E_3, f_8) → j_8
  206. Intersect(h_8, j_8) → F_3
  207. Segment(D_3, C_3) → l_8
  208. Segment(E_3, C_3) → n_8
  209. Segment(C_3, V_2) → p_8
  210. Segment(B_3, C_3) → q_8
  211. Circle(F_3, r) → r_8
  212. Intersect(r_8, j_8, 2) → G_3
  213. Intersect(r_8, h_8, 2) → H_3
  214. Segment(D_3, H_3) → k_8
  215. Segment(E_3, G_3) → m_8
  216. Line(H_3, b_6) → s_8
  217. Circle(H_3, 2) → t_8
  218. Circle(G_3, 2) → e_9
  219. Intersect(n_6, s_8) → I_3
  220. Circle(I_3, 5) → k_9
  221. Intersect(k_9, s_8, 1) → J_3
  222. Intersect(k_9, s_8, 2) → K_3
  223. Circle(W_2, 7) → p_9
  224. Intersect(p_9, t_7, 1) → P_3
  225. Intersect(p_9, t_7, 2) → Q_3
  226. Circle(W_2, 4) → q_9
  227. Intersect(q_9, n_6, 1) → R_3
  228. OrthogonalLine(R_3, n_6) → a_9
  229. Intersect(p_9, a_9, 2) → S_3
  230. Intersect(p_9, a_9, 1) → T_3
  231. Segment(G_3, H_3) → b_9
  232. Segment(B_3, U_2) → b_8
  233. OrthogonalLine(I_1, n_5) → i_9
  234. Circle(I_1, 4) → r_9
  235. Intersect(r_9, i_9, 2) → U_3
  236. Intersect(n_5, l_6) → V_3
  237. Segment(V_3, U_3) → j_9
  238. Circle(U_3, 1) → s_9
  239. Intersect(s_9, i_9, 2) → W_3
  240. Segment(I_1, U_3) → t_9
  241. Polygon(I_1, V_3, U_3) → poly6, u_5, i_{10}, v_4
  242. Segment(U_3, W_3) → a_{10}
  243. Point(l_9) → C_4
  244. Segment(P, Q) → m_9
  245. Segment(P_5, Q_5) → m_{10}
  246. Point(l_9) → F_4
  247. Point(l_9) → G_4
  248. Polygon(E_4, F_4, G_4, H_4) → Botonanima, e_{10}, f_{10}, g_{10}, h_{10}
  249. Point(Circle[I_4, 12]) → J_4
  250. Polygon(I_4, J_4, K_4, L_4) → polígono18, i_{11}, j_{10}, k_{10}, l_{10}
  251. Point(Circle[I_5, 12]) → J_5
  252. Polygon(I_5, J_5, K_5, L_5) → polígono18_1, i_{12}, j_{11}, k_{11}, l_{11}

AI 绘图提示语参考

绘制一个基于西奥·詹森机构的几何构造图。先画一条水平轴和一条竖直轴，以水平轴上一点为圆心作两个同心圆，其中一个半径固定，另一个半径可调。在固定圆上取两点，分别作为旋转中心，将可调圆上的点绕中心旋转特定角度，形成三个对称的顶点。从中心点向这些顶点连线，构成三角形骨架。再以固定圆上的另一点为圆心作圆，与之前的圆相交，得到多个交点，用线段连接这些交点形成连杆结构。在连杆的垂直方向作垂线，与圆相交得到新点，进而构造多边形和三角形，最后在特定点处添加一个小圆作为标记。整体呈现对称的机械运动结构，包含圆、三角形、多边形和线段。
以上提示语为根据原始绘图命令整理而来，仅供参考。