机器人手臂模拟

机器人手臂模拟
几何画板及绘图内容加载中,请稍等……
2020-04-11 22:31
本范例通过几何画板展示了一个机器人手臂的设计,体现了数学与工程的紧密联系。它涉及旋转、几何变换、平移、三角函数等核心数学概念。通过使用Polygon、Point、CircleSector、Intersect、Segment、Circle、Rotate、Vector、Translate、Midpoint、CircleArc、Line、OrthogonalLine等命令,可以构造出一个动态的机器人手臂模型。适合用于中学阶段的STEM教育活动。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Polygon(E, F, G, H) → q2, e, f, g, h
  3. Point(h) → I
  4. CircleSector(I, H, E) → k
  5. Point(e) → J
  6. Intersect(d, g) → K
  7. Segment(J, K) → i
  8. Intersect(f, g) → L
  9. Intersect(d, e) → M
  10. Segment(L, M) → j
  11. Intersect(j, i) → N
  12. Circle(N, O) → p
  13. Rotate(E, (-α), N) → E'
  14. Rotate(F, (-α), N) → F'
  15. Rotate(G, (-α), N) → G'
  16. Rotate(H, (-α), N) → H'
  17. Polygon(E', F', G', H') → q2', e', f', g', h'
  18. Rotate(k, (-α), N) → k'
  19. Rotate(I, (-α), N) → I'
  20. Point(b) → P
  21. Circle(P, 0.75) → q
  22. Point(b) → Q
  23. Circle(Q, 0.75) → r
  24. Vector(Q, P1) → u
  25. Translate(A, u) → A'
  26. Translate(B, u) → B'
  27. Translate(C, u) → C'
  28. Translate(D, u) → D'
  29. Polygon(A', B', C', D') → q1', a', b', c', d'
  30. Translate(E', u) → E''
  31. Translate(F', u) → F''
  32. Translate(G', u) → G''
  33. Translate(H', u) → H''
  34. Polygon(E'', F'', G'', H'') → q2'', e'', f'', g'', h''
  35. Translate(k', u) → k''
  36. Translate(I', u) → I''
  37. Translate(p, u) → p'
  38. Translate(N, u) → N'
  39. Translate(r, u) → r'
  40. Translate(q, u) → q'
  41. Translate(P, u) → P'
  42. Translate(Q, u) → Q'
  43. Polygon(E, H, S, T) → q3, e_1, h_1, s, t
  44. Rotate(E, (-α), N) → E'_1
  45. Rotate(H, (-α), N) → H'_1
  46. Rotate(S, (-α), N) → S'
  47. Rotate(T, (-α), N) → T'
  48. Polygon(E'_1, H'_1, S', T') → q3', e'_1, h'_1, s', t'
  49. Translate(E'_1, u) → U
  50. Translate(H'_1, u) → V
  51. Translate(S', u) → S''
  52. Translate(T', u) → T''
  53. Polygon(U, V, S'', T'') → q3'', u_1, v, s'', t''
  54. Rotate(U, (-β), I'') → U'
  55. Rotate(V, (-β), I'') → V'
  56. Rotate(S'', (-β), I'') → S'''
  57. Rotate(T'', (-β), I'') → T'''
  58. Polygon(U', V', S''', T''') → q3''', u', v', s''', t'''
  59. Rotate(k'', (-β), I'') → k'''
  60. Polygon(T, S, W, Z) → q4, t_1, s_1, w, z_1
  61. Rotate(T, (-α), N) → T'_1
  62. Rotate(S, (-α), N) → S'_1
  63. Rotate(W, (-α), N) → W'
  64. Rotate(Z, (-α), N) → Z'
  65. Polygon(T'_1, S'_1, W', Z') → q4', t'_1, s'_1, w', z'
  66. Translate(T'_1, u) → A_1
  67. Translate(S'_1, u) → B_1
  68. Translate(W', u) → W''
  69. Translate(Z', u) → Z''
  70. Polygon(A_1, B_1, W'', Z'') → q4'', a_1, b_1, w'', z''
  71. Rotate(A_1, (-β), I'') → C_1
  72. Rotate(B_1, (-β), I'') → D_1
  73. Rotate(W'', (-β), I'') → W'''
  74. Rotate(Z'', (-β), I'') → Z'''
  75. Polygon(C_1, D_1, W''', Z''') → q4''', c_1, d_1, w''', z'''
  76. Midpoint(s''') → E_1
  77. Rotate(C_1, (-γ), E_1) → F_1
  78. Rotate(D_1, (-γ), E_1) → G_1
  79. Rotate(W''', (-γ), E_1) → H_1
  80. Rotate(Z''', (-γ), E_1) → I_1
  81. Polygon(F_1, G_1, H_1, I_1) → q5, f_1, g_1, h_2, i_1
  82. Midpoint(s) → J_1
  83. CircleArc(J_1, S, T) → k_1
  84. Rotate(k_1, (-α), N) → p_1
  85. Rotate(J_1, (-α), N) → K_1
  86. Translate(K_1, u) → L_1
  87. Translate(p_1, u) → q_1
  88. Rotate(q_1, (-β), I'') → r_1
  89. Rotate(r_1, (-γ), E_1) → c_2
  90. Rotate(L_1, (-β), I'') → M_1
  91. Midpoint(w) → N_1
  92. Polygon(N_1, W, O_1) → t1, o_1, n_1, w_1
  93. Polygon(Z, N_1, P_1) → t2, p_2, z_2, n_2
  94. Circle(W, O_1) → d_2
  95. Point(d_2) → Q_1
  96. Polygon(O_1, W, Q_1) → t3, q_2, o_2, w_2
  97. Line(W, Q_1) → l
  98. OrthogonalLine(W, l) → m
  99. OrthogonalLine(Q_1, l) → n
  100. Point(m) → R_1
  101. OrthogonalLine(R_1, m) → j_1
  102. Point(m) → S_1
  103. Line(S_1, j_1) → l_1
  104. Point(l_1) → T_1
  105. Point(j_1) → U_1
  106. Intersect(n, l_1) → V_1
  107. Polygon(W, R_1, U_1, T_1, V_1, Q_1) → poly1, w_3, r_2, u_2, t_2, v_1, q_3
  108. Line(T_1, N_1) → m_1
  109. Circle(Z, P_1) → e_2
  110. Point(e_2) → W_1
  111. Polygon(Z, P_1, W_1) → t4, w_4, z_3, p_3
  112. Line(Z, W_1) → f_2
  113. OrthogonalLine(Z, f_2) → g_2
  114. OrthogonalLine(W_1, f_2) → i_2
  115. Point(i_2) → Z_1
  116. OrthogonalLine(Z_1, i_2) → j_2
  117. Point(g_2) → A_2
  118. OrthogonalLine(A_2, g_2) → k_2
  119. Point(k_2) → B_2
  120. Point(j_2) → C_2
  121. Polygon(W_1, Z_1, C_2, B_2, A_2, Z) → poly2, w_5, z_4, c_3, b_2, a_2, z_5
  122. Rotate(N_1, (-α), N) → D_2
  123. Rotate(W, (-α), N) → W'_1
  124. Rotate(O_1, (-α), N) → E_2
  125. Polygon(D_2, W'_1, E_2) → t1', e_3, d_3, w'_1
  126. Rotate(W, (-α), N) → W'_2
  127. Rotate(R_1, (-α), N) → F_2
  128. Rotate(U_1, (-α), N) → G_2
  129. Rotate(T_1, (-α), N) → H_2
  130. Rotate(V_1, (-α), N) → I_2
  131. Rotate(Q_1, (-α), N) → J_2
  132. Polygon(W'_2, F_2, G_2, H_2, I_2, J_2) → poly1', w'_2, f_3, g_3, h_3, i_3, j_3
  133. Rotate(Z, (-α), N) → Z'_1
  134. Rotate(N_1, (-α), N) → K_2
  135. Rotate(P_1, (-α), N) → L_2
  136. Polygon(Z'_1, K_2, L_2) → t2', l_2, z'_1, k_3
  137. Rotate(W_1, (-α), N) → M_2
  138. Rotate(Z_1, (-α), N) → N_2
  139. Rotate(C_2, (-α), N) → O_2
  140. Rotate(B_2, (-α), N) → P_2
  141. Rotate(A_2, (-α), N) → Q_2
  142. Rotate(Z, (-α), N) → Z'_2
  143. Polygon(M_2, N_2, O_2, P_2, Q_2, Z'_2) → poly2', m_2, n_3, o_3, p_4, q_4, z'_2
  144. Translate(M_2, u) → R_2
  145. Translate(N_2, u) → S_2
  146. Translate(O_2, u) → T_2
  147. Translate(P_2, u) → U_2
  148. Translate(Q_2, u) → V_2
  149. Translate(Z'_2, u) → W_2
  150. Polygon(R_2, S_2, T_2, U_2, V_2, W_2) → poly2'', r_3, s_2, t_3, u_3, v_2, w_6
  151. Translate(D_2, u) → Z_2
  152. Translate(W'_1, u) → A_3
  153. Translate(E_2, u) → B_3
  154. Polygon(Z_2, A_3, B_3) → t1'', b_3, z_6, a_3
  155. Translate(W'_2, u) → C_3
  156. Translate(F_2, u) → D_3
  157. Translate(G_2, u) → E_3
  158. Translate(H_2, u) → F_3
  159. Translate(I_2, u) → G_3
  160. Translate(J_2, u) → H_3
  161. Polygon(C_3, D_3, E_3, F_3, G_3, H_3) → poly1'', c_4, d_4, e_4, f_4, g_4, h_4
  162. Translate(Z'_1, u) → I_3
  163. Translate(K_2, u) → J_3
  164. Translate(L_2, u) → K_3
  165. Polygon(I_3, J_3, K_3) → t2'', k_4, i_4, j_4
  166. Rotate(C_3, (-β), I'') → L_3
  167. Rotate(D_3, (-β), I'') → M_3
  168. Rotate(E_3, (-β), I'') → N_3
  169. Rotate(F_3, (-β), I'') → O_3
  170. Rotate(G_3, (-β), I'') → P_3
  171. Rotate(H_3, (-β), I'') → Q_3
  172. Polygon(L_3, M_3, N_3, O_3, P_3, Q_3) → poly1''', l_3, m_3, n_4, o_4, p_5, q_5
  173. Rotate(R_2, (-β), I'') → R_3
  174. Rotate(S_2, (-β), I'') → S_3
  175. Rotate(T_2, (-β), I'') → T_3
  176. Rotate(U_2, (-β), I'') → U_3
  177. Rotate(V_2, (-β), I'') → V_3
  178. Rotate(W_2, (-β), I'') → W_3
  179. Polygon(R_3, S_3, T_3, U_3, V_3, W_3) → poly2''', r_4, s_3, t_4, u_4, v_3, w_7
  180. Rotate(Z_2, (-β), I'') → Z_3
  181. Rotate(A_3, (-β), I'') → A_4
  182. Rotate(B_3, (-β), I'') → B_4
  183. Polygon(Z_3, A_4, B_4) → t1''', b_4, z_7, a_4
  184. Rotate(I_3, (-β), I'') → C_4
  185. Rotate(J_3, (-β), I'') → D_4
  186. Rotate(K_3, (-β), I'') → E_4
  187. Polygon(C_4, D_4, E_4) → t2''', e_5, c_5, d_5
  188. Rotate(R_3, (-γ), E_1) → F_4
  189. Rotate(S_3, (-γ), E_1) → G_4
  190. Rotate(T_3, (-γ), E_1) → H_4
  191. Rotate(U_3, (-γ), E_1) → I_4
  192. Rotate(V_3, (-γ), E_1) → J_4
  193. Rotate(W_3, (-γ), E_1) → K_4
  194. Polygon(F_4, G_4, H_4, I_4, J_4, K_4) → poly3, f_5, g_5, h_5, i_5, j_5, k_5
  195. Rotate(C_4, (-γ), E_1) → L_4
  196. Rotate(D_4, (-γ), E_1) → M_4
  197. Rotate(E_4, (-γ), E_1) → N_4
  198. Polygon(L_4, M_4, N_4) → t5, n_5, l_4, m_4
  199. Rotate(L_3, (-γ), E_1) → O_4
  200. Rotate(M_3, (-γ), E_1) → P_4
  201. Rotate(N_3, (-γ), E_1) → Q_4
  202. Rotate(O_3, (-γ), E_1) → R_4
  203. Rotate(P_3, (-γ), E_1) → S_4
  204. Rotate(Q_3, (-γ), E_1) → T_4
  205. Polygon(O_4, P_4, Q_4, R_4, S_4, T_4) → poly4, o_5, p_6, q_6, r_5, s_4, t_5
  206. Rotate(Z_3, (-γ), E_1) → U_4
  207. Rotate(A_4, (-γ), E_1) → V_4
  208. Rotate(B_4, (-γ), E_1) → W_4
  209. Polygon(U_4, V_4, W_4) → t6, w_8, u_5, v_4
  210. Rotate(O_4, (-δ), H_1) → Z_4
  211. Rotate(P_4, (-δ), H_1) → A_5
  212. Rotate(Q_4, (-δ), H_1) → B_5
  213. Rotate(R_4, (-δ), H_1) → C_5
  214. Rotate(S_4, (-δ), H_1) → D_5
  215. Rotate(T_4, (-δ), H_1) → E_5
  216. Polygon(Z_4, A_5, B_5, C_5, D_5, E_5) → poly4', z_8, a_5, b_5, c_6, d_6, e_6
  217. Rotate(F_4, δ, I_1) → F_5
  218. Rotate(G_4, δ, I_1) → G_5
  219. Rotate(H_4, δ, I_1) → H_5
  220. Rotate(I_4, δ, I_1) → I_5
  221. Rotate(J_4, δ, I_1) → J_5
  222. Rotate(K_4, δ, I_1) → K_5
  223. Polygon(F_5, G_5, H_5, I_5, J_5, K_5) → poly3', f_6, g_6, h_6, i_6, j_6, k_6
  224. Polygon(M_5, N_5, L_5, O_5) → q6, m_5, n_6, l_5, o_6
  225. Point(n_6) → R_5
  226. Polygon(N_5, P_5, Q_5, R_5) → q7, n_7, p_7, q_7, r_6
  227. Polygon(P_5, S_5, T_5, U_5) → q8, p_8, s_5, t_6, u_6
  228. Segment(L_5, R_5) → l_6
  229. Segment(S_5, Q_5) → m_6
  230. Point(q_7) → Z_5
  231. Point(q_7) → A_6
  232. Polygon(V_5, W_5, Z_5, A_6) → q9, v_5, w_9, z_9, a_6

AI 绘图提示语参考

画一个模拟机械臂的图形,包含两个四边形和多个圆形、线段,展示旋转和几何变换。首先绘制一个基础机械臂结构,通过旋转和相交确定关键点,添加圆形和线段表示机械臂的关节和连接。接着,将整个结构沿向量方向平移,并再次旋转部分结构,模拟机械臂的运动。最后,添加辅助圆形和线段,使图形更完整,体现数学与工程的结合。
以上提示语为根据原始绘图命令整理而来,仅供参考。