连杆曲线演示
几何画板及绘图内容加载中,请稍等……
①本范例演示通过连杆机构生成的复杂曲线图形;②涉及的核心数学概念包括参数方程、解析几何、几何变换和三角函数;③作图要点提炼自构造摘要,使用了Ray(射线)、Midpoint(中点)、Line(直线)、Intersect(交点)、Polygon(多边形)、Centroid(重心)、Mirror(镜像)、Circle(圆)、Point(点)、Rotate(旋转)、Segment(线段)、CurveCartesian(笛卡尔曲线)、Semicircle(半圆)等GeoGebra命令和对象;④适合高中及以上学生学习和理解参数曲线的生成过程及几何变换的应用。
GeoGebra 命令及参数
Ray(T, C_1) → c_1Ray(S, B_1) → b_1Midpoint(J, T) → ZMidpoint(Z, T) → A_1Line(H, J) → a_1Line(U, a_1) → d_1Intersect(c_1, d_1) → E_1Intersect(b_1, d_1) → D_1Midpoint(S, I) → VMidpoint(V, S) → WPolygon(D_1, E_1, C_1, A_1, W, B_1) → poly1, e_1, f_2, g_2, h_2, w_1, i_2Midpoint(f_2) → J_1Centroid(poly1) → F_1Mirror(B_1, F_1) → G_1Midpoint(G_1, J_1) → L_1Midpoint(G_1, L_1) → M_1Midpoint(G_1, M_1) → V_1Line(A, xAxis) → nCircle(A, R) → cIntersect(c, n) → E, FPoint(c) → BCircle(A, R + r1) → dRotate(F, (t * w), A) → B'Ray(A, B') → aIntersect(d, a) → C,Circle(C, B') → eRotate(B', (t * w1) + 3.141592653589793, C) → B''Circle(C, r1 + r2) → fRay(C, B'') → bIntersect(f, b) → D,Circle(D, B'') → gRotate(B'', (t * w2) + 3.141592653589793, D) → B'''Segment(D, B''') → hSegment(C, B'') → iSegment(A, B') → jCurveCartesian(x(A) + ((R + r1) * (cos((w * i)) + cos((w1 * i)))), y(A) + ((R + r1) * (sin((w * i)) + sin((w1 * i)))), i, 0, t) → kCurveCartesian(x(A) + ((R + r1) * cos((w * i))) - (r1 * cos(((w1 + w) * i) + 3.141592653589793)), y(A) + ((R + r1) * sin((w * i))) - (r1 * sin(((w1 + w) * i) + 3.141592653589793)), i, 0, t) → oCurveCartesian(x(A) + ((R + r1) * cos((w * i))) - ((r1 + r2) * cos(((w1 + w) * i) + 3.141592653589793)) - (r2 * cos(((w + w1 + w2) * i) + 3.141592653589793)), y(A) + ((R + r1) * sin((w * i))) - ((r1 + r2) * sin(((w1 + w) * i) + 3.141592653589793)) - (r2 * sin(((w + w1 + w2) * i) + 3.141592653589793)), i, 0, t) → lCurveCartesian(x(A) + ((R + r1) * cos((w * i))) - ((r1 + r2) * cos(((w1 + w) * i) + 3.141592653589793)) - (r2 * cos(((w + w1 + w2) * i) + 3.141592653589793)), y(A) + ((R + r1) * sin((w * i))) - ((r1 + r2) * sin(((w1 + w) * i) + 3.141592653589793)) - (r2 * sin(((w + w1 + w2) * i) + 3.141592653589793)), i, 0, t) → mPoint(j) → GSegment(E, G) → sSegment(B', C) → f_1Segment(B'', D) → g_1Segment(D, B''') → h_1Polygon(I, A, J) → t1, p, q, rMidpoint(q) → KMidpoint(J, K) → LMidpoint(p) → MMidpoint(I, M) → NMidpoint(q) → OMidpoint(A, K) → PMidpoint(A, M) → QSegment(I, L) → i_1Segment(L, M) → j_1Segment(M, P) → k_1Segment(P, A) → l_1Segment(J, N) → m_1Segment(N, K) → n_1Segment(K, Q) → p_1Segment(Q, A) → q_1Segment(N, L) → r_1Segment(M, K) → s_1Segment(P, Q) → t_1Mirror(A_1, F_1) → H_1Mirror(W, F_1) → W'Mirror(C_1, F_1) → I_1Midpoint(J_1, C_1) → K_1Midpoint(L_1, J_1) → N_1Midpoint(J_1, K_1) → O_1Midpoint(K_1, C_1) → P_1Segment(Q_1, R_1) → k_2Midpoint(N_1, J_1) → W_1Midpoint(J_1, O_1) → Z_1Midpoint(P_1, C_1) → A_2Segment(R_1, W_1) → l_2Segment(Z_1, T_1) → m_2Segment(T_1, U_1) → n_2Segment(U_1, A_2) → p_2Polygon(B_1, W, T, E_1, H_1, I_1) → poly2, q_2, w_2, t_2, r_2, s_2, a_2Midpoint(E_1, G_1) → B_2Segment(Q_1, B_2) → j_2Midpoint(O_1, K_1) → C_2Midpoint(C_2, O_1) → D_2Midpoint(M_1, L_1) → E_2Circle(E_2, V_1) → d_2Circle(K_1, Distance[E_2, V_1]) → c_2Circle(E_2, M_1) → e_2Circle(K_1, Distance[E_2, M_1]) → c_3Point(a_2) → F_2Point(a_2) → G_2Polygon(F_2, G_2, 4) → poly3, b_2, f_3, g_3, h_3, H_2, I_2Semicircle(I_2, H_2) → d_3Semicircle(I_2, H_2) → e_3Point(w_2) → N_2Intersect(q, m_1) → O_2Segment(N_2, J_2) → i_3Segment(J_2, K_2) → j_3Segment(K_2, L_2) → k_3Segment(L_2, M_2) → l_3Segment(M_2, O_2) → m_3Polygon(Q_2, P_2, S_2, R_2) → q1, n_3, p_3, q_3, r_3
AI 绘图提示语参考
在坐标平面内,先给定一参考点 A 以及以 A 为圆心的若干同心圆,设定半径 R、R+r1、R+r1+r2 等。取与坐标轴成一定关系的若干光线,用两圆与直线的交点生成一组旋转中心与点对。以固定角速度把点围绕旋转中心依次旋转得到多级点(如先从 B' 再到 B'' 再到 B'''),并用若干线段连接这些点。再沿参数 i 从 0 到 t 生成多条曲线:每条曲线分别由与 cos、sin 相关的几何表达式组合而成,曲线以 A 为基准并叠加不同半径项,最终形成类似连杆机构轨迹的复合曲线图。
以上提示语为根据原始绘图命令整理而来,仅供参考。