import math import matplotlib.pyplot as plt # 设置中文字体(防警告) plt.rcParams['font.sans-serif'] = ['SimHei', 'Arial Unicode MS', 'DejaVu Sans'] plt.rcParams['axes.unicode_minus'] = False class TwoLinkArm: def __init__(self, l1=1.0, l2=1.0): self.l1 = l1 self.l2 = l2 self.theta1 = 0.0 # 弧度 self.theta2 = 0.0 # 弧度 self.end_x = l1 + l2 # 初始末端位置 self.end_y = 0.0 self.joint1 = (l1, 0.0) self.joint2 = (l1 + l2, 0.0) self.fig, self.ax = plt.subplots(figsize=(8, 8)) plt.subplots_adjust(bottom=0.2) self.ax.set_xlim(-l1 - l2 - 0.5, l1 + l2 + 0.5) self.ax.set_ylim(-l1 - l2 - 0.5, l1 + l2 + 0.5) self.ax.set_aspect('equal') self.ax.grid(True) self.ax.set_title("拖动末端执行器(粉色点)来移动机械臂") self.ax.set_xlabel("X") self.ax.set_ylabel("Y") # 绘制机械臂 self.line_link1, = self.ax.plot([], [], 'b-', linewidth=4, label=f'连杆1 (L1={l1})') self.line_link2, = self.ax.plot([], [], 'r-', linewidth=4, label=f'连杆2 (L2={l2})') self.joint_point, = self.ax.plot([], [], 'go', markersize=8, label='关节2') self.end_point, = self.ax.plot([], [], 'mo', markersize=8, label='末端执行器') self.base_point, = self.ax.plot(0, 0, 'ko', markersize=10, label='基座') self.angle_text = self.ax.text( -l1 - l2 + 0.2, l1 + l2 - 0.3, '', fontsize=10, bbox=dict(boxstyle="round", facecolor="wheat") ) self.ax.legend() # 拖动相关变量 self.dragging = False self.press_xdata = None self.press_ydata = None # 连接事件 self.cid_press = self.fig.canvas.mpl_connect('button_press_event', self.on_press) self.cid_release = self.fig.canvas.mpl_connect('button_release_event', self.on_release) self.cid_motion = self.fig.canvas.mpl_connect('motion_notify_event', self.on_motion) # 初始绘制 self.update_plot() def fk(self, theta1, theta2): """正向运动学""" x1 = self.l1 * math.cos(theta1) y1 = self.l1 * math.sin(theta1) x2 = x1 + self.l2 * math.cos(theta1 + theta2) y2 = y1 + self.l2 * math.sin(theta1 + theta2) return (x1, y1), (x2, y2) def ik(self, x, y, elbow_up=True): """逆向运动学""" d_sq = x*x + y*y cos_theta2_numerator = d_sq - self.l1**2 - self.l2**2 denominator = 2 * self.l1 * self.l2 if abs(cos_theta2_numerator) > abs(denominator): return None # 不可达 cos_theta2 = max(-1, min(1, cos_theta2_numerator / denominator)) theta2 = math.acos(cos_theta2) if elbow_up else -math.acos(cos_theta2) k1 = self.l1 + self.l2 * math.cos(theta2) k2 = self.l2 * math.sin(theta2) theta1 = math.atan2(y, x) - math.atan2(k2, k1) return theta1, theta2 def update_plot(self): """根据当前末端位置计算 IK 并更新图像""" solution = self.ik(self.end_x, self.end_y, elbow_up=True) # 默认肘上解 if solution is not None: self.theta1, self.theta2 = solution (x1, y1), (x2, y2) = self.fk(self.theta1, self.theta2) self.joint1 = (x1, y1) self.joint2 = (x2, y2) else: # 如果不可达,保持上一个有效姿态,但末端显示为红色 x2, y2 = self.end_x, self.end_y self.end_point.set_color('red') # 更新线条和点 self.line_link1.set_data([0, self.joint1[0]], [0, self.joint1[1]]) self.line_link2.set_data([self.joint1[0], self.joint2[0]], [self.joint1[1], self.joint2[1]]) self.joint_point.set_data(self.joint1[0], self.joint1[1]) self.end_point.set_data(self.joint2[0], self.joint2[1]) self.end_point.set_color('m') # 恢复正常颜色 # 显示角度(现在是弧度) angle_str = f"θ1 = {self.theta1:+.3f} rad\nθ2= {self.theta2:+.3f} rad" self.angle_text.set_text(angle_str) self.fig.canvas.draw_idle() def on_press(self, event): if event.inaxes != self.ax: return if self.end_point.contains(event)[0]: # 点中末端点 self.dragging = True self.press_xdata = event.xdata self.press_ydata = event.ydata else: self.dragging = False def on_release(self, event): self.dragging = False def on_motion(self, event): if not self.dragging or event.inaxes != self.ax: return # 更新末端位置 dx = event.xdata - self.press_xdata dy = event.ydata - self.press_ydata self.end_x += dx self.end_y += dy self.press_xdata = event.xdata self.press_ydata = event.ydata self.update_plot() def show(self): plt.show() # ======================== # 主程序 # ======================== if __name__ == "__main__": print("拖动末端执行器(粉色点)来交互式控制两连杆机械臂!") arm = TwoLinkArm(l1=1.0, l2=1.0) arm.show()