G3圆弧路径规划

gcode命令

• G3: 用于绘制一个逆时针方向的圆弧，G3 X<目标X> Y<目标Y> I<圆心X> J<圆心Y> F<速度> E<流量>
• G2：绘制一个顺时针方向的圆弧

调试数据

• G3 X0 Y-155 I155 Z0.3 E30 F2000

coords 结果

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 [-2.0038407263003424, -154.98704662759278, 0.3008230452674897],
 [-1.0019412964636176, -154.9967616230689, 0.3004115226337448],
 [0.0, -155.0, 0.3]]

• 长度243，243个坐标点
• 逆时针的四分之一圆弧

代码解析

def cmd_G2(self, gcmd):
    self._cmd_inner(gcmd, True)

def cmd_G3(self, gcmd):
    self._cmd_inner(gcmd, False)

def _cmd_inner(self, gcmd, clockwise):
    gcodestatus = self.gcode_move.get_status()

    # 只支持绝对坐标模式
    if not gcodestatus['absolute_coordinates']:
        raise gcmd.error("G2/G3 does not support relative move mode")
    currentPos = gcodestatus['gcode_position']

    # Parse parameters
    # 参数解析
    asX = gcmd.get_float("X", currentPos[0])
    asY = gcmd.get_float("Y", currentPos[1])
    asZ = gcmd.get_float("Z", currentPos[2])
    if gcmd.get_float("R", None) is not None:
        raise gcmd.error("G2/G3 does not support R moves")
    asI = gcmd.get_float("I", 0.)
    asJ = gcmd.get_float("J", 0.)
    if not asI and not asJ:
        raise gcmd.error("G2/G3 neither I nor J given")
    asE = gcmd.get_float("E", None)
    asF = gcmd.get_float("F", None)

    # Build list of linear coordinates to move to
    # 构建圆弧线性移动的坐标
    coords = self.planArc(currentPos, [asX, asY, asZ], [asI, asJ],
                          clockwise)
    e_per_move = e_base = 0.
    if asE is not None:
        if gcodestatus['absolute_extrude']:
            e_base = currentPos[3]
        e_per_move = (asE - e_base) / len(coords)

    # Convert coords into G1 commands
    # 遍历列表坐标，调用G1移动命令
    for coord in coords:
        g1_params = {'X': coord[0], 'Y': coord[1], 'Z': coord[2]}
        if e_per_move:
            g1_params['E'] = e_base + e_per_move
            if gcodestatus['absolute_extrude']:
                e_base += e_per_move
        if asF is not None:
            g1_params['F'] = asF
        g1_gcmd = self.gcode.create_gcode_command("G1", "G1", g1_params)
        self.gcode_move.cmd_G1(g1_gcmd)

• 获取G2 或G3 命令参数值
• 构建圆弧线性移动坐标列表
• 遍历坐标列表，调用G1移动命令

路径生成算法

def planArc(self, currentPos, targetPos, offset, clockwise):
    # todo: sometimes produces full circles
    X_AXIS = 0
    Y_AXIS = 1
    Z_AXIS = 2

    # Radius vector from center to current location
    r_P = -offset[0]
    r_Q = -offset[1]

    # Determine angular travel
    center_P = currentPos[X_AXIS] - r_P
    center_Q = currentPos[Y_AXIS] - r_Q
    rt_X = targetPos[X_AXIS] - center_P
    rt_Y = targetPos[Y_AXIS] - center_Q
    angular_travel = math.atan2(r_P * rt_Y - r_Q * rt_X,
                                r_P * rt_X + r_Q * rt_Y)
    if angular_travel < 0.:
        angular_travel += 2. * math.pi
    if clockwise:
        angular_travel -= 2. * math.pi

    if (angular_travel == 0.
        and currentPos[X_AXIS] == targetPos[X_AXIS]
        and currentPos[Y_AXIS] == targetPos[Y_AXIS]):
        # Make a circle if the angular rotation is 0 and the
        # target is current position
        angular_travel = 2. * math.pi

    # Determine number of segments
    linear_travel = targetPos[Z_AXIS] - currentPos[Z_AXIS]
    radius = math.hypot(r_P, r_Q)
    flat_mm = radius * angular_travel
    if linear_travel:
        mm_of_travel = math.hypot(flat_mm, linear_travel)
    else:
        mm_of_travel = math.fabs(flat_mm)
    segments = max(1., math.floor(mm_of_travel / self.mm_per_arc_segment))

    # Generate coordinates
    theta_per_segment = angular_travel / segments
    linear_per_segment = linear_travel / segments
    coords = []
    for i in range(1, int(segments)):
        dist_Z = i * linear_per_segment
        cos_Ti = math.cos(i * theta_per_segment)
        sin_Ti = math.sin(i * theta_per_segment)
        r_P = -offset[0] * cos_Ti + offset[1] * sin_Ti
        r_Q = -offset[0] * sin_Ti - offset[1] * cos_Ti

        c = [center_P + r_P, center_Q + r_Q, currentPos[Z_AXIS] + dist_Z]
        coords.append(c)

    coords.append(targetPos)
    return coords

1. 参数说明：
   • currentPos: 当前的位置，是一个三维坐标 [X, Y, Z]。
   • targetPos: 目标位置，同样是一个三维坐标 [X, Y, Z]。
   • offset: 当前点到圆心的偏移量 [X_offset, Y_offset]，用于计算圆心位置。
   • clockwise: 表示弧线是否为顺时针（True）或逆时针（False）。
2. 计算角度变化：
   • r_P 和 r_Q: 分别为当前点到圆心的水平和垂直向量。用来计算当前位置与目标位置之间的角度。
   • center_P 和 center_Q: 圆心的坐标。通过将当前点的坐标减去偏移量计算得到。
   • angular_travel: 从当前点到目标点的角度（弧度）。利用两点的向量叉乘和点积，结合 atan2 函数计算出角度。如果计算出来的角度小于零，则加上 2π 使其成为正值。
3. 调整角度方向：
   • 如果是顺时针运动，需要将 angular_travel 减去 2π 进行调整。逆时针则不需要做调整。
   • 如果 angular_travel 等于0，并且当前位置等于目标位置，说明这个弧线是一个完整的圆，因此将角度设为 2π。
4. 分段计算：
   • linear_travel: Z轴上的位移量，计算当前Z坐标和目标Z坐标的差。
   • radius: 当前点到圆心的半径。
   • flat_mm: 沿XY平面的弧线距离，使用 radius * angular_travel 计算。
   • mm_of_travel: 总的路径长度，如果存在Z轴位移，就计算沿XY和Z轴的斜线长度；否则仅计算XY平面的路径长度。
   • segments: 将整个弧线分割成的线段数。通常将路径长度按预设的 mm_per_arc_segment 来分割，以确保路径平滑。
5. 生成坐标点：
   • theta_per_segment: 每段线段的角度。
   • linear_per_segment: 每段线段沿Z轴的位移量。
   • 循环遍历每一段，计算新的坐标，并将这些分段坐标存储在 coords 数组中。最后，目标位置 targetPos 被添加到 coords 中。
6. 返回值：
   • 函数返回的是一系列沿着弧线的坐标点列表 coords，每个点都是 [X, Y, Z] 的三维坐标。3D打印机将按照这些坐标依次移动，从而在空间中绘制出弧形路径。
7. 此函数的用途是生成弧形插值路径，用于控制3D打印机或CNC机床沿着圆弧形轨迹运动，确保在弧线段上以预定的分段步长平稳地移动，避免直线插值导致的路径不平滑问题。