513 lines
19 KiB
Python
513 lines
19 KiB
Python
from casadi import *
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import matplotlib.pyplot as plt
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import math
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import operator
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def svg_circle(id, name, c, r):
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# create circle object in svg notation
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text = [' <circle\n',
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' id="circle{}"\n'.format(id),
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' inkscape:label="{}"\n'.format(name),
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' style="fill:none;stroke:#000000;stroke-width:0.1mm"\n',
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' r="{}mm"\n'.format(r),
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' cy="{}mm"\n'.format(c[1]),
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' cx="{}mm" />\n'.format(c[0])]
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return text
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def svg_rectangle(id, name, c, width, heigth, angle):
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x = np.sqrt(c[0]**2 + c[1]**2) - width/2
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y = - heigth
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text = ['<g transform="rotate({})">\n '
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'<rect x="{}mm" y="{}mm" width="{}mm" height="{}mm" style="fill:none;stroke-width:0.1mm;stroke:rgb(0,0,0)" />\n '
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'</g>\n'
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.format(angle, x, y ,width, heigth)]
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return text
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def svg_line(p1, p2, width=1.0):
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text = ['<line x1="{}mm" y1="{}mm" x2="{}mm" y2="{}mm" style="stroke:rgb(0,0,0);stroke-width:{}mm" />'.format(p1[0], p1[1], p2[0], p2[1], width)]
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return text
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# this function reads and processes data for optimal circle packaging obtained form packomania.com
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def read_circle_data(N):
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coords_raw = open('cci/cci{}.txt'.format(N))
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radii_raw = open('cci/radii.txt'.format(N))
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coords_raw = coords_raw.readlines()
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coords_raw = [c.split() for c in coords_raw if c[0] != '#']
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coords = {}
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for c in coords_raw:
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coords[int(c[0])] = (float(c[1]), float(c[2]))
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coords = sort_ccw(coords, (0,0))
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radii_raw = radii_raw.readlines()
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radii_raw = [r.split() for r in radii_raw if r[0] != '#']
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radii = {}
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for r in radii_raw:
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radii[int(r[0])] = float(r[1])
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return radii[N], coords
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# this function sorts enclosed circle coordinates counter-clockwise w.r.t. the center point
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# TODO: there is a problem when circles are present that are not touching the boundary of the enclosing circle (e.g. N = 7)
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def sort_ccw(coords, center):
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a = {}
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for c in coords:
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a[c] = math.atan2(coords[c][1] - center[1], coords[c][0] - center[0])
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a_sort = sorted(a.items(), key=operator.itemgetter(1))
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coords_sort = []
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for a in a_sort:
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coords_sort.append(coords[a[0]])
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return coords_sort
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# compute the two tangential points at the circle with center c and radius r intersecting the point p
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def compute_tangent_points(p, c, r):
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b = sqrt((p[0] - c[0]) ** 2 + (p[1] - c[1]) ** 2)
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th = acos(r / b) # angle theta
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d = atan2(p[1] - c[1], p[0] - c[0]) # direction angle of point p from c
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d1 = d + th # direction angle of point T1 from c
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d2 = d - th # direction angle of point T2 from c
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T1x = c[0] + r * cos(d1)
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T1y = c[1] + r * sin(d1)
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T2x = c[0] + r * cos(d2)
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T2y = c[1] + r * sin(d2)
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return (T1x, T1y), (T2x, T2y)
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class PlateLayout:
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def __init__(self, N, plate_radius):
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self.N = N # number of enclosed circles
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self.plate_radius = plate_radius
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def compute_layout(self):
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# read radius and center coordinates for enclosed circles
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rtilde, coords = read_circle_data(self.N)
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c = (0.0, 0.0) # center of big circle
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R = 1.0 # radius of big circle
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plt.xlim((-1, 1))
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plt.ylim((-1, 1))
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plt.gca().set_aspect('equal', 'box')
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plt.ion()
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plt.show()
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for p in coords:
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plt.plot(p[0], p[1], 'o')
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circle = plt.Circle(p, rtilde, fill=False)
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plt.gca().add_artist(circle)
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circle = plt.Circle(c, R, fill=False)
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plt.gca().add_artist(circle)
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plt.plot(c[0], c[1], 'o')
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coords_2 = []
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for k in range(0, self.N):
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p1 = coords[k]
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p2 = coords[(k+1) % self.N]
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# midpoint between center of two circles
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m = np.mean([p1, p2], axis=0)
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# vector in direction of midpoint
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v = m - np.array(c)
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v = v/np.linalg.norm(v)
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#plt.plot(m[0], m[1], 'o')
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# optimization problem for computing position and radius for a maximal circle fitting in space between two big circles
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# and being fully contained in enclosing circle
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opti = casadi.Opti()
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r = opti.variable(1) # radius of new circle
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p = opti.variable(2) # center of new circle
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lamb = opti.variable(1) # distance of center of new circle to center of enclosing circle
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opti.minimize(-r)
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opti.subject_to(p == c + v * lamb)
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opti.subject_to((p[0] - p1[0])**2 + (p[1] - p1[1])**2 >= (rtilde + r)**2)
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opti.subject_to(R == lamb + r)
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opti.subject_to(r >= 0)
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opti.subject_to(r <= R)
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opti.solver('ipopt')
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init_r = 0.1
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init_lamb = R - init_r
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init_p = c + v * init_lamb
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opti.set_initial(r, init_r)
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opti.set_initial(p, init_p)
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opti.set_initial(lamb, init_lamb)
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sol = opti.solve()
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p = sol.value(p)
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r = sol.value(r)
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lamb = sol.value(lamb)
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print("p = {}".format(p))
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print("r = {}".format(r))
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print("lambda = {}".format(lamb))
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print("v = {}".format(v))
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coords_2.append(p)
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plt.plot(p[0], p[1], 'o')
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circle = plt.Circle(p, r, fill=False)
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plt.gca().add_artist(circle)
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tube1 = {}
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tube2 = {}
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# postprocessing solution:
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# - output radii for circles
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# - output center coordinates, angle w.r.t. origin and distance from origin
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outer_radius = self.plate_radius # desired plate radius in meters
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tube1_radius = outer_radius * rtilde
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tube2_radius = outer_radius * r
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print("\n------------------")
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print("optimal values")
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print("plate radius = {:6.3} m = {:6.2f} mm".format(outer_radius / 1000, outer_radius))
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print("big circles:")
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print(" radius = {:6.3} m = {:6.2f} mm".format(tube1_radius / 1000, tube1_radius))
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print(" diameter = {:6.3} m = {:6.2f} mm".format(2 * tube1_radius / 1000, 2 * tube1_radius))
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print("small circles:")
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print(" radius = {:6.3} m = {:6.2f} mm".format(tube2_radius, tube2_radius * 1000))
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print(" diameter = {:6.3} m = {:6.2f} mm".format(2*tube2_radius, 2*tube2_radius * 1000))
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# compute coordinates and various measurements for fixed radii of plate and tubes
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self.target_plate_radius = 160.0
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self.target_center_hole_radius = 7.5
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self.target_radius_1 = 50.2
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self.target_radius_2 = 20.0
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teeth = 200
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D = 2 * self.target_plate_radius
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self.plate_module = D/teeth
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print("plate radius = {:6.2f} mm".format(self.target_plate_radius))
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print("big circle radius = {:6.2f} mm".format(self.target_radius_1))
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print("small circle radius = {:6.2f} mm".format(self.target_radius_2))
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print("number of teeth: N = {}".format(teeth))
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print("pitch diameter: D = {} mm".format(D))
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print("module: M = {} mm".format(self.plate_module))
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# parameters for dispenser gears
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self.dispenser_module = 1.0
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dispenser_1_target_pitch_diameter_big = 50.0
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dispenser_1_target_pitch_diameter_small = 15.0
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dispenser_1_teeth_big = int(dispenser_1_target_pitch_diameter_big/self.dispenser_module)
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dispenser_1_teeth_small = int(dispenser_1_target_pitch_diameter_small/ self.dispenser_module)
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dispenser_1_pitch_diameter_big = self.dispenser_module * dispenser_1_teeth_big
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dispenser_1_outer_diameter_big = dispenser_1_pitch_diameter_big + 2 * self.dispenser_module
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dispenser_1_pitch_diameter_small = self.dispenser_module * dispenser_1_teeth_small
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dispenser_1_outer_diameter_small = dispenser_1_pitch_diameter_small + 2 * self.dispenser_module
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dispenser_2_target_pitch_diameter_big = 20.0
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dispenser_2_target_pitch_diameter_small = 15.0
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dispenser_2_teeth_big = int(dispenser_2_target_pitch_diameter_big / self.dispenser_module)
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dispenser_2_teeth_small = int(dispenser_2_target_pitch_diameter_small / self.dispenser_module)
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dispenser_2_pitch_diameter_big = self.dispenser_module * dispenser_2_teeth_big
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dispenser_2_outer_diameter_big = dispenser_2_pitch_diameter_big + 2 * self.dispenser_module
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dispenser_2_pitch_diameter_small = self.dispenser_module * dispenser_2_teeth_small
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dispenser_2_outer_diameter_small = dispenser_2_pitch_diameter_small + 2 * self.dispenser_module
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print("parameters for dispenser gears:")
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print(" big container:")
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print(" module = {}".format(self.dispenser_module))
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print(" pitch diameter big gear = {}".format(dispenser_1_pitch_diameter_big))
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print(" number of teeth big gear = {}".format(dispenser_1_teeth_big))
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print(" pitch diameter small gear = {}".format(dispenser_1_pitch_diameter_small))
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print(" number of teeth small gear = {}".format(dispenser_1_teeth_small))
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print(" small container:")
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print(" module = {}".format(self.dispenser_module))
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print(" pitch diameter big gear = {}".format(dispenser_2_pitch_diameter_big))
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print(" number of teeth big gear = {}".format(dispenser_2_teeth_big))
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print(" pitch diameter small gear = {}".format(dispenser_2_pitch_diameter_small))
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print(" number of teeth small gear = {}".format(dispenser_2_teeth_small))
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# plot plate
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plt.figure(2)
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plt.plot(0.0, 0.0, 'o')
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circle = plt.Circle((0.0, 0.0), self.target_plate_radius, fill=False)
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plt.gca().add_artist(circle)
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plt.xlim((-self.target_plate_radius*1.1, self.target_plate_radius*1.1))
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plt.ylim((-self.target_plate_radius*1.1, self.target_plate_radius*1.1))
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plt.gca().set_aspect('equal', 'box')
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# plate coordinates
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print("plate coordinates: (x,y) = ({:8.3f}, {:8.3f})".format(0.0, 0.0))
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self.tube_1_coords = {}
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self.tube_2_coords = {}
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self.tube_1_angles = {}
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self.tube_2_angles = {}
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self.tube_1_tangents = {}
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self.tube_1_tangent_angles = {}
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self.tube_1_cuts = {}
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self.tube_2_tangents = {}
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self.tube_2_tangent_angles = {}
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self.tube_2_cuts = {}
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print(" big circle coordinates:")
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for k in range(0,self.N):
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x = coords[k][0] * outer_radius
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y = coords[k][1] * outer_radius
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angle = arctan2(y, x) * 360.0 / (2.0 * math.pi)
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self.tube_1_coords[k] = (x,y)
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self.tube_1_angles[k] = angle
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print(" k = {}, (x,y) = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg".format(k, x, y, angle))
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circle = plt.Circle((x,y), self.target_radius_1, fill=False)
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plt.gca().add_artist(circle)
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p1 = dispenser_1_pitch_diameter_big
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p2 = dispenser_1_pitch_diameter_small
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a1 = self.dispenser_module
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a2 = self.dispenser_module
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offset_1 = sqrt((p1 / 2 + p2 / 2) ** 2 - (p1 / 2 + a1) ** 2) - p2 / 2 - a2
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print("dispenser 1 offset = {}".format(offset_1))
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print(" big circle tangent points: ")
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for k in range(0, self.N):
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x = coords[k][0] * outer_radius
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y = coords[k][1] * outer_radius
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t1, t2 = compute_tangent_points((0, 0), (x, y), self.target_radius_1)
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angle1_rad = arctan2(t1[1], t1[0])
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angle2_rad = arctan2(t2[1], t2[0])
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angle1_deg = angle1_rad * 360.0 / (2.0 * math.pi)
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angle2_deg = angle2_rad * 360.0 / (2.0 * math.pi)
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self.tube_1_tangents[k] = (t1, t2)
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self.tube_1_tangent_angles[k] = (angle1_deg, angle2_deg)
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print(
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" k = {}, t1 = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg\n t2 = ({:8.3f}, {:8.3f}), angle "
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"= {:8.3f} deg".format(k, t1[0], t1[1], angle1_deg, t2[0], t2[1], angle2_deg))
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plt.plot(t1[0], t1[1], 'o')
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plt.plot(t2[0], t2[1], 'o')
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## compute position of cut for dispenser gear
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# vector pointing from center in direction of tangent point
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v = np.array([math.cos(angle1_rad), math.sin(angle1_rad)])
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cut_center = np.array(t1) - v * (offset_1 + dispenser_1_outer_diameter_small/2.0)
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self.tube_1_cuts[k] = {}
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self.tube_1_cuts[k]['center'] = cut_center
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self.tube_1_cuts[k]['tangent_point'] = t1
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self.tube_1_cuts[k]['angle_deg'] = angle1_deg
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self.tube_1_cuts[k]['length'] = dispenser_1_outer_diameter_small
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self.tube_1_cuts[k]['width'] = 5.0
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plt.plot(cut_center[0], cut_center[1], 'o')
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pass
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print(" small circle coordinates:")
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for k in range(0,self.N):
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x = coords_2[k][0] * outer_radius
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y = coords_2[k][1] * outer_radius
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angle = arctan2(y, x) * 360.0 / (2.0 * math.pi)
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self.tube_2_coords[k] = (x, y)
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self.tube_2_angles[k] = angle
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print(" k = {}, (x,y) = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg".format(k, x, y, angle))
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circle = plt.Circle((x, y), self.target_radius_2, fill=False)
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plt.gca().add_artist(circle)
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p1 = dispenser_2_pitch_diameter_big
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p2 = dispenser_2_pitch_diameter_small
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a1 = self.dispenser_module
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a2 = self.dispenser_module
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offset_2 = sqrt((p1 / 2 + p2 / 2) ** 2 - (p1 / 2 + a1) ** 2) - p2 / 2 - a2
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print("dispenser 2 offset = {}".format(offset_2))
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print(" small circle tangent points: ")
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for k in range(0, self.N):
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x = coords_2[k][0] * outer_radius
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y = coords_2[k][1] * outer_radius
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t1, t2 = compute_tangent_points((0, 0), (x, y), self.target_radius_2)
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angle1_rad = arctan2(t1[1], t1[0])
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angle2_rad = arctan2(t2[1], t2[0])
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angle1_deg = angle1_rad * 360.0 / (2.0 * math.pi)
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angle2_deg = angle2_rad * 360.0 / (2.0 * math.pi)
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self.tube_2_tangents[k] = (t1, t2)
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self.tube_2_tangent_angles[k] = (angle1_deg, angle2_deg)
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print(" k = {}, t1 = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg\n t2 = ({:8.3f}, {:8.3f}), angle "
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"= {:8.3f} deg".format(k, t1[0], t1[1], angle1_deg, t2[0], t2[1], angle2_deg))
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plt.plot(t1[0], t1[1], 'o')
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plt.plot(t2[0], t2[1], 'o')
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## compute position of cut for dispenser gear
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# vector pointing from center in direction of tangent point
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v = np.array([math.cos(angle1_rad), math.sin(angle1_rad)])
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cut_center = np.array(t1) + v * (offset_2 + dispenser_2_outer_diameter_small/2.0)
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self.tube_2_cuts[k] = {}
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self.tube_2_cuts[k]['center'] = cut_center
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self.tube_2_cuts[k]['tangent_point'] = t1
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self.tube_2_cuts[k]['angle_deg'] = angle1_deg
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self.tube_2_cuts[k]['length'] = dispenser_2_outer_diameter_small
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self.tube_2_cuts[k]['width'] = 5.0
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plt.plot(cut_center[0], cut_center[1], 'o')
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pass
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pass
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"""
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input: file = svg with plate gear centered at (0,0)
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"""
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def generate_svg(self, file):
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f = open(file)
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f_lines = f.readlines()
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f.close()
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circle_found = False
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for k in range(len(f_lines)):
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current_line = f_lines[k]
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if 'transform' in current_line:
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# rotate gear such that teeth match the cut lines
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index = current_line.find('"\n')
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f_lines[k] = current_line[0:index] + " rotate(0.9)" + current_line[-2:]
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if 'd="m ' in current_line:
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# remove center whole drawn by gear-dev
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gear_data = current_line
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index = gear_data.find('z') # end of path containing gear outline coordinates
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f_lines[k] = gear_data[0:index+1] + gear_data[-2:]
|
|
|
|
|
|
if '<circle' in current_line:
|
|
circle_found = True
|
|
|
|
if circle_found and 'r=' in current_line:
|
|
# adjust center hole radius
|
|
f_lines[k] = ' r="{}mm"\n'.format(self.target_center_hole_radius)
|
|
|
|
# delete last line with </svg> command
|
|
f_lines.remove(f_lines[-1])
|
|
|
|
# output plate as svg
|
|
text = svg_circle(0, 'plate', (0,0), self.target_plate_radius)
|
|
f_lines = f_lines + text
|
|
|
|
# output big circles as svg
|
|
for k, c in self.tube_1_coords.items():
|
|
text = svg_circle(k, 'big circle', c, self.target_radius_1)
|
|
f_lines = f_lines + text
|
|
pass
|
|
|
|
# output small circles as svg
|
|
for k, c in self.tube_2_coords.items():
|
|
text = svg_circle(k, 'small circle', c, self.target_radius_2)
|
|
f_lines = f_lines + text
|
|
pass
|
|
|
|
# gear markings for big cirlces and small circles
|
|
for k, c in self.tube_1_tangents.items():
|
|
circle_midpoint = self.tube_1_coords[k]
|
|
v = np.array(c[0]) - np.array(circle_midpoint)
|
|
v = v/np.linalg.norm(v)
|
|
|
|
marking_length = 5.0
|
|
|
|
p1 = c[0]
|
|
p2 = c[0] + v * marking_length
|
|
|
|
text = svg_line(p1, p2)
|
|
f_lines = f_lines + text
|
|
pass
|
|
|
|
for k, c in self.tube_2_tangents.items():
|
|
circle_midpoint = self.tube_2_coords[k]
|
|
v = np.array(c[0]) - np.array(circle_midpoint)
|
|
v = v/np.linalg.norm(v)
|
|
|
|
marking_length = 5.0
|
|
|
|
p1 = c[0]
|
|
p2 = c[0] + v * marking_length
|
|
|
|
text = svg_line(p1, p2)
|
|
f_lines = f_lines + text
|
|
pass
|
|
|
|
# output cuts for big circles
|
|
for k, c in self.tube_1_cuts.items():
|
|
text = svg_rectangle(k, 'cut', c['center'], c['length'], c['width'], c['angle_deg'])
|
|
f_lines = f_lines + text
|
|
pass
|
|
|
|
# output cuts for small circles
|
|
for k, c in self.tube_2_cuts.items():
|
|
text = svg_rectangle(k, 'cut', c['center'], c['length'], c['width'], c['angle_deg'])
|
|
f_lines = f_lines + text
|
|
pass
|
|
|
|
# lines for manufacturing out of multiple pieces
|
|
for k, a in self.tube_1_angles.items():
|
|
a = a/360.0 * 2.0 * np.pi
|
|
r1 = np.linalg.norm(np.array(self.tube_1_coords[k])) - self.target_radius_1
|
|
vunit = np.array([np.cos(a), np.sin(a)])
|
|
p1 = vunit * self.target_center_hole_radius
|
|
p2 = vunit * r1
|
|
text = svg_line(p1, p2, 0.1)
|
|
f_lines = f_lines + text
|
|
|
|
r2 = np.linalg.norm(np.array(self.tube_1_coords[k])) + self.target_radius_1
|
|
p3 = vunit * r2
|
|
r3 = self.target_plate_radius - self.plate_module
|
|
p4 = vunit * r3
|
|
text = svg_line(p3, p4, 0.1)
|
|
f_lines = f_lines + text
|
|
|
|
pass
|
|
|
|
f_lines.append('</svg>\n')
|
|
|
|
# write new svg image
|
|
fw = open('output.svg', 'w')
|
|
fw.writelines(f_lines)
|
|
fw.close()
|
|
|
|
pass
|