MAD Cycloidal Actuator
New Method (Updated 2023-09-30)
# generate_cycloidal_profile.py
import numpy as np
import matplotlib.pyplot as plt
import ezdxf
def generateCycloidalGearProfile(r_housing=36, r_roller=4, N=16, eccentricity=2):
theta = np.arange(0, 2*np.pi, 0.001)
psi = - np.arctan(np.sin((1 - N) * theta) / (r_housing / (eccentricity * N) - np.cos((1 - N)*theta)))
x = r_housing * np.cos(theta) - r_roller * np.cos(theta - psi) - eccentricity * np.cos(N * theta)
y = -r_housing * np.sin(theta) + r_roller * np.sin(theta - psi) + eccentricity * np.sin(N * theta)
return np.concatenate(([x], [y]), axis=0)
def writeDXF(filename, fit_points, ref_circle_radius=10):
doc = ezdxf.new("R2010") # create a new DXF drawing in R2010 fromat
msp = doc.modelspace()
fit_points = fit_points.T.tolist()
start_point = fit_points[0]
# close the loop
fit_points.append(start_point)
spline = msp.add_spline(fit_points)
spline.set_closed([(start_point[0], start_point[1], 0)])
print(spline.dxf.n_fit_points)
circle = msp.add_circle((0, 0), radius=ref_circle_radius)
doc.saveas(filename)
# 5010
fit_points = generateCycloidalGearProfile(
r_housing=29.,
r_roller=2.5,
N=16.,
eccentricity=1.25
)
'''
#fit_points_ = generateCycloidalGearProfile(
# r_housing=29.,
# r_roller=3.,
# N=16.,
# eccentricity=1.25
# )
'''
# M6C12
'''
fit_points = generateCycloidalGearProfile(
r_housing=36,
r_roller=4,
N=16,
eccentricity=2
)
'''
print(fit_points.shape)
x, y = fit_points
#x_, y_ = fit_points_
plt.plot(x, y)
#plt.plot(x_, y_)
plt.show()
writeDXF("cycloidal_profile.dxf", fit_points, ref_circle_radius=31)
RI-60 Parameters
Housing Radius | 29 | mm |
Housing Roller Diameter | 5 | mm |
Central Hole Diameter | 18 | mm |
Side Hole Diameter | 13 | mm |
Eccentricity | 1.25 | mm |
Spacing Radius of Side Hole | 17 | mm |
RI-70 Parameters
Housing Radius | 36 | mm |
Housing Roller Diameter | 8 | mm |
Central Hole Diameter | 18 | mm |
Side Hole Diameter | 13 | mm |
Eccentricity | 2 | mm |
Spacing Radius of Side Hole | 20 | mm |
Old Method
Go in an active sketch plane
Run the following script:
import math
import adsk.core, adsk.fusion, traceback
def generateCycloidalOutline(n_planet_teeth, n_housing_teeth, e, pin_to_center_distance):
intersectsItself = False
lastMaxAngle = -math.pi / 2
origin = adsk.core.Point3D.create(0, 0, 0)
halfAngle = 2 * math.pi / n_planet_teeth / 2
N = 101
points = adsk.core.ObjectCollection.create()
for ip in range(N + 1):
angle = (2 * math.pi / n_planet_teeth) / N * ip
x = pin_to_center_distance * math.cos(angle) + e * math.cos(n_housing_teeth * angle)# - e
y = pin_to_center_distance * math.sin(angle) + e * math.sin(n_housing_teeth * angle)
p = adsk.core.Point3D.create(x, y, 0)
points.add(p)
#currentAngle = Angle.getToPoint(origin, p)
currentAngle = math.atan2(p.y - origin.y, p.x - origin.x)
# if not intersectsItself and currentAngle < lastMaxAngle:
# intersectsItself = True
# if intersectsItself and currentAngle <= halfAngle:
# break
lastMaxAngle = currentAngle
# if intersectsItself:
# upperPoints = [adsk.core.Point3D.create(p.x, -p.y, 0) for p in points]
# upperPoints = [getRotated(p, Matrix.getForRotation(2 * halfAngle, origin)) for p in upperPoints]
# return [points, upperPoints]
return points
def run(context):
'''
## Etch M6C12 params
reduction_ratio = 15
eccentricity = 2
pin_diameter = 8
housing_inner_diameter = 72
'''
## Etch 5010 params
reduction_ratio = 15
eccentricity = 1.5
pin_diameter = 5
housing_inner_diameter = 56
n_planet_teeth = reduction_ratio
n_housing_teeth = reduction_ratio + 1
eccentricity *= 0.1
pin_diameter *= 0.1
housing_inner_diameter *= 0.1
ui = None
try:
app = adsk.core.Application.get()
ui = app.userInterface
design = adsk.fusion.Design.cast(app.activeProduct)
if not design:
ui.messageBox('No active Fusion 360 design', 'No Design')
return
rootComp = design.rootComponent
sketch = app.activeEditObject
origin_point = adsk.core.Point3D.create(0, 0, 0)
points = generateCycloidalOutline(
n_planet_teeth=n_planet_teeth,
n_housing_teeth=n_housing_teeth,
e=eccentricity,
pin_to_center_distance=housing_inner_diameter/2
)
cycloidSpline = sketch.sketchCurves.sketchFittedSplines.add(points)
cycloidSplinecoll = adsk.core.ObjectCollection.create()
cycloidSplinecoll.add(cycloidSpline)
offsetSpline = sketch.offset(cycloidSplinecoll, adsk.core.Point3D.create(), pin_diameter / 2).item(0)
cycloidSpline.deleteMe()
#endSplinePoint = getRotated(offsetSpline.startSketchPoint.geometry, getForRotation(math.tau / n_planet_teeth, origin_point))
p = offsetSpline.startSketchPoint.geometry.copy()
mat = adsk.core.Matrix3D.create()
mat.setToRotation(math.tau / n_planet_teeth, adsk.core.Vector3D.create(0, 0, 0.5), origin_point)
p.transformBy(mat)
endSplinePoint = p
circularFeatures = [offsetSpline]
# If profile will be probably open, make more accurate segment
if not endSplinePoint.isEqualToByTolerance(offsetSpline.endSketchPoint.geometry, 1e-8):
#line = Sketch.Draw.lines(sketch, [endSplinePoint, offsetSpline.endSketchPoint.geometry])[0]
points = [endSplinePoint, offsetSpline.endSketchPoint.geometry]
asConstruction = False
close = False
lines = []
for ip in range(1, len(points)):
line = sketch.sketchCurves.sketchLines.addByTwoPoints(points[ip - 1], points[ip])
line.isConstruction = asConstruction
lines.append(line)
if close:
line = sketch.sketchCurves.sketchLines.addByTwoPoints(points[len(points) - 1], points[0])
line.isConstruction = asConstruction
lines.append(line)
circularFeatures.append(lines[0])
#Sketch.Pattern.circular(sketch, circularFeatures, n_planet_teeth, origin=origin_point)
sketchObjectOrObjects = circularFeatures
quantity = n_planet_teeth
angle = 2 * math.pi
origin = origin_point
objects = adsk.core.ObjectCollection.create()
for o in sketchObjectOrObjects:
objects.add(o)
#objects = getCollection(sketchObjectOrObjects)
for step in range(quantity - 1):
stepAngle = angle / quantity * (step + 1)
transformMatrix = adsk.core.Matrix3D.create()
transformMatrix.setToRotation(stepAngle, adsk.core.Vector3D.create(0, 0, 0.5), origin)
sketch.copy(objects, transformMatrix, sketch)
except:
if ui:
ui.messageBox('Failed:\n{}'.format(traceback.format_exc()))
Then we get the cycloidal gear profile
Pins and housing
════════════════
rr 28.0000 mm
dr 5.0000 mm
zr 16
Planets(s)
══════════
dc 8.0000 mm
ds 13.0000 mm
e 1.5000 mm
df 48.0000 mm
da 54.0000 mm
tp 3.5000 mm
N 2
ap 0.5000 mm
Input
═════
dc 8.0000 mm
e 1.5000 mm
tp 3.5000 mm
N 2
ap 0.5000 mm
Output
══════
rb 16.0000 mm
db 10.0000 mm
zs 6
to 1.0000 mm
ao 0.5000 mm
To adapt to the motor we are using, we need to edit the model a bit.
Last updated
