def involute( radius, phi=None ):
"""Compute involute dimensions given radius
and optional angle phi.
:param radius: Radius of circle
:param phi: optional angle in radians.
:returns: dictionary with numerous values for the
involute.
- radius, given
- diameter, :math:`2 \\times r`
- baseline, :math:`\\pi \\times r`
- involute circumference
If Phi is provided
- phi, given
- C_X, C_Y, location of point C on the involate at angle phi
- CO length of the line from origin to C
- CE length of the line from circumference to C
- OCE the angle at C (on involute) between O and E (on circumference)
- COE the angle at O between C (on involute) and E (on circumference)
"""
args = AttrDict()
args.radius= radius
args.diameter = 2*args.radius
args.baseline = math.pi*args.radius
args.involute = args.radius*math.pi**2/2
if phi is not None:
args.phi= phi
args.C_X= args.radius*(math.sin(phi)-phi*math.cos(phi))
args.C_Y= args.radius*(math.cos(phi)-phi*math.sin(phi))
args.CO= math.sqrt( args.C_X**2 + args.C_Y**2 )
try:
args.CE= math.sqrt( args.CO**2 - args.radius**2 )
except ValueError as e:
print( "{0} computing sqrt({CO:7.3f}**2-{radius:7.3f}**2)".format(e,**args) )
args.CE = args.COE = args.OCE = float("NaN")
return args
args.OCE = math.atan2( args.radius, args.CE )
args.COE = math.pi/2-args.OCE
return args
