Hello
I am working on CREO parametric v1.0.
I have to make a gear using the method of the involute of a circle, the Cartesian equation of which I have managed to reprove:
x=r(cos(t)-t*sin(t))
y=r(sin(t)+t*cos(t))
z=0
The problem is that my corube is tangential to the circle and not normal to the circle as it should and I don't see where it comes from.
I wonder if it's not a story with the t or if my equation is totally wrong.
Thank you in advance for your answers
Kind regards.
Try with:
x=r(cos(t)+t*sin(t))
y=r(sin(t)-t*cos(t))
In my opinion you just reversed 2 signs.
Do you want the exact shape or a representation of the gear.
If it's just a representation, I have a parameterized file in which you enter the number of teeth, the module, etc... to draw the piece.
On the other hand, I'm not sure if it's the exact shape (but it looks a lot like it).
Well in fact it wasn't the signs even if I think you're right I made a mistake in making mine.
Otherwise I don't have an imperative of representation but I have to explain everything I do so I can't take a ready-made model unless I explain it
EDIT: Small problem with the equation:
x=(d1/2)*(cos(t)+t*cos(t-(pi/2)))
y=(d1/2)*(sin(t)-t*sin(t-(pi/2)))
z=0
Gives a not bad involute, normal to the circle and turning well but its radius of curvature seems huge to me, like it doesn't rotate tight enough but I don't see where it comes from.
Simplifying we are supposed to get this:
x=(d1/2)*(cos(t)+t*sin(t))
y=(d1/2)*(sin(t)+t*cos(t))
z=0
But it doesn't work so I wonder if there's not a f***ing on the parameterization with t.
For me t corresponds to your angle of end of involving. In your case how much is it?
So after having redone a nice diagram I find as an equation:
x=r(cos(t)+t*cos(pi/2-t))
y=r(sin(t)-t*sin(pi/2-t))
And as always, simplifying by
x=r(cos(t)+t*sin(t))
y=r(sin(t)-t*cos(t))
It doesn't work anymore.
I really don't see what's wrong, I have a 90° angle between the two curves parameterized by these two systems of equations.
If you can't take the template, below are the parameters followed by the relationships:
INPUT
Z NUMBER = 30.000000
"GIVE THE NUMBER OF TEETH"
Y NUMBER = 1.000000
"GIVE THE COEFFICIENT OF PROTRUSION"
X NUMBER = 1.250000
"GIVE THE COEFFICIENT OF THE HOLLOW"
M0 NUMBER = 1.250000
"GIVE THE MODULE"
ALPHAD NUMBER = 20.000000
"GIVE THE ANGLE OF PRESSURE"
DELTA NUMBER = 0.000000
"GIVE THE OFFSET COEFFICIENT"
LONG NUMBER = 10.000000
"GIVE THE DEPTH OF THE TOOTH"
END INPUT
RELATIONS
RPRIM=M0*Z/2
SPRIM=M0*(PI/2+2*DELTA*TAN(ALPHAD))
BETA=360/Z
/*"----------"
P1=Z
RT=M0*(Z/2+DELTA+Y)
INVALPHAZ=TAN(ALPHAD)-(ALPHAD*PI/180)
RB=M0*Z*COS(ALPHAD)/2
RP=M0*(Z/2+DELTA-X)
DP=RP*2
DT=RT*2
RM=(RT+RP)/2
ALPHAP=ACOS(COS(ALPHAD)*RPRIM/RP)
GAMAPRIM=((PI/Z)-(SPRIM/(2*RPRIM)))*180/PI
ALPHAT=ACOS(COS(ALPHAD)*RPRIM/RT)
INVALPHAP=TAN(ALPHAP)-(ALPHAP*PI/180)
INVALPHAT=TAN(ALPHAT)-(ALPHAT*PI/180)
ALPHAM=ACOS(COS(ALPHAD)*RPRIM/RM)
YPRIM=RPRIM*COS(GAMAPRIM)
XPRIM=RPRIM*SIN(GAMAPRIM)
SP=RP*(SPRIM/RPRIM+2*(INVALPHAZ-INVALPHAP))
ST=RT*(SPRIM/RPRIM+2*(INVALPHAZ-INVALPHAT))
INVALPHAM=TAN(ALPHAM)-(ALPHAM*PI/180)
SM=RM*(SPRIM/RPRIM+2*(INVALPHAZ-INVALPHAM))
GAMAT=((PI/Z)-(ST/(2*RT)))*180/PI
GAMAP=((PI/Z)-(SP/(2*RP)))*180/PI
YT=RT*COS(GAMAT)
XT=RT*SIN(GAMAT)
YP=RP*COS(GAMAP)
XP=RP*SIN(GAMAP)
GAMAM=((PI/Z)-(SM/(2*RM)))*180/PI
YM=RM*COS(GAMAM)
XM=RM*SIN(GAMAM)
END RELATIONS
+ a tooth construction image.
Aren't you going to give us an azfboom bomb;)
Hello
First of all, thank you for your relationships, how cool is it;)
I can take a model already made but my problem is that all the pretty relationships that perfect it have to explain them on a sheet of paper so I don't know if I'll get there (I'll try anyway) so if you have any explanations I'll take it and is your model made with a circle developer? Pcq that's what I want to work on.
EDIT: My teacher gave me the solution which comes from the logic of our American Creo friends, indeed Theta must be written in rafiant but the cos returns degrees and you have to enter the rad in the cos a real mess in short.
So the equation of the curve gives
z=0
ALPHA=t*pi/180
R=(d17/2)*sqrt(1+ALPHA*ALPHA)
THETA=(180/ft)*ALPHA-atan(ALPHA)