Involute in 2D Sketch via Spline by equation

[Anonymous]

I am trying to design a toothprofile in a 2D-sketch and want to insert the involute spline via equation (german version of inventor so sry for wrong terms).

I am using the equations "y(t)=cos(t)+t*sin(t)" and "x(t)=sin(t)-t*cos(t)" for the unit circle from wikipedia and inventor changes those to "x(t)=1 mm * cos(1 grd * t) + 1 mm * t * sin(1 grd * t)" and "y(t)=1 mm * sin(1 grd * t) - 1 mm * t * cos(1 grd * t)" if i click "show units". I dont get the correct involute for the unit circle and I'm not sure if i got the math wrong or am using the inventor function in a wrong way.

[Anonymous]

I am trying to design a toothprofile in a 2D-sketch and want to insert the involute spline via equation (german version of inventor so sry for wrong terms).

I am using the equations "y(t)=cos(t)+t*sin(t)" and "x(t)=sin(t)-t*cos(t)" for the unit circle from wikipedia and inventor changes those to "x(t)=1 mm * cos(1 grd * t) + 1 mm * t * sin(1 grd * t)" and "y(t)=1 mm * sin(1 grd * t) - 1 mm * t * cos(1 grd * t)" if i click "show units". I dont get the correct involute for the unit circle and I'm not sure if i got the math wrong or am using the inventor function in a wrong way.

[johnsonshiue]

Hi! The unit of t should angular unit, right? Is it degree or radian? You need to make sure the desirable unit is consistent with the document angular unit (Tools -> Doc Settings -> Units).

Many thanks!

[johnsonshiue]

Hi! The unit of t should angular unit, right? Is it degree or radian? You need to make sure the desirable unit is consistent with the document angular unit (Tools -> Doc Settings -> Units).

Many thanks!

[WHolzwarth · Accepted solution]

Try this (2019 IPT).

You can check it by changing tmax to 90, 180, 270, 360. In all cases one distance to the origin must be 100 mm, for this sample.

[WHolzwarth · Accepted solution]

Try this (2019 IPT).

You can check it by changing tmax to 90, 180, 270, 360. In all cases one distance to the origin must be 100 mm, for this sample.

[Anonymous · Accepted solution]

Thank you for your replies. I checked your File and corrected my equations to "x(t)=100mm*(cos(t) + t*PI/180 * sin(t))" and "y(t)=100mm*(sin(t) - t*PI/180 * cos(t))". So i missed the "PI/180"-Part (or (2*PI)/360)! So now it fits and i can scale the size to the desired scale. And I tested the length of multiple tangents at different angles and was able to verify that this is correct now!

[Anonymous · Accepted solution]

Thank you for your replies. I checked your File and corrected my equations to "x(t)=100mm*(cos(t) + t*PI/180 * sin(t))" and "y(t)=100mm*(sin(t) - t*PI/180 * cos(t))". So i missed the "PI/180"-Part (or (2*PI)/360)! So now it fits and i can scale the size to the desired scale. And I tested the length of multiple tangents at different angles and was able to verify that this is correct now!