# Inverse of Involute function Calculator

## Calculates the inverse of the involute function using Newton method.

 $inv(\theta)=\tan \theta-\theta\frac{\pi}{180}$

 involute inv(θ) radian 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit pressure angle θ degree = radian
 $\normal Newton\ method\\[10](1)\ x_0=(3inv(\theta))^{\frac{1}{3}}\hspace{35}at\ y\le1.2\\\hspace{25}x_0=tan^{\tiny-1}(inv(\theta))\hspace{20}at\ y>1.2\\\vspace{5}(2)\ x_{n+1}=x_{n}-{\large\frac{f(x_{n})}{f'(x_{n})}}\\\hspace{25}f(x)=\tan x-x-inv(\theta)\\\hspace{25}f'(x)=\tan^{\tiny2} x\\$

Inverse of Involute function
 [1-10] /15 Disp-Num5103050100200
[1]  2018/08/25 05:15   - / - / - / - /
Bug report
Is x0 really (3*inv(theta))^(1/3) for y < 1.2?
I made a script to calculate the inverse of the involute and it never converged by this formula. When I tried just inv(theta)^(1/3), it started to converge.
from Keisan
Thank you for your advice.We've fixed it as below.
(3*inv(theta))^(-1/3)
-> (3*inv(theta))^(1/3)
[2]  2018/07/19 23:20   Male / 60 years old level or over / An engineer / Very /
Purpose of use
calculating over wires dimensions. I don''t have access to Buckingham''s involute tables
Comment/Request
This is an enormous help in my job. I am learning splines pretty late in life
[3]  2018/02/12 04:08   Male / 40 years old level / Self-employed people / Very /
Purpose of use
Studying the Newton''s method.
[4]  2017/12/01 03:06   Male / 20 years old level / An engineer / Very /
Purpose of use
Calculating for over pin dia in gears and also for referencing for use for making own excel calculator with excel programming
[5]  2017/08/23 03:28   Male / 20 years old level / An engineer / Very /
Purpose of use
Inverse of involute function was used during one step of calculating the distance between pins of an internal involute spline.
[6]  2017/06/15 09:16   Male / 30 years old level / An engineer / Useful /
Purpose of use
to collect the Involute function for Shifted Profile Gear
[7]  2016/09/08 14:52   Male / 20 years old level / An office worker / A public employee / Useful /
Purpose of use
Gear cutting tool designing
[8]  2016/08/18 21:54   Male / 60 years old level or over / Self-employed people / Very /
Purpose of use
Useful for calculating centres of Addendum Modified gears
[9]  2015/05/06 22:57   Male / 60 years old level or over / An engineer / Useful /
Purpose of use
verify answers from separate calculations
[10]  2015/05/04 02:42   Male / 60 years old level or over / An engineer / Very /
Purpose of use
calculate the dimention over wires for spur gears and helical gears also for the dimention
between wires for internal gears

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