Find the angle from Inverse involute function

[Manoj vijay]

Greetings,

I have a given angle (a) 24 degrees and 44 minutes

I have converted this angle to radians by applying below mentioned formula

a =(24+44/60)/180*PI()

and using the below formula I got Inverse involute function of this angle.

Inv (a)=tan(a) - a

I get the 0.028976.

But now if I want to re calculate angle 24 degrees and 44 minutes from 0.028976 what will be the formula?

Kindly advice.

Regards Manoj Vijay

 

[Manoj vijay]

I found that Laskin & Cheng developed below mentioned formula's to solve above query. But I don't know how to cenvert them in excel.

Can anybody advice?

[FONT=&quot]Laskin's method[/FONT]

[FONT=&quot]Based on Newton's method, which consists of an iterative calculation procedure[/FONT]

[FONT=&quot]The Know-How of this thing is in the choice of the initial values, which by the method of Laskin is calculated as[/FONT]

[FONT=&quot], where I - initial value of the involute [/FONT]

[FONT=&quot]To calculate the next approximation after the disclosure of derivative we'll obtain the expression[/FONT]

[FONT=&quot]There are five iterations used in the calculator, but four should provide the accuracy to six decimal places. This method works for the values of involute from 0 to 1 i.e. you can find the angles from 0 to 64.87 degrees. In practice, that is enough. There are tables for finding the involute that are similar to the tables of trigonometric functions and they have a range of angle from 0 to 60.[/FONT]


[FONT=&quot]Cheng's method[/FONT]
[FONT=&quot]Based on the determination of an approximate value using the asymptotic curves. Cheng brought the following formula:[/FONT]

[FONT=&quot]This method can be used for finding the involute values that are strictly less than 1.8 i.e. it can find the angles up to 71.87. And you don't actually need those above - approaching the 90 the tangent tends to infinity, with all the ensuing consequences. Also, there are no tooth gearings with such large angles.[/FONT]

 

[Mark Main]

Greetings,

I have a given angle (a) 24 degrees and 44 minutes

I have converted this angle to radians by applying below mentioned formula

a =(24+44/60)/180*PI()

and using the below formula I got Inverse involute function of this angle.

Inv (a)=tan(a) - a

I get the 0.028976.

But now if I want to re calculate angle 24 degrees and 44 minutes from 0.028976 what will be the formula?

Kindly advice.

Regards Manoj Vijay

This seems to do what you are talking about.
http://www.gearsolutions.com/articl...-angle-in-microsoft-excel-without-programming

 

[Fazza]

what about if you made a table with say a thousand entries, saving it on a worksheet. could be values only to avoid recalculation

then looked up a value close to the one you want to solve for, and the value after it too, and then interpolate between the two to get the desired result

if that wasn't accurate enough, then make a table with 10,000 values