Involute (Inverse Involute)
Use the involute function for calculating gears etc. to find the angle of obliquity from the initial value and involute value.
Conversely, calculate the involute value from the angle of obliquity.
Calculation
Involute function : inv θ = tan θ - θ [rad]
Use Newton's method to find the inverse involute:
θ i +1 = θ i - | f'(θ ) | = θ i - | tanθ i - θ i |
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f(θ i) | tan2 θ i | ||||
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f (θ ) = a - invθ |
| SP : involute curve | |||
| θ |
P |
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S a | q |
| θ |
| Rg |
| 0 |
FLOWCHART
PROGRAMME LIST(REAL MODE)
Title : INVOLUTE
Start
start
Selection of type
Enter 1 or 2.
Label START ClrT
Print "SELECT 1 or 2 Input S
S = 1
N
Y
To calculation of involute.
To inverse involute calculation Returns to START if entry
If S=1 Goto ANGLE
If S=2 Goto INVO
Goto START
Label ANGLE
Print "Input BEGIN
N | S = 2 | ANGLE |
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Entry of initial
Yvalue and involute value
CALPRESS
neither 1 nor 2.
Calculation of involute. Enter initial value and involute value.
Input B
B Z
Print "Input INVO
Input I
I J
Label CALPRESS
INVO
Calculation of angle of obliquity
int(108 
D)
0 Y
N
Display of angle of obliquity
Angle of obliquity calculated.
Judgment on repetition of calculation of angle of obliquity.
tan Z T
π | Z/180.0 | R | |
D |
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180.0 | Z | ||
If int (10ˆ8 D)≠ | 0 Goto CALPRESS | ||
Z | A |
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Print "ANGLE |
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Print A |
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End |
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Entry of angle
of obliquity
Calculation of involute
value (display)
End
Calculation of inverse involute. Enter angle of obliquity.
Involute value calculated. Involute value displayed.
Label INVO |
Print "Input ANGLE |
Input A | |
A | θ |
tanθ |
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Print "INVOLUTE
Print I
End
PARAMETERS
Name of parameter | Content | Name of parameter | Content |
D, R, T, J | working variable for calculating | θ | angle of obliquity |
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S | selecting calculation type | I | involute value |
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| (S=1: involute calculation) | A | input and output of angle |
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| (S=2: inverse involute calculation) | B | input of initial value |
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Z | initial value, angle of obliquity |
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