Sharp EL-9900 Selection of type, Label Start ClrT Print Select 1 or 2 Input S, Label Invo

S : involute starting point

θ : angle of obliquity of point P

EL-9900 Graphing Calculator

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 -a
	f(θ i)		tan2 θ i
f (θ ) = a - invθ			SP : involute curve

	θ
P
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

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
(T-R-J)/T2		D
180.0 (R-D)/π			Z
If int (10ˆ8 D)≠			0 Goto CALPRESS
Z	A
Print "ANGLE
Print A
End

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	-π θ /180 I

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
S	selecting calculation type	I	involute value
	(S=1: involute calculation)	A	input and output of angle
	(S=2: inverse involute calculation)	B	input of initial value
Z	initial value, angle of obliquity

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