6. Page Layout |
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| Programme List | ||||
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| Involute (Inverse Involute) |
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Introduction |
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Use the involute function for calculating gears etc. to find the angle of obliquity from |
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Brief explanation and | the initial value and involute value. |
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Conversely, calculate the involute value from the angle of obliquity. |
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purpose of the section | Calculation |
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Involute function : inv | θ = tan θ - θ[rad] | P | θ |
| Exercise | |
| Use Newton's method to find the inverse involute: |
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| θ i +1 = θ i - f(θ i) = q i - | tan2 θ i | S a | θ | q | |
| f'(θ) | tanθ i - θ i |
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| Example of problem to be |
| S : involute starting point |
| Rg |
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Calculation | f ( θ) = a - inv q | SP : involute curve |
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| θ : angle of obliquity of point P |
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The formula to be used |
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| Start | FLOWCHART |
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| Title : INVOLUTE |
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| PROGRAM LIST(REAL MODE) |
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in calculation and |
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| Enter 1 or 2. |
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| Input S |
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| start |
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| Print "SELECT 1/2 |
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definition of terms |
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| Y |
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| If S=1 Goto ANGLE |
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| Set Up Condition | ||||||||||||||||
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| Goto START |
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| S = 1 |
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| If S=2 Goto INVO |
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| Returns to START if entry | Print "InputExerciseBEGIN |
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| To calculation of involute | Label ANGLE |
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| N | N |
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| To inverse involute calculation |
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| Important set up condition | ||||||||||||
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| ANGLE | neither 1 nor 2. |
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| Calculation of involute. | Print "Input INVOvalue is 10. |
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| value and |
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| Entry of initial |
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| B Z | (1) Find the angle of obliquity when the involute value is 0.0050912 and the initial |
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| involute value |
| Enter initial value and | Input I |
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| before starting the exercise | ||||||||
Flowchart |
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| involute value. |
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| I J | (2) Find the involute value when the angle of obliquity is 14.1. |
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| Calculation of |
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| Angle of obliquity | tan Z | T |
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| CALPRESS |
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| Label CALPRESS |
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| D | Float Pt Mode. |
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| angle of obliquity |
| calculated. |
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| π Z/180.0 | R | Set up condition: angle unit in Deg Mode and decimal point in |
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Summary of steps from |
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| int(108 D) 0 Y | of calculation of angle | If int (10ˆ8 | D)≠0 Goto2nd FCALPSET UPRESB S* 1 * C * 1 | * | CL |
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| Judgment on repetition | 180.0 | Z |
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| answers |
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| N | of obliquity. |
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| Print "ANGLE |
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| Z A |
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start to end |
| INVO |
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| End |
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| Display of angle of obliquity |
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| Print A |
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| Step |
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| Key Operation | Display |
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| Entry of angle |
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| Calculation of inverse | Label INVO |
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| involute. Enter angle |
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| of obliquity |
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| of obliquity. |
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| Input A |
| Specify the program mode. |
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| Calculation of involute |
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| Involute value calculated. | A θ1 |
| Select the title INVOLUTE. |
| 2nd F |
| PRGM | A | * |
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| value (display) |
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| Involute value displayed. | tanθ | θ/180 | I |
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| Print "INVOLUTE |
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| Key Operation | ||||||||||||||
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| End |
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| PARAMETERS | Print I |
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| 1 | ENTER |
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Parameters |
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| End |
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| Illustration of the keys to be | |||||
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| Name of parameter |
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| Content |
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Definition of the |
| D, R, T, J |
| working variable for calculating | θ |
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| angle of obliquity |
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| S |
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| (S=1: involute calculation) | A |
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| input and output of angle |
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| selecting calculation type | I |
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| involute value |
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parameters used in the |
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| (S=2: inverse involute calculation) |
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| involute value. |
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| B |
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| Enter the initial value | and the | 1 | 0 | ENTER |
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| input of initial value |
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| Z |
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| initial value, angle of obliquity |
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| 0 | • | 0 | 0 5 0 9 1 | 2 |
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programme |
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| When the mark appears on the key: | ||
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| ENTER |
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| (Display of angle of obliquity) |
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| ● Same series of key strokes can be done | ||
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| with screen touch. | ||
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| calculation. |
| ENTER |
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| Select inverse involute |
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| 2 | ENTER |
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| Enter the value of the angel | 1 | 4 | • | 1 |
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| of obliquity. |
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| Display |
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Step |
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| ENTER |
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| (Display of involute value) |
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A |
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| Illustration of the calculator | |||||||||||||||
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| screen as it should appear | ||||||||||||||||
and an explanation of the display |
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| 5 | correctly |
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Note: This handbook is only an example of how to use programming function of the
Contents
1. | Heron's Formula | 1 | |
2. | Calculating Tension | 2 | |
3. | Involute (Inverse Involute) | 4 | |
4. | Calculating Illuminance and Luminous Intensity | 6 | |
5. | Calculating Simple Harmonic Oscillation | 8 | |
6. | Electric Power Consumed on an AC Circuit | 10 | |
7. | Angle of Vector* | 12 | |
8. | Linear Transformation* | 14 | |
9. | Moving Average | 16 | |
10. | Creating a Graph of Experimental Data | 18 | |
11. | Ordinary Differential Equations | 20 | |
12. | Analysing with | 22 | |
13. | Calculating Parabolic Motion | 25 |
*only for
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