Involute

Involute of Circle

1 ] Draw the involute of a circle. String length is equal to the circumference of a circle.

Solution Steps:

1. Point or end P of sting AP is exactly πD distance away from A. Means if this string is wound round the circle, it will completely cover the given circle. B will meet A after winding.


2. Divide πD ( AP ) distance into 8 number of equal parts.


3. Divide circle also into 8 equal parts.


4. Name after A 1, 2, 3, 4, etc up to 8 on πD line AP as well as on circle ( in anticlockwise direction).


5. To radius C1, C2, C3 up to C8 draw tangents from 1, 2, 3, 4, etc to circle.


6. Take distance 1 to P in compass and mark it on a tangent from point 1 on the circle.


7. Name this point P1.


8. Take 2P distance in compass and mark it on the tangent from point 2. Name it point P2.


9. Similarly, take 3 to P, 4 to P, 5 to P up to 7 to P distance in compass and mark on respective tangents and locate P3, P4, P5 up to P8.


10. Join them in a smooth curve it is an involute of a given circle.

 

2 ] Draw the involute of a circle. String length is more than the circumference of circle.

Solution Steps:

1. In this case string length is more then πD.


2. But remember whatever may be the length of string, mark πD distance horizontal i.e along the string and divide it in 8 number of equal parts, and not any other distance.


3. Name after A 1, 2, 3, 4, etc up to 8 on πD line AP as well as on circle ( in anticlockwise direction).


4. To radius C1, C2, C3 up to C8 draw tangents from 1, 2, 3, 4, etc to circle.


5. Take distance 1 to P in compass and mark it on a tangent from point 1 on the circle.


6. Name this point P1.


7. Take 2P distance in compass and mark it on the tangent from point 2. Name it point P2.


8. Similarly, take 3 to P, 4 to P, 5 to P up to 7 to P distance in compass and mark on respective tangents and locate P3, P4, P5 up to P8.


9. Join them in a smooth curve it is an involute of a given circle.

3 ] draw the involute of a circle. String length is less than the circumference of circle.

Solution Steps:

1. In this case string length is less then πD.


2. But remember whatever may be the length of string, mark πD distance horizontal i.e along the string and divide it in 8 number of equal parts, and not any other distance.


3. Name after A 1, 2, 3, 4, etc up to 8 on πD line AP as well as on circle ( in anticlockwise direction).


4. To radius C1, C2, C3 up to C8 draw tangents from 1, 2, 3, 4, etc to circle.


5. Take distance 1 to P in compass and mark it on a tangent from point 1 on the circle.


6. Name this point P1.


7. Take 2P distance in compass and mark it on the tangent from point 2. Name it point P2.


8. Similarly, take 3 to P, 4 to P, 5 to P up to 7 to P distance in compass and mark on respective tangents and locate P3, P4, P5 up to P8.


9. Join them in a smooth curve it is an involute of a given circle.

 

Involute Of Composit Shaped Pole

1 ] A pole is of a shape of half hexagon and semicircle. A string is to be wound having equal to the pole perimeter, Draw the path of free end P of a string when would completely. ( take hex 30 mm sides and a semicircle of 60 mm diameter. )

Solution Steps:

1. Draw pole shape as per dimensions.


2. Divide semicircle in 4 parts and name those along with corners of hexagon.


3. Calculate perimeter length.


4. Show it as string AP. On this line mark 30 mm from 1 and dividing it into 4 parts names 2, 3, 4, 5.


5. Mark point 6 on line 30 mm from 5. Now draw tangents from all points of a pole and proper lengths as done in all previous involute's problems and complete the curve.

 

 

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