1. Engineering Graphics - Lect 6
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Engineering Graphics - Lect 6

2. Involute
Involute is defined as path generated by loose end of the thread when it is wound or unwound from a polygon or circle, the thread is being kept tight.
Involute can also be defined as a locus of the end point of a piece of thread wound or unwound from a circle or a polygon, keeping the thread always tight.

3. INVOLUTE
Suppose a thread is wound around a square of side 20mm and step by step we have to unwind it from the square, keeping the thread tight.

4. Let B is a fixed end of the thread and A is a loose end of a thread (both are on the same position).

5. When we start unwinding, loose end A will move to point A1 and this distance will be 20mm (equal to the side of square).

6. Similarly we will get points A2, A3, and A4
Similarly we will get points A2, A3, and A4. This is nothing but path generated by a loose end of the thread when unwound.

9. In this example a polygon (square) is given, so use compass to draw a curve passing through A1, A2, A3 and A4, by taking 1, 2, 3, 4 as a centre and 20,40,60,80 as radius.

10. INVOLUTE
Draw an involute of a pentagon of side 29 mm (unwinding).

11. Draw a regular pentagon of 29 mm side each and mark its corners as 1, 2, 3, 4 and 5.

12. Extend line 1-5 such that P-5’=145=perimeter of the pentagon.
Divide line 5-5’ into five equal parts and name them as shown in the figure.

13. Extend lines 1-2, 2-3, 3-4, 4-5 and 1-5.

14. Now with centre 1 and radius equal to P1 draw an ark to cut extended line 2-1 at point P1.

15. With centre 2 and radius equal to P2’ draw an ark cutting to line 2-3 at point P2.

16. Similarly with centre 3, 4, 5 and radii P-3’, P-4’, P-5’ respectively draw arcs at points P3, P4 and P5.

17. Similarly with centre 3, 4, 5 and radii 1-2’, 1-3’, 1-4’ respectively draw arcs at points P3, P4 and P5.

18. The curve thus obtained is the involute of the pentagon.

19. INVOLUTE
Draw an involute of a circle of 120mm diameter (unwinding).

20. Draw a circle of 120 mm diameter

21. divide it into eight (or twelve) equal parts and mark them as 1, 2, 3, … 8.

22. Draw a horizontal tangent at point 8 (marked as P) of length equal to the circumference of the circle (i.e. 2πr=377mm).

23. Divide horizontal tangent into eight equal parts and mark them as 1’, 2’, 3’…8’. Here the length of each part is equal to the (1/8)th the circumference of the circle.
377/8=47.1

24. Draw tangents to the circle at points 1, 2, 3… etc
Draw tangents to the circle at points 1, 2, 3… etc. as shown in the figure.

25. With 1 as centre and radius equal to P-1, draw an arc to cut tangent through 1 at point P1.

26. With 2 as center and radius equal to P-2, draw an arc to cut tangent through 2 at point P2.
Repeat the procedure for remaining points.

28. Join points P, P1, P2, P3…, P4 by smooth curve to get involute of circle.