How to draw a Involute of a circle,Square, pentagon,HexagonInvolute_Engineering Drawing. A step by step procedure for all Diploma,Engineering students

1. An involute is a curve traced by a point on a perfectly
flexible string, while unwinding from around a circle or
polygon the string being kept taut (tight).
It is also a curve traced by a point on a straight line
while the line is rolling around a circle or polygon
without slipping.

2. C
To draw an involute of a given Triangle
AB=30MM
B
A

3. A as center AB as the radius draw the arc
,then increase the AC Line .
A
C
B
P1
R
1
=
3
0

4. C as the center CP1 as the radius draw the
arc ,then increase the BC Line upto P2.
A
C
B
P1
R
1
=
3
0
P2
R2=CP1=60

5. B as the center BP2 as the radius draw the
arc ,then increase the AB Line upto P3.
A
C
B
P1
R
1
=
3
0
P2
R2=CP1=60
P3
R
3
=
B
P
3
=
9
0

6. FOR Tangent and normal Line mark M at any point on the ARC
A
C
B
P1
R
1
=
3
0
P2
R2=CP1=60
P3
R
3
=
B
P
3
=
9
0
M

7. Now join the point M and B and then increse the line uppto N
A
C
B
P1
R
1
=
3
0
P2
R2=CP1=60
P3
R
3
=
B
P
3
=
9
0
M
N

8. Now draw the Line through the point M perpendicular to MN Line .
A
C
B
P1
R
1
=
3
0
P2
R2=CP1=60
P3
R
3
=
B
P
3
=
9
0
M
N
N
N

9. An involute is a curve traced by a point on a perfectly
flexible string, while unwinding from around a circle or
polygon the string being kept taut (tight).
It is also a curve traced by a point on a straight line
while the line is rolling around a circle or polygon
without slipping.

10. To draw an involute of a given square.
A
B
C D

11. Taking A as the starting point, with centre B and radius BA=40MM
draw an arc to intersect the line CB produced at P1.
A
B
C D

12. Taking A as the starting point, with centre B and radius BA=40MM
draw an arc to intersect the line CB produced at P1.
A
B
C D
P1
R
1
=
A
B
=
4
0

13. P2
With Centre C and radius CP 1 =2*40=80, draw on
arc to intersect the line DC produced at P 2.
R2=CP1=80
A
B
C D
P1
R
1
=
A
B
=
4
0

14. R
3
=
D
P
2
=
1
2
0
With Centre D and radius DP 2 =3*40=120,
draw on arc to intersect the line AD produced
at P3.
P2
P3
R2=CP1=80
A
B
C D
P1
R
1
=
A
B
=
4
0

15. R
4
=
A
P
3
=
1
6
0
R
3
=
D
P
2
=
1
2
0
With Centre A and radius
AP3 =4*40=160, draw on
arc to intersect the line
AB produced at P4.
P2
P3
R2=CP1=80
A
B
C D
P1
R
1
=
A
B
=
4
0
4*AB=120 (equal to the perimeter of the square)

16. R
3
=
D
P
2
=
1
2
0
R
4
=
A
P
3
=
1
6
0
P2
To draw a normal
and tangent to the
curve at any point,
say M on it,
R2=CP1=80
P3
A
B
C D
P1
R
1
=
A
B
=
4
0
4*AB=120 (equal to the perimeter of the square)
M

17. R
3
=
D
P
2
=
1
2
0
R
4
=
A
P
3
=
1
6
0
P2
M lies on the arc
P3 P4 with its
centre at A, the
line AMN is the
normal
P3
R2=CP1=80
A
B
C D
P1
R
1
=
A
B
=
4
0 4*AB=120 (equal to the perimeter of the square)
M
N

18. R
3
=
D
P
2
=
1
2
0
R
4
=
A
P
3
=
1
6
0
P2
R2=CP1=80
P3
A
B
C D
P1
R
1
=
A
B
=
4
0 4*AB=120 (equal to the perimeter of the square)
M
N
N
T
T'
and the line TT
drawn through M and
perpendicular to MA
is the tangent to the
curve.

19. Draw the Involuteof the Pentagon of side AB is 30mm
Draw the pentagon by using any one of the method AB=30 MM
B A
C
D
E

20. E
D
C
A
Draw the arc B as the center AB as the radius AB=30MM
R
1
=
A
B
=
3
0
M
M
B

21. E
D
C
A
Now increase the Line BC upto P1
R
1
=
A
B
=
3
0
M
M
P1
B

22. E
D
C
A
C as the center CP1 as the Radius Draw the arc
R
1
=
A
B
=
3
0
M
M
P1
P2
R
2
=
C
P
1
=
6
0
B

23. E
D
C
A
D as the center DP2 as the Radius Draw the arc upto P3
R
1
=
A
B
=
3
0
M
M
P1
P2
R
2
=
C
P
1
=
6
0
P3
R3=DP2=90
B

24. E
D
C
A
D as the center DP2 as the Radius Draw the arc upto P3
R
1
=
A
B
=
3
0
M
M
P1
P2
R
2
=
C
P
1
=
6
0
P3
R3=DP2=90
B

25. E
D
C
A
E as the center EP3 as the Radius Draw the arc upto P4
R
1
=
A
B
=
3
0
M
M
P1
P2
R
2
=
C
P
1
=
6
0
P3
R3=DP2=90
P4
R
4
=
E
P
4
=
1
2
0
B

26. E
D
C
A
A as the center AP4 as the Radius Draw the arc upto P5
R
1
=
A
B
=
3
0
M
M
P1
P2
R
2
=
C
P
1
=
6
0
P3
R3=DP2=90
P4
R
4
=
E
P
4
=
1
2
0
P5
R
5
=
A
P
5
=
1
5
0
5*AB=150
B

27. Draw the Involute of a hexagon of side AB=25MM
Draw the hexagon of side AB=25MM By using any Method
A
B
C
D E
F

28. A
B
C
D E
F
B as the Center BA as the Radius Draw the arc P1=AB=25MM
P1
R1=AB=25MM

29. A
B
C
D E
F
C as the Center CP1 as the Radius Draw the arc P2=50MM
P1
R1=AB=25MM
P2
R
2
=
C
P
1
=
5
0
M
M

30. A
B
C
D E
F
D as the Center DP2 as the Radius Draw the arc Upto P3=75MM
P1
R1=AB=25MM
P2
R
2
=
C
P
1
=
5
0
M
M
P3
R3=DP2=75MM

31. A
B
C
D E
F
E as the Center EP3 as the Radius Draw the arc Upto P4=100MM
P1
R1=AB=25MM
P2
R
2
=
C
P
1
=
5
0
M
M
P3
R3=DP2=75MM
P4
R4=EP4=100MM

32. A
B
C
D E
F
F as the Center FP4 as the Radius Draw the arc Upto P5=125MM
P1
R1=AB=25MM
P2
R
2
=
C
P
1
=
5
0
M
M
P3
R3=DP2=75MM
P4
R4=EP4=100MM
P5
R
5
=
1
2
5
P6
R
6
=
1
5
0
6*AB=150

33. To draw an involute of a given circle of radus R
1. With 0 as centre and radius R, draw the given circle.
2. Taking P as the starting point, draw the tangent PA equal in length to the circumference of the
circle.
3. Divide the line PA and the circle into the same number of equal pats and number the points.
4. Draw tangents to the circle at the points 1,2,3 etc., and locate the points PI' P2 , P3 etc., such
that !PI = PI 1, 2P2 = P21 etc. A smooth curve through the points P, PI' P 2 etc., is the required
involute.
Note: 1. The tangent to the circle is a normal to the involute. Hence, to draw a normal and tangent
at a point M on it, first draw the tangent BMN to the circle. This is the normal to the curve and.
a line IT drawn through M and perpendicular to BM is the tangent to the curve.

34. 1. With 0 as centre and radius R=25MM, draw the given circle.
O
R=25MM

35. P1
Divide the circle into 8 parts 360/8=45
Then draw the Tangent through the point 1 according to the figure

36. P1
P2
Then draw the Tangent through the point 2 according to the
figure and draw the arc 2 as the center 2P1 as the radius

37. P1
P2
P3
Then draw the Tangent through the point 3
according to the figure and draw the arc 3 as
the center 3P3 as the radius

38. P1
P2
P3
P4
Then draw the Tangent through the point 4 according to
the figure and draw the arc 4 as the center 4P3 as the
radius

39. P1
P2
P3
P4
P5
Then draw the Tangent through the point 5
according to the figure and draw the arc 5 as
the center 5P4 as the radius

40. P1
P2
P3
P4
P5
P6
Then draw the Tangent through the point 6 according to the figure and draw the arc 6
as the center 6P5 as the radius

41. P1
P2
P3
P4
P5
P6
P7
Then draw the Tangent through the point 7 according to the figure and draw the arc
7 as the center 7P6 as the radius

42. P1
P2
P3
P4
P5
P6
P7
P8
(PIE)II D=II*25=
Then draw the Tangent through the point 8 according to the figure and draw the arc 8 as the center 8P7 as
the radius

43. P1
P2
P3
P4
P5
P6
P7
P8
(PIE)II D=II*25=
M
Mark M on the arc

44. P1
P2
P3
P4
P5
P6
P7
P8
(PIE)II D=II*25=
M
N
join M and N

45. P1
P2
P3
P4
P5
P6
P7
P8
(PIE)II D=II*25=
M
N
T
T'
Draw the line through M perpendiculr to MN

46. P1
P2
P3
P4
P5
P6
P7
P8
(PIE)II D=II*25=
M
N
T
T'
Draw the line through M perpendiculr to MN