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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.
C
To draw an involute of a given Triangle
AB=30MM
B
A
A as center AB as the radius draw the arc
,then increase the AC Line .
A
C
B
P1
R
1
=
3
0
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
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
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
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
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
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.
To draw an involute of a given square.
A
B
C D
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
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
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
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
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)
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
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
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.
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
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
E
D
C
A
Now increase the Line BC upto P1
R
1
=
A
B
=
3
0
M
M
P1
B
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
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
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
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
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
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
A
B
C
D E
F
B as the Center BA as the Radius Draw the arc P1=AB=25MM
P1
R1=AB=25MM
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
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
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
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
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.
1. With 0 as centre and radius R=25MM, draw the given circle.
O
R=25MM
P1
Divide the circle into 8 parts 360/8=45
Then draw the Tangent through the point 1 according to the figure
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
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
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
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
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
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
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
P1
P2
P3
P4
P5
P6
P7
P8
(PIE)II D=II*25=
M
Mark M on the arc
P1
P2
P3
P4
P5
P6
P7
P8
(PIE)II D=II*25=
M
N
join M and N
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
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

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Involute of a circle,Square, pentagon,HexagonInvolute_Engineering Drawing.pdf

  • 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