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ENGINEERING GRAPHICS

SHEET NO. 4 : ENGINEERING CURVES CURVESQuestion No. 1

Method of Drawing the Involute Curve of a Circle of Diameter DSteps of Construction:

Draw a circle O of given diameter D.On the circumference, take a point P as shown in figure 16.46 (a).Draw a tangent PA equal to its circumference.Divide the circle and PA in 12 equal parts and name them 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, A.Draw tangents on all points at circumference and cut P1, P2, P3, P4, P5, P6, P7, P8, P9, P10, and P11, respectively to get points P1, P2, P3, P4, P5, P6, P7, P8, P9, P10, P11with a smooth curve to get required involute curve.

Figure for Question no. 1 : Involute curve of a circle of diameter D

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Question No. 2

Method of Drawing the Involute Curve of an Equilateral TriangleSteps of Construction:Figure is self explanatory

Figure for Question No. 2 : Involute of an equilateral triangle

Question No. 3

Method of Drawing the Involute Curve of a Right HexagonSteps of Construction:Figure is self explanatory

Figure for Question No. 3 : Involute of a Hexagon

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Question No. 4

To Draw Archemedian SpiralDraw archemedian spiral when the length of the rod is given 100 cm, and swing either sideof the normal by 30. The rod is left from one end, then a point P starts from the top end Awith uniform speed and reaches at the end B in one complete revolution.

Steps of Construction:As shown in following figure, take a line AB = 100 cm = rod length.Line AB swings from AB1 to AB8, 60.Divide the line in 16 equal parts and number them as 1, 2, 3, 4, ....., 15, 1.Divide the swing length into half the number of line (8) and number them as 1, 2, 3, 4, ......, 8and reverse as 8, 9, ......., 15, 1.When the rod swings in different positions, point p is located as P1, P2, P3, P4, P5, P6, P7, P8,P9, P10, P11, P12, P13, P14, P15, P1.Join all the above points with a smooth curve to get Archemedian Spiral.

Figure forQuestion No. 4 :Archemedian spiral

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Question No. 5

To Draw Archemedian Spiral for One Revolution when Two Small and Big Radiusof Concentric Circles are given

Steps of Construction:As shown in figure 16.49, take two concentric circles of given radii with O as a pole.Point A moves with uniform speed and reaches at B when OA rotates one revolution alongO.Divide the distance AB and circles into same equal parts.Locate points A1, A2, A3, A4, A5, .....Join all points A1, A2, A3, A4, A5, ..... with a smooth cur ve, which gives the required

Archemedian Spiral.

Figure for question No. 5 :Archemedian spir