Projection of Cone

Sample Problem1:
Draw the projection of  cone , base 30 mm diameter and axis 50 mm long , resting on HP on a point of its base circle with the axis making an angle of 45º with HP and parallel to VP.

Steps for Projection of Cone :

Simple Position:

1. when the cone has to rest with a point of its base circle on HP, first assume the cone in its simple position, i.e., resting with its base on HP and the axis ⊥r to HP. For this position , draw the top view first and then the front view.

2. Top view is a circle abcd in which point c is on right side.

3. front view is a triangle a’o’c’ in which c’ is on the right side. Also the axis of the cone is perpendicular to XY.

Second Position:

4. Cone has to rets with a point of its base circle on HP, such that its axis has to make θ=45º with HP. Hence, tilt the first front view such that c’ is on XY and its base is inclined at 45º,(i.e., 90º-θ) to XY. Thus obtain second front view with axis inclined at 45º to XY.

5. Project the corresponding second top view in which the base is seen as an ellipse and the axis is parallel to XY. Inner portion of ellipse b1(c1)d1 between the tangents is shown as dashed line.

Sample problem 2:
Draw the top and front views of a cone of base diameter 46 mm and height 65 mm lying with one of its generators on HP. The axis is parallel to VP.

Steps for Projection of Cone :

1. Cone lies with its one of its genertaors on HP(given). So, axis is inclined to HP.

2.Initially assume the axis to be perpendicular to HP and parallel to VP.

3.Tilt the front view such that the cone is lying on XY on one of its generators and draw second front view.

 

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