Problem 8.6 Development of Surfaces of Solids – A cylinder of diameter of base 60 mm and axis height 110 mm is resting on its base on H.P. It is cut by a cutting plane perpendicular to V.P. and inclined at an angle 60° with the H.P. and passing through the distance of 20 mm form the top end of the cylinder and on the axis. Develop the lateral surface of the cylinder.
Step-1 Draw a horizontal x-y line of some suitable length.
Step-2 Draw a circle of radius 30 mm below the x-y line at some suitable distance from it. Divide this circle into 4 equal divisions as shown in the figure. Give notations on it. It is top view of the cylinder.
Step-3 From the center of the circle in the top view, draw a vertical center line of length 110 mm from the x-y line as shown in the figure. And from the all notations of the circle draw vertical projectors of length 110 mm from the x-y line as shown in the figure. It is a rectangular shape. And Give the notations on it. It is front view of the cylinder.
Step-4 Draw a cutting plane line passing through the distance 15 mm below the top end of the cylinder and on the center vertical axis and should be inclined at an angle of 60° with the x-y line as shown in the figure. And because of the cutting of the cylinder in this profile, draw the lower half of the front view of the cylinder with medium dark lines, as shown in the front view.
Step-5 Draw a line from the top of the cylinder in the front view exactly parallel with the x-y line, and make a vertical line between the x-y line and the line drawn from the top of the cylinder at some suitable distance from the line c’, as shown in the figure. And give the notations A on it as per the figure given above. From the point A draw another vertical line at the distance equal to πD, where D= Diameter of the circle in the top view.
Step-6 Then divide this rectangle in 4 equal divisions, because of the 4 divisions of the circle. Then give the notations on it in capital letters like, A, B, C etc. as shown in the figure, connects these all the points with light straight lines, these are the generators of the cylinder. It is a rectangle. And it is the development of the vertical surface of the cylinder.
Step-7 Now from the cutting points of the profile with the respective vertical generators of the cylinder in the front view, draw horizontal light parallel lines, up to the respective generators in the development of the vertical surface of the cylinder. Then connect the respective points either with medium dark straight lines or medium dark free hand curves, depending on the cutting profile of the cylinder given in the front view.
Step-8 This is the development of the vertical surface of the cylinder.
Step-9 Give the dimensions by any one method of dimensions and give the notations as shown into the figure.