Draw the isometric projection of an upright cone (diameter 60 mm, axis 90 mm). It is placed on H.P. on its base. Indicate the direction of viewing. Give all the dimensions.
Show Hint
In any isometric drawing, never write the calculated foreshortened values on the dimension lines! Always write the true dimensions ($\phi 60$ and $90$) followed by a note “Isometric Scale Used”.
Step 1: Calculations for the Cone:
Using the constructed isometric scale (or multiplying by $0.816$), we obtain the isometric dimensions of the cone:
• True base diameter ($D$): $60\text{ mm} \implies Isometric Base Diameter (D_{\text{iso}}) = 60 \times 0.816 = \mathbf{49\text{ mm}}$
• True height of axis ($H$): $90\text{ mm} \implies Isometric Height (H_{\text{iso}}) = 90 \times 0.816 = \mathbf{73.4\text{ mm}}$
Step 2: Drawing Steps for the Isometric Projection of the Cone: • Draw the Isometric Box (Rhombus) for the Base: • Draw a horizontal reference line. From a chosen point $O$, draw two isometric axes inclined at $30^{\circ}$ to the left and $30^{\circ}$ to the right.
• Along these axes, measure the isometric diameter $49\text{ mm}$ (obtained from your isometric scale) and complete the rhombus $ABCD$ of side $49\text{ mm}$.
• Draw the Base Ellipse (Four-Center Method): • Find the midpoints of the four sides of the rhombus $ABCD$: $1, 2, 3,$ and $4$.
• Join the obtuse-angle corners (say $B$ and $D$) to the midpoints of their opposite sides.
• These lines intersect at two points, which serve as centers for the smaller side arcs. The obtuse corners $B$ and $D$ serve as centers for the larger top and bottom arcs.
• Draw the four circular arcs to form a smooth continuous ellipse representing the isometric projection of the circular base of the cone.
• Draw the Axis and Locate Apex: • Find the center of the base ellipse (the intersection point of the diagonals of the rhombus $ABCD$). Let this point be $O'$.
• From $O'$, draw a vertical centerline upwards.
• Along this vertical centerline, measure the isometric height of the axis ($H_{\text{iso}} = 73.4\text{ mm}$) and mark the apex (vertex) $V$.
• Complete the Cone Profile: • From the apex $V$, draw two straight lines tangent to the outer curves of the base ellipse on the left and right sides.
• Draw the front half of the base ellipse and the tangent lines as thick, dark lines (visible boundary).
• Draw the rear half of the base ellipse inside the tangents as a dashed line (hidden boundary).
• Final details: • Draw an arrow labeled 'F' pointing from the front-right side at $30^{\circ}$ to show the direction of viewing.
• Add clear dimension lines indicating the true diameter of $60\text{ mm}$ (written as $\phi 60$) and height of $90\text{ mm}$, noting that the projection is drawn using the isometric scale.
