Redraw the TWO given views to scale 1:1 and show the interpenetration curve on the front view and ALL construction lines needed to project the curve of interpenetration.

• Draw the Front View of the T-end:
  • Draw a horizontal line 130 mm long for the base.
  • Draw vertical lines 25 mm high at both ends of the base. Connect their tops with a horizontal line.
  • From the center of the 130 mm base, measure 25 mm to the left and 25 mm to the right to define the 50 mm wide stem. Draw vertical lines upwards from these points ($x=40$ and $x=90$) to the total height of 72 mm.
  • Draw the top horizontal line of the T-bar, 130 mm long, at $y=72$ mm.
  • Draw the $R30$ fillets:
    • For the left fillet, locate the center at $(70, 42)$ mm. Draw an arc with radius 30 mm connecting the vertical edge of the stem ($x=40$) to the underside of the top bar ($y=72$).
    • For the right fillet, locate the center at $(60, 42)$ mm. Draw an arc with radius 30 mm connecting the vertical edge of the stem ($x=90$) to the underside of the top bar ($y=72$).
• Draw the Top View of the T-end:
  • Draw a rectangle 130 mm long and 50 mm wide.
  • At each end of the 130 mm length, draw semicircles with radius $R25$ to form the rounded ends of the slotted shape.
  • Draw the centerlines for the $\emptyset 50$ cylinder: a horizontal line at $y=25$ mm and a vertical line at $x=65$ mm (relative to the top view's origin).
  • Draw the $\emptyset 50$ circle, centered at the intersection of these centerlines. This represents the end view of the intersecting cylinder.

• Divide the $\emptyset 50$ circle in the Top View into 12 or 16 equal parts (e.g., every $30^\circ$ or $22.5^\circ$). Label these points (e.g., $P_1, P_2, \dots, P_{12}$).
• From each of these points on the $\emptyset 50$ circle, draw horizontal projection lines across the top view. These lines represent elements on the surface of the cylinder.
• From each of these points on the $\emptyset 50$ circle, project vertical construction lines downwards towards the Front View. These lines will define the horizontal positions of points on the interpenetration curve.
• In the Front View, draw the horizontal axis of the cylinder at $y=48.5$ mm.
• Draw the vertical center line of the T-end at $x=65$ mm.

• The interpenetration curve occurs where the cylinder intersects the $R30$ fillets.
• For each horizontal projection line from the top view (representing an element on the cylinder's surface), measure its distance from the cylinder's axis in the top view. This distance represents the "depth" or "offset" of that element from the cylinder's central plane.
• In the front view, for each vertical projection line from the top view:
  • Locate the corresponding point on the cylinder's circumference. The cylinder's profile in the front view is a rectangle of width 50 mm (from $x=40$ to $x=90$) and height 50 mm (from $y=23.5$ to $y=73.5$).
  • The curve will be formed by points where the cylinder's surface meets the $R30$ fillets.
  • Consider a point $P_i$ on the $\emptyset 50$ circle in the top view. Its horizontal projection line gives its depth from the cylinder's axis.
  • Project $P_i$ vertically down to the front view. This gives an $x$-coordinate.
  • The $y$-coordinate for the interpenetration curve point will be found by intersecting the cylinder's surface with the T-end's surface.
  • Since the cylinder's axis is at $y=48.5$ and its radius is 25, its equation in the front view (for the curved part) is $(y-48.5)^2 + z^2 = 25^2$, where $z$ is the depth from the center plane of the cylinder.
  • The $R30$ fillets are defined by $(x-70)^2 + (y-42)^2 = 30^2$ (left) and $(x-60)^2 + (y-42)^2 = 30^2$ (right).
  • For each projected vertical line from the top view (which gives an $x$-coordinate in the front view), find the corresponding $y$-coordinate on the $R30$ fillet.
  • For example, take a point $P_k$ on the $\emptyset 50$ circle. Its vertical projection gives an $x$-value. Its horizontal projection gives a $z$-value (distance from the center of the $\emptyset 50$ circle).
  • In the front view, for that $x$-value, find the $y$-value on the $R30$ fillet. Then, from the cylinder's axis ($y=48.5$), measure $z$ upwards and downwards to find two points on the cylinder's surface.
  • The interpenetration curve points are where these cylinder surface points coincide with the T-end's surface.
  • Specifically, for each vertical projection line from the top view (which gives an $x$-coordinate in the front view), measure the corresponding $y$-coordinate on the $R30$ fillet. This $y$-coordinate is a point on the T-end's surface.
  • Now, for the same $x$-coordinate, find the $y$-coordinate on the cylinder's surface. The cylinder's surface is defined by $y_{cyl} = 48.5 \pm \sqrt{25^2 - z^2}$, where $z$ is the horizontal distance from the cylinder's center line ($x=65$) in the top view.
  • The points of interpenetration are where $y_{fillet} = y_{cyl}$. This is a graphical process.
  • For each vertical projection line from the top view (e.g., from $P_1, P_2, \dots$), measure the horizontal distance from the center line of the cylinder in the top view. Let this be $d$.
  • In the front view, for the same vertical projection line, measure $d$ horizontally from the cylinder's axis ($y=48.5$). This gives points on the cylinder's profile.
  • The curve will be formed by connecting the points where the cylinder's profile intersects the $R30$ fillets.

• Connect the located points in the front view with a smooth curve. This curve will be symmetrical about the vertical center line ($x=65$ mm).
• The curve will start at the points where the cylinder's top/bottom surfaces intersect the vertical edges of the stem, and extend inwards to meet the $R30$ fillets.
• The curve will be visible on both the left and right sides of the stem where the cylinder passes through the $R30$ fillets.

• Ensure all projection lines from the top view to the front view are visible.
• Show the division of the $\emptyset 50$ circle in the top view.
• Show the horizontal lines from these divisions in the top view.
• Show the vertical projection lines from the top view to the front view.
• Show the horizontal axis of the cylinder in the front view.
• Show the center lines for both views.

The final drawing will show the T-end with a smooth, symmetrical curve on its front view, representing the intersection of the $\emptyset 50$ cylinder with the $R30$ fillets.

Since I cannot draw the solution, the description above outlines the precise steps you would take with drafting tools.