Exercises: Rough sketch, dimensioned sketch and views

Order these three drawings of the same lamp according to how detailed they are, and explain what each one contains: (a) a freehand drawing, without dimensions, made in one minute to note down the idea; (b) a freehand drawing but with the main dimensions marked; (c) a ruler drawing, to scale and with all the details. State the name of each type (rough sketch, dimensioned sketch or scaled drawing) and what stage each one is useful for.

In orthographic projection, a part is drawn three times: from the front (front view), from above (plan view) and from the side (side view). Explain why a single photo of the part is not enough to manufacture it and what each of the three views shows: which dimensions are visible in each one (length, width and height).

The figure shows a part made of three cubes and, beside it, its three views, labelled as view a, view b and view c, without specifying which is which.

State which view (a, b or c) is the front view, which is the plan view, and which is the side view of the part, justifying your answer by explaining from where the part is viewed in each case.

You have to manufacture a shelf bracket. Explain which view (front view, plan view or side view) you need to look at to find out: (a) how tall it is, (b) how far it sticks out from the wall, and (c) how wide it is from the front. Justify why no single view alone gives all three measurements.

Think of a chair in your classroom. Describe in words what would be seen in each of its three views (front view, plan view and side view): which parts stand out in each one and which of the three views you think gives the most information about the chair. Why?

The figure shows a part made of three cubes with its front view and side view already drawn, but the plan view is covered with a question mark.

Look closely at the part: draw or describe what its plan view looks like (how many squares it has and how they are positioned) and explain why the front view and side view, which are identical, are not sufficient to know what the part looks like.

You can do it on paper and send a photo with your answer.

In technical drawings, not all lines are the same: visible edges are drawn with a continuous line and those that are hidden behind the part with a dashed line. A cube that is hollow inside, like a box without a lid, has hidden edges. State, with reasoning, which edges of this box would be drawn as continuous lines and which as dashed lines in the front view.

A drawing at scale $1:1$ draws the part at its actual size. Explain what that means and deduce, measuring with a ruler from the description, what size a $80\ \text{mm}$ part drawn at scale $1:1$ would be on paper. What if the drawing took up half the size, what scale would it be?

You can do it on paper and send a photo with your answer.

Choose an object from the classroom (a stapler, a pencil case or a ruler) and describe the dimensioned sketch you would make of it: which three views you would draw freehand, which four or five dimensions you would measure with the ruler, and where you would note them down. Explain the difference between this dimensioned sketch and the initial rough sketch you made when thinking of the object for the first time.

Match each object with the description of its views: (a) a cylindrical glass, (b) a closed book, and (c) an ice cream cone, with these descriptions: rectangular front view and circular plan view; rectangular front and side views and rectangular plan view; triangular front view and circular plan view. Explain what gave you the clue in each case.

The figure shows a block with a square recess that does not go all the way through (a blind slot), together with its front view and plan view.

Explain why in the plan view the slot is drawn with a continuous line and in the front view it appears with dashed lines, and what those three dashed lines in the front view represent: which edges of the part they stand for.

You can do it on paper and send a photo with your answer.

The technical drawing of a cubbyhole unit shows these real measurements: $40\ \text{cm}$ wide, $30\ \text{cm}$ deep and $180\ \text{cm}$ high. Draw or describe accurately its front view and plan view, indicating which measurement goes on each side of each view, and justify why the front view and plan view are sufficient to manufacture it if we already know it is a prism.

You can do it on paper and send a photo with your answer.

In a drawing at scale $1:2$, each millimetre on paper represents $2\ \text{mm}$ of the real part. You measure a part on the drawing and its drawn length is $45\ \text{mm}$: calculate its actual length. Then, if the real part is $30\ \text{mm}$ high, calculate how tall that height will be on the drawing. Explain what operation you perform in each direction.

A very small screw, $10\ \text{mm}$ long, is drawn at scale $2:1$ to see it better. Explain what that scale means (which is double which) and calculate how long the screw will be in the drawing. Also state what scale you would use to draw a $5\ \text{mm}$ nut if you want it to occupy $25\ \text{mm}$ on paper.

You can do it on paper and send a photo with your answer.

Guess which object it is in each case from its views, and justify it: (a) circular front view, circular top view and circular side view; (b) square front view, square top view and square side view, all three identical; (c) triangular front view, rectangular top view and rectangular side view (think of an A-frame ridge tent). Indicate which view was the decisive one in each case.

You have an A4 sheet of paper (about $297\ \text{mm}$ long) and you need to draw a table $1.500\ \text{mm}$ long. Reason which scale you would choose among $1:1$, $1:2$, $1:10$ and $2:1$ so that the table fits comfortably on the sheet, carrying out the calculations for how much space it would take up with each scale. What about drawing a $12\ \text{mm}$ button in detail?

The figure shows a part and its three views, but one of the views contains an error and does not correspond to the part.

Find which view is wrong, explain why it cannot belong to this part, and draw or describe what that view should look like correctly. Reason what would happen in the workshop if someone manufactured the part relying only on the incorrect view.

You can do it on paper and send a photo with your answer.

An initial part is made of four identical cubes with an edge length of $2\ \text{cm}$: three forming an "L" resting on the base and a fourth cube on top of the corner cube on the upper level (forming an "L" both in the front view and in the side view). In the workshop you need to modify it by adding an identical fifth cube, but the manufacturing drawing imposes a strict technical constraint: the front view and the side view must continue to look exactly the same (neither the outer silhouette nor the number of visible squares in either of those two views can change).

1. a) Reasonably predict in which exact position or positions in space you could place that fifth cube to meet the constraint, justifying why neither the front view nor the side view is altered.
2. b) Explain how the top view of the part will change when adding that fifth cube, and draw or describe its final shape indicating the resulting grid.
3. c) If a customer asked you to add yet a sixth cube while keeping the original front and side views unchanged, justify with geometric arguments whether it would be physically possible or not.

You can do it on paper and send a photo with your answer.

The technical drawing of a bookshelf at a $1:15$ scale shows the following dimensioned measurements on paper: $60\ \text{mm}$ wide, $120\ \text{mm}$ high, and $24\ \text{mm}$ deep. You want to install it in a recess between a pillar and a door where you have a clear width of $95\ \text{cm}$, a clear height of $1,90\ \text{m}$, and a maximum walkway depth of $40\ \text{cm}$. However, at the base of the wall there is a continuous skirting board (baseboard) that is $2,5\ \text{cm}$ thick and $10\ \text{cm}$ high, and the bookshelf rests directly on the floor without legs or a rear cutout.

1. a) Calculate the real dimensions of the bookshelf in centimeters by correctly interpreting the $1:15$ scale.
2. b) Analyze with numerical data whether the bookshelf fits and whether it can sit completely flush against the vertical wall, or what spatial problem the skirting board will cause regarding the total depth the furniture will occupy in the walkway area.
3. c) To transport the assembled bookshelf to that room, you must go through a door with a clear width of $80\ \text{cm}$. Mathematically justify in which position (standing upright, on its side, or lying flat) it must pass through the door so that it goes through without rubbing.

In the technical office of a workshop, a drawing of a piece is received: its front elevation is a rectangle with a continuous line circle in the center, and its plan view is simply a rectangle with continuous outer lines, without any dashed lines or annotations inside.

1. a) An operator claims: "This drawing is ambiguous; with this information, I can manufacture at least three completely different three-dimensional pieces and none would contradict the drawing." Justify the operator's claim by describing or sketching those three different pieces (think about whether the hole is through, blind, or if it is a protruding cylinder).
2. b) If the piece that is actually needed is a solid block completely traversed from side to side by a cylindrical through-hole, draw or describe with standardized precision how the plan view and side elevation should be represented, specifying which lines must be dashed, what the centerlines (axes of symmetry) indicate, and why they are mandatory.
3. c) Predict what economic and technical consequences would occur in the machining of a batch of 500 pieces if the drafter had omitted the dashed lines in the workshop drawing.

You can do this on paper and submit a photo with your answer.

A Technology student claims: "If two pieces have exactly the same front elevation and the same plan view, they must necessarily be the same piece in reality."

1. a) Refute the student's claim: design two DIFFERENT three-dimensional pieces, each constructed with exactly 4 identical cubes, that share an identical front elevation and plan view, but whose side elevations are clearly different. Draw or describe the three views of both pieces to prove it.
2. b) Does this always happen? Now design a simple piece (not a single cube) where ONLY TWO views (front elevation and plan view) are enough for it to be completely defined without any possibility of confusion. Justify why, in that case, the side elevation would not provide any new information.
3. c) Based on both cases, state a general technical criterion to know when it is strictly necessary to draw the three main views in a manufacturing drawing and when the side elevation can be omitted.

You can do this on paper and submit a photo with your answer.

To manufacture a metal bracket in the school workshop, two teams present the following sketch proposals:

• Team A: They have drawn a very detailed isometric perspective with artistic shading. They dimensioned the total height and width, but the dimension lines touch the edges of the part directly, one dimension crosses over another, and they have not indicated the thickness of the material or the position of the holes.

• Team B: They have drawn the three orthographic views freehand as provided. They have dimensioned absolutely all visible and hidden edges, repeating the same height measurement in both the front and side views, and have dimensioned the position of a hole with respect to three different edges at the same time (overdimensioning).

1. a) Technically analyze both sketches: identify at least two failures regarding UNE standards or technical function for each team, explaining why they hinder manufacturing in the workshop.
2. b) Explain the real problem that Team B's overdimensioning would cause if the operator cuts the sheet metal with a small deviation of $1\ \text{mm}$ (conflict of dimensions and tolerances).
3. c) Reasonably justify what essential elements make up a correct dimensioning (dimension lines, extension lines, arrowheads, and dimension values) and what basic rule prohibits repeating unnecessary dimensions.

You can do it on paper and submit a photo with your answer.

On the floor plan of a home at a $1:50$ scale, you measure with a ruler that a rectangular room measures $64\ \text{mm}$ wide by $80\ \text{mm}$ long on the paper. The drawing shows a $16\ \text{mm}$ wide door located in a corner that opens inward at $90^\circ$, and on the opposite wall a centered French window $30\ \text{mm}$ wide that also opens inward.

1. a) Interpret the scale to calculate the real dimensions of the room (in meters) and its total usable floor area.
2. b) You want to place a $2,00\times 1,50\ \text{m}$ bed and a wardrobe $1,20\ \text{m}$ wide by $0,60\ \text{m}$ deep. According to functionality standards, no furniture can encroach on the opening swing of the door or the French window, and there must be a clear passage corridor of at least $70\ \text{cm}$ around the accessible sides of the bed. Justify with calculations and a dimensioned diagram on which wall or position you would place each piece of furniture to meet the requirements, or prove if the space is insufficient.
3. c) If you are asked to redraw only that room at a $1:20$ scale on a DIN A4 sheet ($210\times 297\ \text{mm}$), justify mathematically whether it will fit on the paper leaving a perimeter margin of $15\ \text{mm}$.

For the technology workshop, you are going to design a desktop stand for mobile phones made from a single sheet metal or plastic strip of $3\ \text{mm}$ thickness formed using two bends. The stand must hold phones up to $160\times 80\times 9\ \text{mm}$ at an inclination of $60^\circ$ relative to the horizontal, allow connecting the charging cable at the bottom through a central slot $18\ \text{mm}$ wide, and be stable enough not to tip over when touching the screen.

1. a) Design the stand by reasonably determining the main dimensions of each section (support base, backrest, and front retaining lip).
2. b) Decide which orthographic views are strictly necessary for the workshop to manufacture the part without ambiguity. Justify whether two views would suffice or if it is essential to include the third.
3. c) Choose a standardized scale ($1:1$, $1:2$, or $2:1$) to draw the plan on a DIN A4 sheet ($210\times 297\ \text{mm}$), justifying your choice based on the size of the object and the clarity of dimensioning.
4. d) Explain which lines in the drawing must be represented with dashed lines (hidden edges) and which functional dimensions are critical so that the workshop makes no manufacturing errors.