Exercises: Dimensioning and scales

Name the four elements of a dimension (dimension line, projection lines, arrowheads and dimension text), describe the function of each one, and draw a small freehand diagram showing all of them on a rectangular component.

The figure shows a dimensioned rectangular component, with the elements of the dimension labelled with letters.

Name the element labelled by each letter (dimension line, projection line, arrowhead and dimension text) and explain what the value indicates: the drawing measurement or that of the real component?

Explain these two basic rules of dimensioning in your own words and give an example of what happens if they are broken: (a) the dimension value always expresses the real measurement of the component, even if the drawing is larger or smaller; (b) the same measurement is never dimensioned twice.

State whether these statements are true or false and justify each answer: (a) dimensions are measured directly on the paper with a ruler; (b) the dimension text is written in millimetres and without indicating the unit; (c) dimension lines should avoid crossing the component; (d) projection lines start from the edges to be measured.

Explain what scales 1:1, 1:10 and 10:1 mean, and give an example of an object suitable for drawing with each one: something your size, something much larger and something very small.

Topic challenge. Match each drawing with the most reasonable scale and justify one of your choices.

Drawings:

1. a) The floor plan of a house drawn on a sheet of paper.

1. b) A watch part $4\ \text{mm}$ long.

1. c) A notebook drawn at full size.

Available scales (each one is used only once):

• E 1:1

• E 1:100

• E 5:1

Also, state what type of scale each one is (reduction, enlargement or full size).

You will be assessed on: matching each drawing with its scale correctly, justifying one of your choices, and classifying each scale correctly.

Classify these scales as reduction, enlargement or full scale, and order the reduction scales from largest to smallest reduction: 1:50, 10:1, 1:1, 2:1, 1:5, 1:200.

You want to dimension a rectangle measuring $60\ \text{mm}$ by $30\ \text{mm}$. Explain how many dimensions are needed as a minimum, where you would place each one so the drawing remains clear, and why it is not necessary to dimension all four sides.

The figure shows a step-shaped component dimensioned with three dimensions, one of which is covered.

The total length of the component is $80\ \text{mm}$ and the upper step measures $50\ \text{mm}$. Calculate the missing dimension value, explain how you obtained it, and reason whether more length dimensions need to be added or if the component is already fully defined in that direction.

A bracket is drawn to a scale of 1:5 and measures $40\ \text{mm}$ on the drawing. Calculate its real measurement in millimetres and in centimetres, and explain in your own words what 1:5 scale means: which number represents the drawing and which represents reality.

A real component measures $300\ \text{mm}$ and must be drawn to a scale of 1:20. Calculate how much it will measure on paper and reason whether the same component, at a scale of 1:50, would take up more or less space on the drawing.

A $8\ \text{mm}$ screw is drawn to a scale of 4:1. Calculate its length on the drawing and then do the reverse: if on another drawing at a scale of 2:1 a component measures $30\ \text{mm}$ on paper, how much does it measure in reality?

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

The diagram summarises the situation of a drawing made to a scale of 1:4 (the drawing is not to actual scale).

On the drawing, the component measures $25\ \text{mm}$. Calculate its real measurement, explain the step you took (multiply or divide, and why), and describe what would happen to the drawing measurement if the scale were 1:10 instead of 1:4.

A drawing has these dimensioning errors: the same length is dimensioned twice, a dimension value says '$45\ \text{mm}$' written as text, and a dimension line passes right through the middle of the component. Explain why each is an error according to the rules and how to correct it.

An L-shaped component has a longer side of $90\ \text{mm}$, a shorter side of $50\ \text{mm}$, a thickness of $20\ \text{mm}$ in the vertical part and $15\ \text{mm}$ in the horizontal part. State which dimensions you would place to define it completely without repeating any measurement and justify your choice.

On a school floor plan, the classroom measures $45\ \text{mm}$ long and in reality measures $9\ \text{m}$. Calculate the scale of the plan step by step (first convert everything to the same unit) and then deduce how long a $15\ \text{m}$ corridor measures on the plan.

You need to draw a table measuring $120\ \text{cm}$ by $80\ \text{cm}$ on an A4 sheet of paper ($210\ \text{mm}$ by $297\ \text{mm}$). Check what happens with a scale of 1:5 and 1:10, choose the appropriate scale leaving a margin for dimensions, and justify your decision with calculations.

Draw a dimensioned floor plan of your bedroom: take the main real measurements (length, width, door and window), choose a scale that fits on an A4 sheet of paper, calculate the paper dimensions, and explain each decision (scale, dimensions placed, door and window symbols).

In the machining workshop, they have received the drawing of a rectangular plate $90\ \text{mm}$ long with a centered through-slot of $30\ \text{mm}$. A student draws four consecutive chain dimensions to define it: the distance from the left edge to the slot ($30\ \text{mm}$), the width of the slot ($30\ \text{mm}$), the distance from the slot to the right edge ($30\ \text{mm}$), and, above them, the overall dimension of the plate ($90\ \text{mm}$).

1. a) Technically justify why this drawing violates dimensioning standards (principle of redundant dimensioning or over-dimensioning) and what conflict it would cause the manufacturer if working with a machining tolerance of $\pm 0,5\ \text{mm}$.
2. b) Design the correct solution indicating which minimum dimensions must appear on the drawing and classify them into size dimensions and location (or position) dimensions.

An electronic component measuring $12\ \text{mm}$ by $5\ \text{mm}$ is drawn to a scale of 2:1. Calculate its paper dimensions and work out how many times larger its drawn area is compared to its real area. What conclusion do you draw about how scale affects lengths and surface areas?

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

On the topographic map of a region, two villages separated by $6\ \text{km}$ in a straight line are drawn at a distance of $3\ \text{cm}$.

1. a) Deduce the numerical scale of the map and justify through calculations whether a third village, located $15\ \text{km}$ from the first, will fit on an A4 sheet ($210\ \text{mm} \times 297\ \text{mm}$) drawn alongside them.
2. b) If this map is photocopied reducing it to $50\ \%$ to be handed out as a pocket leaflet, calculate the resulting new numerical scale and explain why, if the original map had included a graphic scale, hikers would still be able to measure real distances directly with a ruler on the photocopy without recalculating anything.

Analyze this workshop case: a part with an overall length of $100\ \text{mm}$ has a step and has been dimensioned in successive sections with $40\ \text{mm}$ and $60\ \text{mm}$, additionally including the overall dimension of $100\ \text{mm}$. On the same drawing sheet, a vertical dimension has its value written horizontally below the dimension line, and another dimension line has been drawn crossing an edge of the body without arrowheads at its ends.

1. a) Accurately explain the four violations of UNE dimensioning standards committed and what problems of interpretation or tolerances over-dimensioning causes for the operator machining the part.
2. b) Describe how the corrected drawing should look according to the standard, indicating which longitudinal dimension must be omitted, how the figures must be oriented on vertical dimensions, and what rule governs the crossing of lines.

Design a pencil case measuring $200\ \text{mm}$ by $60\ \text{mm}$ by $30\ \text{mm}$ on paper: decide which views are needed to dimension it completely, what dimensions each view would have, and at what scale you would draw it on an A4 sheet in portrait orientation if you want it to occupy approximately half the width. Justify all three decisions.

A metal fabrication workshop receives the drawing of a structure where the width of the main opening is indicated with the value «$3,50$» and the cross-section of the metal profile that must fit into it bears the value «$80$». The operator cuts the profile to $80\ \text{mm}$, but hesitates about whether the opening measures $3,50\ \text{m}$ or $3,50\ \text{mm}$.

1. a) Justify why mechanical drawing standards establish the millimeter as the default unit without writing the symbol «mm», while architectural and civil engineering drawings use meters or centimeters. Relate your argument to the order of magnitude of the parts and the level of precision or tolerance managed in each sector.
2. b) Explain which two technical standardization principles have been violated in this mixed drawing and propose how the dimensioning and the general drawing note should be written to eliminate any ambiguity in the workshop.

Unit challenge. Have you ever wondered how to document an object to have it manufactured? Your challenge is to produce the standardized technical drawing of an everyday object from your study area (for example, a phone stand, a pencil holder, or a pencil case).

Follow these stages:

1. Real data collection: Choose the object and measure its actual dimensions (length, width, and thickness) in millimeters using a graduated ruler. Record the values on a preliminary freehand sketch.

2. Determining the scale: Based on the measured size and the space available on an A4 sheet, calculate and justify the most appropriate standardized scale (for example, a reduction scale of $1:2$ or an enlargement scale of $2:1$).

3. Drafting and dimensioning: Draw the required views (front, top, and side view) at the chosen scale, on paper or using a free digital tool such as LibreOffice Draw or Tinkercad. Strictly apply dimensioning standards: extension lines, arrows, properly oriented dimension values, and no redundancies.

Assessment criteria:

• Accuracy in taking real measurements and justification of the scale calculation.

• Rigorous application of dimensioning standards (arrangement of dimensions, arrows, and line hierarchy).

• Graphic clarity, neatness, and technical finish of the final drawing.