ZIMSEC O Level · Technical Graphics and Design · Form 3, Form 4
Loci
A locus is the path traced by a point moving under given conditions.
- Points on a crank and connecting rod mechanism, a ladder sliding down a wall, or a point on a rolling wheel (cycloid).
Engineering curves
- Ellipse: constructed by the concentric circles method or trammel method.
- Involute: the path of the end of a string unwinding from a circle (used in gear teeth).
- Archimedean spiral: a point moving away from a centre at a constant rate while rotating (used in cams).
- Helix: the path around a cylinder rising steadily (screw threads, springs).
Development of surfaces
A development (net) is the flat shape of a surface that can be folded to make a solid.
- Prisms and cylinders: parallel-line development; the length of a cylinder's development is πd.
- Pyramids and cones: radial-line development using the true length of the slant edges.
- Truncated solids: project cut points carefully to find true positions.
Uses: sheet-metal work, packaging, ducting.
Exam tip: Find true lengths before drawing a radial development – using apparent lengths gives a wrong shape.
Check yourself
- What is the length of the development of a cylinder with a diameter of 50 mm?
- Which curve is used to shape gear teeth?
- Give one practical use of developments.
Show answers
- π × 50 ≈ 157 mm
- The involute.
- Any one: sheet-metal products, packaging boxes, ducts, funnels.
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