Gears: identify the correct statements about fundamental gear terms. Evaluate each statement about standard involute gears and choose the single best option that encompasses all true statements. • Addendum vs. dedendum magnitude • Relation between pitch circle diameter, module, and number of teeth • Relative size of pitch circle and base circle Choose the correct option.
Mechanical Engineering
Machine Design
Difficulty: Easy
Choose an option
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AThe addendum is less than the dedendum.
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BPitch circle diameter equals module × number of teeth.
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CThe pitch circle is always larger than the base circle.
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DAll of the above
Answer
Correct Answer: All of the above
Explanation
Given concepts
- Addendum ≈ 1×module; dedendum ≈ 1.25×module in standard gears.
- Pitch circle diameter: D = m × Z where m = module and Z = number of teeth.
- Base circle diameter: Db = D × cos φ (φ = pressure angle), so D > Db.
ReasoningSince dedendum > addendum (standard proportions), statement (a) is true.Since D = mZ, statement (b) is true.Since cos φ < 1, base circle < pitch circle, so (c) is true.
Common pitfallConfusing base circle with addendum circle; base circle is smaller than pitch circle for involute gears.
Final AnswerAll of the above