What mathematical formula relates the number of links (L) and pairs (P) in a chain___________________?
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Answer: C. P = 2L+2
Explanation
Grubler's criterion for planar mechanisms establishes standard equations relating links and kinematic pairs. Option C represents the recognized formula convention among the given multiple-choice selections. Linkage mobility formulas use these counts to determine the degrees of freedom of a chain. Planar kinematic chains consist of rigid links connected by lower pairs allowing relative motion. Grubler's equation helps engineers verify whether a linkage forms a rigid structure or a mechanism. Counting binary, ternary, and quaternary links is essential for accurate mobility calculations.
Mechanism design requires strict adherence to mobility criteria to ensure predictable machine operation. Automated linkage synthesis tools use these mathematical relations to develop new mechanical devices. Incorrect link-pair ratios can lead to locked mechanisms or unconstrained chaotic motion. Options A, B, and D provide alternative algebraic expressions that do not match standard conventions. Option E subtracts four from links, failing to account for proper kinematic pair constraints. Option E is mathematically invalid for standard planar kinematic mobility equations.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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