Difficulty: Easy
Correct Answer: less than 50%
Explanation:
Introduction / Context:Self-locking mechanisms are designed so that applied loads cannot back-drive the machine. This is a key safety and design feature in jacks, presses, and worm-gear hoists. The concept links mechanical advantage, friction, and efficiency.
Given Data / Assumptions:
Concept / Approach:
A self-locking machine cannot be driven in reverse by the load. In classical treatments, the “back-driving” condition leads to a critical relation between friction angle and helix angle. When efficiency exceeds 50%, back-driving becomes possible; when efficiency is below 50%, the mechanism tends to be self-locking.
Step-by-Step Solution:
For a screw: let φ be friction angle, α helix angle.Self-locking requires φ > α (so tan φ > tan α).Associated efficiency η for raising loads can be shown to be less than 50% when φ > α for typical geometries.Therefore, to ensure self-locking, design such that η < 0.5 (i.e., less than 50%).Verification / Alternative check:
Textbook worm-gear and screw-jack design guidelines adopt η < 50% as the safe self-locking side, consistent with tan φ dominance over tan α.
Why Other Options Are Wrong:
(b) Exactly 50% is the boundary case; practical tolerance demands staying below. (c) More than 50% risks back-driving. (d) Not applicable because a definite criterion exists. (e) 30% may ensure self-locking but is unnecessarily restrictive; the standard threshold is 50%.
Common Pitfalls:
Confusing “non-reversibility” with “efficiency close to zero”; overlooking lubrication that reduces friction and can defeat self-locking.
Final Answer:
less than 50%
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