Self-locking machines – efficiency criterion For a self-locking machine (e.g., a self-locking screw or worm mechanism), what should be the efficiency threshold to ensure self-locking under idealized dry friction conditions?

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:

• Dry friction model; no elastic deformations or lubrication effects.
• Ideal screw/worm geometry where classical derivations apply.
• Efficiency η defined as output work over input work per cycle.

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:

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%