Worm-Geared Pulley Block — Velocity Ratio Change In a worm-geared pulley block with a single-start worm, if the number of teeth on the worm wheel is doubled, what happens to the velocity ratio (VR)?

Introduction / Context: Worm-geared pulley blocks achieve high mechanical advantage via the gear ratio between a worm and a worm wheel. The velocity ratio (VR) is directly tied to the gear teeth count for a given worm start count.

Given Data / Assumptions:

• Single-start worm (one thread), common in hoisting blocks.
• Other parts and diameters unchanged.
• VR is proportional to the worm wheel teeth count z for a single-start worm.

Concept / Approach: For a single-start worm, each worm revolution advances the worm wheel by one tooth. Thus, the gear ratio equals z (number of teeth on the worm wheel). The overall VR for the block scales with that ratio (with additional factors from the sheave system if present, assumed constant here).

Step-by-Step Solution:

Verification / Alternative check: Compare rotations: one worm turn moves the wheel by 1 tooth; with twice the teeth, it takes twice the turns for one wheel revolution, doubling distance ratio between effort and load path, hence VR doubles.

Why Other Options Are Wrong: 'Remains unchanged' contradicts the direct proportionality; 'half' or 'four times' would require changing worm starts or reeving pattern, which is not stated.

Common Pitfalls: Confusing worm starts (single vs multi-start) with teeth count; ignoring additional pulley stages that also affect VR but are assumed constant here.

Final Answer: True — the velocity ratio doubles.