Machines – Improving Velocity Ratio of a Single-Purchase Crab Winch Which action increases the velocity ratio (VR) of a single-purchase crab winch?

Introduction / Context:
In hoisting machines like a single-purchase crab winch, the velocity ratio (VR) determines how much movement of effort produces how much lift of the load. Understanding how design parameters affect VR helps in selecting easier hand effort or faster lift.

Given Data / Assumptions:

• Single-purchase arrangement: one gear and one pinion stage.
• Let L = handle length, r = load drum radius, Zg = gear teeth, Zp = pinion teeth.
• Ideal kinematics (no slip).

Concept / Approach:
A typical VR expression is VR = (Zg / Zp) * (L / r). Thus, VR increases if (Zg / Zp) increases, if L increases, or if r decreases. The question asks which listed action increases VR.

Step-by-Step Solution:
Check handle length: increasing L increases VR directly. Check drum radius: increasing r decreases VR (opposite effect). Check pinion teeth: increasing Zp reduces (Zg / Zp), thereby reducing VR. Therefore, only increasing L (option A) increases VR among the choices.

Verification / Alternative check:
Consider proportional changes: doubling L doubles VR; doubling r halves VR; increasing Zp by 20% lowers gear ratio and thus VR by 20% if Zg fixed.

Why Other Options Are Wrong:
Increasing drum radius reduces VR, making lifting harder. Increasing pinion teeth lowers gear ratio and VR. “All of the above” contradicts the correct trends. Reducing gear ratio reduces VR (opposite of desired).

Common Pitfalls:
Confusing mechanical advantage with VR and assuming any “increase” helps lifting. Ignoring that VR trades speed for force.

Final Answer:
Increasing the length of the handle