Worm and Worm Wheel – Velocity Ratio Calculation (Single-Start Worm) A single-start worm drives a worm wheel with 50 teeth. The effort wheel diameter is 100 mm and the load drum diameter is 50 mm. What is the velocity ratio (VR) of the lifting machine?

Introduction / Context: Velocity ratio (VR) links the movement of effort to the movement of load in simple machines. For a worm and worm wheel hoist with effort wheel and load drum, VR combines gear ratio and pulley radii effects.

Given Data / Assumptions:

• Single-start worm (starts = 1).
• Number of teeth on worm wheel = 50.
• Diameter of effort wheel = 100 mm.
• Diameter of load drum = 50 mm.
• No slip; ideal kinematics.

Concept / Approach: For worm gear hoists, VR = (teeth on worm wheel / worm starts) * (diameter of effort wheel / diameter of load drum). The gear part converts one worm revolution into many drum revolutions depending on wheel teeth, and the pulley part converts rotation to rope travel.

Step-by-Step Solution: Gear ratio = 50 / 1 = 50. Pulley ratio = 100 / 50 = 2. Overall VR = 50 * 2 = 100. Thus, the effort must move 100 units while the load rises 1 unit (ideally).

Verification / Alternative check: Dimensional/logic check: More wheel teeth and a larger effort wheel both increase VR, so a value larger than 50 is expected; 100 is consistent.

Why Other Options Are Wrong: 50: ignores the wheel/ drum diameters ratio. 150 / 200: overestimates by multiplying with an incorrect factor. 25: would imply a half gear ratio or reversed diameters, which is not the case.

Common Pitfalls: Confusing the number of worm starts with wheel teeth. Using radii instead of diameters inconsistently (ratio is the same but stay consistent).

Final Answer: 100