The single and double purchase winch crab experiment determines the velocity ratio, mechanical advantage and efficiency of a geared lifting machine, and shows how adding a second gear stage multiplies the mechanical advantage. A winch crab uses gear trains to let a modest effort at the handle raise a heavy load on the drum — the mechanism behind cranes and hoisting winches.
Aim of the experiment
To determine the velocity ratio, mechanical advantage and efficiency of single-purchase and double-purchase winch crabs and to compare them.
Theory
In a winch crab, an effort P applied at a handle of radius R turns a pinion that drives a gear on the load-drum axle of radius r; the load W is wound on the drum. A single-purchase crab has one gear reduction; a double-purchase crab has two.
- Single purchase: VR = (R / r) × (T₂ / T₁), where T₁ is the pinion teeth (effort side) and T₂ the gear teeth (load side).
- Double purchase: VR = (R / r) × (T₂ / T₁) × (T₄ / T₃), the product of both gear reductions.
- MA = W / P and η = (MA / VR) × 100%
The double-purchase arrangement has a much larger velocity ratio, so it lifts heavier loads for the same effort. Both follow the law of the machine, P = mW + C.
Apparatus required
- Winch crab apparatus with interchangeable single- and double-purchase gearing
- Load drum, effort handle/pulley, weights and hangers
- Steel rule for radii; tooth counts of pinions and gears
Procedure
- Record the gear tooth numbers and the effort and drum radii; calculate the velocity ratio for the single-purchase setup.
- Apply a known load and increase the effort until the load rises steadily; record the effort.
- Repeat for several loads; then reconfigure to double purchase and repeat.
- Compute MA and efficiency for each; compare the two arrangements and plot effort vs load.
Observations and result
The double-purchase crab shows roughly double (or more) the velocity ratio and mechanical advantage of the single-purchase crab, at the cost of slower lifting. Efficiency for both is found from η = MA/VR, and the effort-vs-load plot is linear.
Applications
Winch crabs and geared winches lift loads in cranes, workshops, and construction hoists. The experiment completes the simple-machines set alongside the screw jack and worm and worm wheel experiments, and connects to gear analysis in the epicyclic gear train experiment. See related terms in the engineering lab glossary.
Frequently asked questions
What is the difference between a single and double purchase winch crab?
A single-purchase crab has one gear reduction; a double-purchase crab has two, giving a much higher velocity ratio and mechanical advantage but slower lifting.
What is the velocity ratio of a single-purchase winch crab?
VR = (R / r) × (T₂ / T₁), where R and r are the effort and drum radii and T₁, T₂ the pinion and gear teeth.
How is the efficiency of a winch crab found?
Efficiency is the ratio of mechanical advantage to velocity ratio, η = (MA / VR) × 100%, at each load.
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