2.6 Basic Machines, Mechanical Advantage, Velocity Ratio & Efficiency

Basic Machines, Mechanical Advantage, Velocity Ratio & Efficiency

Every lifting appliance—from a hand chain block to a mobile crane—is a collection of basic machines arranged to multiply force or change its direction. Understanding how machines trade effort against movement explains why a rigger can hoist 5 tonnes with one hand, and it supplies three exam-critical calculations: Mechanical Advantage (MA), Velocity Ratio (VR), and Efficiency (EFF).

---

1. Simple and Compound Machines

The Six Simple Machines

Compound Machines

A compound machine is a collection of simple machines working together to do more complex work and offer greater advantage than any single simple machine. A mobile crane, for example, combines levers (the jib), pulleys (the sheaves), screws (limit switches and adjusters), and wheels and axles (the drive train). A hand chain block combines a lever-class hand wheel, a geared wheel-and-axle train, and a screw-friction (Weston) brake—Section 7.1.

---

2. Mechanical Advantage (MA)

In a lifting machine, a small weight or force (the effort, $P$) is used to lift a larger weight or force (the load, $W$). When effort and load are balanced, the machine is in equilibrium; any further increase in effort moves the load. The relationship between them is the Mechanical Advantage:

$\text{Mechanical Advantage (MA)} = \frac{\text{Load}}{\text{Effort}} = \frac{W}{P}$

MA is a simple mathematical ratio, so no units of measure are used.

Worked Example

A machine lifts a load of $300\text{ kg}$ with an applied effort of $50\text{ kg}$:

$\text{MA} = \frac{300}{50} = 6$

The machine multiplies the effort sixfold.

Reeving Lines: MA in Practice

Increasing the lines of cable between a winch and the load multiplies what the winch can pull (ignoring friction):

• $1\text{ t}$ WLL winch + 1 line of cable = $1\text{ t}$ maximum tow
• $1\text{ t}$ WLL winch + 2 lines of cable = $2\text{ t}$ maximum tow
• $1\text{ t}$ WLL winch + 3 lines of cable = $3\text{ t}$ maximum tow

The same principle lets the gearbox of a hand chain hoist multiply the hand-chain force by as much as 30 times.

---

3. Velocity Ratio (VR)

Machines give nothing for free: to move the load a short distance, the effort must travel a proportionally greater distance. The ratio of these movements is the Velocity Ratio:

$\text{Velocity Ratio (VR)} = \frac{\text{Distance moved by Effort}}{\text{Distance moved by Load}} = \frac{D_{ME}}{D_{ML}}$

Worked Example

The effort on a machine moves $75\text{ m}$ while the load moves $3\text{ m}$:

$\text{VR} = \frac{75}{3} = 25$

Like MA, VR is a dimensionless ratio.

---

4. Efficiency (EFF)

No machine is perfect: friction in gears, bearings, sheaves, and ropes wastes part of the input energy. Efficiency expresses how good a machine is at converting input energy into useful work, and links MA to VR:

$\text{Efficiency} = \frac{\text{MA}}{\text{VR}} \times 100\%$

Worked Example

Using the machine above ($\text{MA} = 6$, $\text{VR} = 25$):

$\text{Efficiency} = \frac{6}{25} \times 100\% = 24\%$

Engineering Significance

• A machine with $ ext{MA} = \text{VR}$ would be 100% efficient—impossible in practice.
• Low efficiency is not wasted design: in a manual hoist, the friction that lowers efficiency also powers the self-sustaining screw brake that holds the load when pulling stops (Weston brake, Section 7.1).
• When comparing appliances, remember that published capacities already assume realistic efficiency—rigging calculations must still respect the marked WLL, never a theoretical frictionless figure.

---

A Safe Tackle Calculation Workflow

Count the rope parts that actually support the moving block, not every visible span. Draw the fixed block, moving block, rope anchor and hauling end, then mark the tension direction in each supporting part. The ideal velocity ratio equals the number of equally tensioned supporting parts only for the simple arrangement assumed. Real capacity is lower because every sheave and bearing adds friction, and the anchor, blocks, rope and supporting structure each need an adequate rating.

For example, an ideal three-part system lifting 600 kg needs 200 kgf of rope tension. At 75% efficiency, required effort is 200 / 0.75 = 266.7 kgf. This does not authorize a lift: verify component WLLs, side loads, anchorage and the manufacturer's reeving instructions first.