A movable lower pulley is a single sheave attached directly to the load, with a rope passing under it so both rope ends share the weight. The sheave itself — the grooved wheel that rolls along the rope — is the working component, redirecting tension while travelling vertically with the load. It exists to halve the input force needed to lift a given weight, giving a mechanical advantage of 2 at the cost of pulling twice as much rope. Riggers use it on elevator counterweights, theatre fly systems, and arborist lifts to move loads of 200-500 kg with hand force alone.
Movable Lower Pulley Interactive Calculator
Vary rope pull distance and rope angle to see load rise, effective mechanical advantage, pull force fraction, and hook load.
Equation Used
The ideal single movable pulley has two rope segments supporting the load, so a vertical system gives MA = 2 and input force = W/2. If the supporting rope segments angle away from vertical, only the vertical component contributes to lifting, so effective MA becomes 2*cos(theta). Rope travel remains twice the ideal load rise.
- Single movable lower sheave with two supporting rope segments.
- Rope and sheave losses are ignored.
- Angle is measured from vertical for the supporting rope segments.
- Load hook or shackle carries the full load W.
How the Movable Lower Pulley (single-movable) Works
The geometry is simple but the force balance trips people up. You anchor one end of the rope at the top, run the rope down under a sheave fixed to the load, then back up to where you pull. Two rope segments now support the load — one from the anchor, one from your hand — so each carries half the weight. Pull 1 metre of rope and the load only rises 0.5 metres, because the rope has to shorten on both sides of the sheave at the same time. That 2:1 trade is the whole point: half the force, double the rope travel.
The single movable pulley only delivers its full mechanical advantage of 2 when the two rope segments run perfectly parallel and vertical. Let the rope angle out to 30° from vertical and the effective lift force per segment drops to cos(30°) ≈ 0.87 of nominal — your 2:1 advantage drops to about 1.73:1, and you're suddenly working harder than the textbook said you would. Riggers fix this by adding a fixed upper pulley to redirect the haul line, which keeps the load-side ropes vertical regardless of where the operator stands.
Failures here are usually not the sheave itself — it's the attachment hardware. The shackle or hook connecting the sheave to the load sees the full load weight, not half. We've seen people spec a 250 kg shackle for a 400 kg load on a 2:1 system thinking the shackle only sees 200 kg. Wrong. The shackle carries the entire load. The 2:1 advantage applies to the hauler's hand, not to the load-bearing pulley axle, which actually sees roughly 2× the rope tension. Get that wrong and you snap the axle pin under what you thought was a safe load.
Key Components
- Sheave (grooved wheel): The rotating wheel the rope rides in. Groove radius must match rope diameter within +5% / -0% — too tight and the rope binds, too loose and the rope flattens and wears prematurely. For a 12 mm rope use a 12.5-13 mm groove.
- Sheave bearing: Either a bronze bushing for slow lifts under 0.5 m/s or a sealed ball bearing for repeated cycling. Bushing efficiency runs around 92-95%, ball bearing 96-98%, which directly reduces the theoretical 2:1 advantage you actually feel at the haul end.
- Side plates / cheeks: The two steel plates flanking the sheave, joined by the axle pin. These transfer the full load weight (not half) into the load-attachment point below. Standard rigging cheek plates are rated 2× the working load limit of the sheave to handle shock loading.
- Axle pin: Carries roughly 2× the rope tension — one tension from each rope segment pulling up on the sheave. A single movable pulley rated for a 500 kg load needs an axle pin rated for at least 1000 kg pin-shear load.
- Load attachment (hook, shackle, or becket): Connects the lower pulley assembly to the load. This component sees the full load weight. Spec it to the full load, never to half.
- Anchor point (dead-end): The fixed termination of the standing rope end at the overhead structure. Sees exactly half the load weight in steady state, but must be rated for the full load to handle dynamic shock if the haul end slips.
Industries That Rely on the Movable Lower Pulley (single-movable)
The single movable lower pulley shows up wherever you need to halve hand force on a vertical lift and you have headroom for double the rope travel. It's almost never used alone in modern rigging — most systems pair it with a fixed upper pulley to redirect the haul line — but the load-side pulley itself is the workhorse that carries the mechanical advantage. The reason it's still everywhere despite being one of the oldest machines on Earth is simple: it's the cheapest, lightest way to double a person's lifting capacity without any electrical input.
- Theatre rigging: Counterweight fly systems at venues like the Royal Opera House use movable lower pulleys on each batten to let stagehands raise 300-500 kg of lighting trusses by hand.
- Arboriculture: Petzl Naja and similar arborist rigging blocks act as movable lower pulleys when lowering large limbs — the tree-side pulley travels with the cut piece while the arborist controls descent from the ground.
- Construction lifting: Gin pole rigs on residential roofing jobs use a single movable pulley at the load to lift bundles of asphalt shingles up to second-storey roofs with hand-line haul.
- Elevator counterweights: Older Otis traction elevators use a 2:1 roping arrangement with a movable pulley on the car frame, halving the cable tension at the drive sheave so a smaller motor can move a heavier cab.
- Sailing and yachting: Mainsheet systems on dinghies like the Laser use a movable lower pulley on the boom to give sailors 2:1 purchase when sheeting in against 200+ kg of sail force.
- Industrial maintenance: Mechanics use single movable pulleys on overhead I-beam trolleys to lift gearboxes and motors of 100-300 kg out of machinery for service work.
The Formula Behind the Movable Lower Pulley (single-movable)
The core relationship tells you the input force required at the haul rope to lift a given load. At the low end of typical rigging — say a 50 kg load — the formula predicts a 25 kg pull, but in practice friction at the sheave and any rope angle off vertical will push that closer to 28-30 kg. At nominal 200-300 kg loads with a clean ball-bearing sheave and parallel rope segments, you'll feel almost exactly the predicted half. Push to the high end — 500 kg or more — and even small inefficiencies become muscle-breaking. The sweet spot for human-powered single movable pulley use sits at 100-300 kg loads with rope segments within 10° of vertical.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Fin | Input force required at the haul rope | N | lbf |
| W | Mass of the load being lifted | kg | lb |
| g | Gravitational acceleration (9.81) | m/s² | ft/s² |
| η | Sheave efficiency (0.92-0.98 typical) | dimensionless | dimensionless |
Worked Example: Movable Lower Pulley (single-movable) in a museum artefact lift in a heritage gallery
You're rigging a single movable lower pulley to lift a 180 kg cast-bronze sculpture from a wooden crate up onto a display plinth in a heritage gallery in Edinburgh. The rigger uses a Harken 75 mm aluminium block with a sealed ball-bearing sheave (η = 0.96) and a 12 mm polyester rope. The haul line runs back over a fixed upper pulley so both load-side rope segments are within 5° of vertical. You need to know whether one person can pull this safely.
Given
- W = 180 kg
- g = 9.81 m/s²
- η = 0.96 dimensionless
- Mechanical advantage = 2 —
Solution
Step 1 — calculate the total load weight in newtons:
Step 2 — at the nominal 180 kg load with an efficient ball-bearing sheave, calculate the haul force:
That's a hard pull but achievable for a fit adult using body weight on the rope. Now check the low end of the typical museum-lift range — say a 60 kg crated artefact:
That's a comfortable one-arm pull — you'd barely notice the load. Now the high end — a 350 kg stone plinth:
That's beyond any single person. Above roughly 250 kg you need two haulers, a winch, or a 4:1 system with a second movable pulley. The sweet spot for a one-person 2:1 lift sits between 60 and 200 kg.
Result
The nominal 180 kg sculpture requires roughly 920 N (≈ 94 kg) of haul force — manageable for one fit person leaning back on the line, but not casual. At 60 kg the pull drops to a trivial 31 kg; at 350 kg it climbs to an impossible 182 kg, which is why riggers reach for compound block-and-tackle once loads exceed about 250 kg on a 2:1. If your measured haul force is significantly higher than predicted, suspect three causes: (1) the haul rope running off-axis at more than 15° from vertical at the load pulley, which kills cosine effective force; (2) a dry or contaminated sheave bearing dragging η down from 0.96 toward 0.85, adding 12-15% to required pull; or (3) rope diameter mismatched to sheave groove — an 11 mm rope in a 16 mm groove pinches and binds at the flange edges, behaving like a brake.
Choosing the Movable Lower Pulley (single-movable): Pros and Cons
The single movable lower pulley competes with the fixed pulley (no mechanical advantage but redirects force) and compound block-and-tackle systems (higher mechanical advantage at the cost of more rope and more friction). Pick based on load weight, available headroom, and how much rope travel you can stomach.
| Property | Single movable lower pulley | Fixed pulley | Compound block-and-tackle (4:1) |
|---|---|---|---|
| Mechanical advantage | 2:1 | 1:1 | 4:1 to 8:1 |
| Rope travel per unit lift | 2× load distance | 1× load distance | 4-8× load distance |
| Practical load range (one person) | 60-250 kg | 20-80 kg | 200-1000 kg |
| System efficiency | 92-98% (1 sheave) | 92-98% (1 sheave) | 75-88% (multiple sheaves) |
| Hardware cost (typical rigging block) | $40-150 | $25-80 | $200-600 |
| Headroom required above load | Moderate — 1 sheave height | Low — single redirect | High — block separation distance |
| Setup complexity | Low — single anchor + single block | Lowest — single redirect | High — reeving sequence matters |
| Best application fit | Hand-lifting 100-200 kg loads | Direction change only | Heavy industrial or rescue loads |
Frequently Asked Questions About Movable Lower Pulley (single-movable)
Two causes dominate. First, your rope segments aren't parallel — if the haul side angles outward at 30° from vertical the effective vertical lift force drops by cos(30°) ��� 0.87, and your 2:1 collapses toward 1.73:1. Add a fixed redirect pulley at the top so both load-side ropes hang truly vertical.
Second, sheave efficiency. A dry bronze bushing or a corroded ball bearing can drag efficiency down from 0.96 to 0.85 or worse. Spin the bare sheave with no load — it should rotate freely for at least 3-4 seconds after a flick. If it stops dead in under a second, the bearing is the problem.
No, and this is a common rigging mistake. In steady-state lift the anchor sees half the load weight, but the moment the haul line slips, jerks, or the load swings, the anchor can momentarily see the full load plus dynamic shock multiplier of 2-4×. Always rate the anchor point to the full working load limit at minimum, with a safety factor of 5:1 for overhead lifting of personnel-adjacent loads.
Rule of thumb: when the predicted haul force exceeds 40% of the hauler's body weight, step up the mechanical advantage. For an 80 kg rigger that's 32 kg of pull, which corresponds to roughly a 60-65 kg load on a 2:1 with a fresh sheave. Above that you're using body weight rather than arm strength and control gets sketchy.
The other trigger is rope travel. A 4:1 system needs four times the load lift in haul rope. If your overhead clearance or rope length runs out before the load reaches its destination, stick with 2:1 and add haulers instead.
Almost always groove-to-rope diameter mismatch or fleet angle problems. A rope running at more than 4° fleet angle (the angle between the rope and the plane of the sheave) climbs the flange and pops out. Check that your haul line and anchor line both run square to the sheave face.
The other cause is a groove diameter too large for the rope — a 10 mm rope in a 16 mm groove sits loose and rolls sideways under shock loading. Match groove to rope within +0.5 to +1 mm of rope diameter.
The full load, plus margin. The pulley axle pin sees the sum of both rope tensions — which equals the full load weight, not half. The cheek plates and load-attachment hook transfer that full load into whatever you've hung underneath. The only component that sees half the load is the rope itself. When manufacturers stamp a working load limit on a rigging block, that figure refers to the load suspended below the block, not the rope tension.
Three likely causes. First, the sheave bearing has a flat spot or contamination — listen for a tick once per revolution and replace the bearing if you hear it. Second, the rope is mismatched in lay or has a localised stiff spot from prior kinking, which makes it grip the sheave inconsistently. Third — and most common on cheap hardware — the sheave is slightly out of round or wobbles on its axle, typical of stamped-steel utility blocks under $30. A precision-machined aluminium block from Petzl, Harken, or CMI eliminates this.
Only with the right hardware and a proper backup. Life-safety rigging requires double the safety factor of cargo rigging — typically 10:1 on the working load limit. A single movable pulley on a 100 kg rescuer needs a block rated for at least 1000 kg working load, plus an independent belay line. Standard utility blocks from a hardware store are not rated for life safety. Use only blocks marked NFPA-G (general use) or CE EN 12278, and never rely on the 2:1 system as the sole load path — always have a separate backup line.
References & Further Reading
- Wikipedia contributors. Pulley. Wikipedia
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