Rubber Band Assist Calculator
Where to anchor bands on a parallel 4-bar so the assist curve matches gravity instead of fighting it. The geometry is exact; the band force is measured from your bands, not assumed.
Inputs
A 4-bar is two parallel bars carrying an end effector that stays level as it rises. The usual way to band one isdiagonally between the two bars, so the band pulls them toward each other and the linkage swings up. Measure to the center of each bolt, not to the edge of the metal.
Everything is drawn to scale at the defaults below. The band runs from 8 inches out on the lower bar to 2 inches out on the upper one, and it is that difference that does the work: anchor both at the same distance and the band keeps a constant length through the whole sweep, doing nothing at all.
Where the bands go
Between the bars is the usual answer on a 4-bar: the band pulls the two bars toward each other and the linkage rises. Tower to bar is the other option, and on a 4-bar it has to reach the upper bar or it fouls the linkage.
Pivot to pivot up the tower, from the lower bar's bolt to the upper bar's. It is the same distance as the end effector's two pivots, because the linkage is a parallelogram. Usually 2 to 4 inches.
How far out along the lower bar the band hooks on, measured from that bar's pivot on the tower.
Same measurement on the upper bar, from its own pivot. This one must sit CLOSER in than the lower anchor or the band works against you. Equal distances give a band that never changes length and does nothing at all.
From the middle of the pivot bolt that bar turns on, to the middle of the screw the band hooks over on the tower. This anchor does not move when the linkage swings. Holes in VEX C-channel are half an inch apart, so counting holes works if you cannot get a tape in there.
Which direction that anchor sits from the pivot, not how far away it is. Looking at the robot from the side with the linkage reaching out to your right: 0 is level with the pivot and to the right, −90 straight below, +90 straight above, 180 straight behind. It has to be above and behind, around 120 to 150, or the band stretches as the lift rises and fights it.
From the same pivot out along the bar to the screw the other end of the band hooks over. This is the anchor that travels as the bars swing, and sliding it in or out is the strongest single change you can make to the shape of the assist.
How far the anchor sits off the line of the bar, as an angle measured at the pivot. A screw through the bar itself is 0. A standoff square to it is 90, or −90 the other way. If you are unsure, it is 0.
The band
Sets the free length and the safe stretch limit only. It does not set the force, which comes from your own measurements at the bottom of this page.
How many bands run side by side between the same two anchors. Force adds up, so four bands pull four times as hard as one. A single loop folded double counts as 2.
How far apart the anchors would be with the band straight but not yet pulling. Easiest way to get it: hook one band over both anchors and move the linkage until the band is straight but still loose enough to push sideways with a finger, then measure between the anchors. One #64 loop over two anchors spans about its flat length, 3.5 inches. Loop it twice and this halves to about 1.75.
The linkage and its load
Everything carried by the moving end: the game object, the claw or intake gripping it, and the end effector frame itself. Weigh the effector on a kitchen scale with an object in it. Because the bars stay parallel, it does not matter how far forward any of it sits.
Pivot to pivot along one bar: from the bolt it turns on at the tower to the bolt it turns on at the end effector. This is the only distance the load cares about. A claw reaching six inches further forward lifts through the same radius and adds nothing here, though it still moves your center of gravity and can tip the robot.
Every bar that swings, added together, weighed without the end effector on. A 4-bar normally has two; a double-wide build has four. They cost less than their weight suggests, because it is spread along their length instead of hanging at the end.
From the pivot to where one bar balances across a finger. A bare C-channel balances at its middle, so half the bar length is the usual answer. A motor or a pile of standoffs bolted partway out drags it outward.
Sweep
Where the bars sit at the bottom of their travel, measured from horizontal. 0 is dead level and negative points downhill. Resting a little below level is normal, so −10 is a reasonable starting point.
Where they stop at the top, from horizontal. 90 is straight up. Use where the linkage actually stops in a match rather than the mechanical limit, or the match quality below gets judged over a range you never use.
Your measured band force
This is the one measurement that makes the rest of the page real, and it takes about ten minutes.
- Hook one band over something fixed so it hangs freely, and measure it hanging empty. That length is your zero.
- Hang a known weight from it and measure again. Thestretch is the new length minus the empty length, not the total length.
- Repeat at four or five weights spread across the range you expect to use. Rows can go in any order.
Enter the pull for one band. The count above multiplies it, so do not add your bands together here. Weights do not need to be round numbers, and anything you can put on a scale works: a bag of washers, a water bottle, a spare battery.
Results
Band force data
—
Everything above depends on this.
Peak torque left for the motors
—lb·in
The widest gap between gravity and assist anywhere in the sweep. Size the lift motors against this, not against the ungeared number below it.
Same in newton-meters
—N·m
The units motor specs use. One V5 motor on a 100 RPM cartridge stalls at 2.1 N·m, and you should be nowhere near stall.
Peak without any bands
—lb·in
What the linkage would need with no bands fitted at all, for comparison.
Bands take off
—%
How much of that peak the bands remove. A high number here is not the goal on its own; the match below matters more.
Peak assist
—lb·in
The hardest the bands ever pull, which is not necessarily where you need help.
How well the curves match
—
Whether the assist follows the shape of gravity across the sweep, or peaks in the wrong place. This is the number worth tuning against.
Most the band stretches
—in
Beyond the free span, at whichever end of the sweep stretches it furthest.
Of its safe working range
—%
Against a ceiling of 35% of the published breaking elongation. Read conservatively: 720% is treated as stretching to 7.2 times its length rather than 8.2, so if anything this overstates how hard you are working the band.
Gravity against assist, through the sweep
The gap between the two is what your motors have to supply. Where the assist rises above gravity, the bands are fighting you.
gravity band assist left for the motors
Show the numbers behind this chart
Every point on the chart above, at two degree steps. Gravity is what the arm needs, assist is what the bands give, and the last column is what is left for the motors.
How this is calculated
A band only assists while it is getting shorter as the lift rises, because that is when it hands energy back. A band that gets longer as the lift rises is being charged up by the lift, and the motors pay for it twice: once on the way up, and again holding it down. Both layouts here come down to that one question.
Between the two bars
With the bars parallel and separated by d, an anchorp along the lower bar and q along the upper one, the band spans:
k = q − p L = √(d² + k² + 2dk·sin θ) dL = d·k·cos θ ÷ L assist torque T = force(L − free span) × (−dL) × number of bandsEverything hangs on k. It has to benegative, meaning the lower anchor sits further out than the upper one. Anchor both at the same distance and k is zero, the band sits at a constant length d through the entire sweep, and it does exactly nothing. Anchor the upper one further out and the band fights the lift the whole way.
The useful part is that cos θ in the middle of it. It is the same cosine gravity follows, so this layout starts out with roughly the right shape before you have tuned anything. That is the real argument for banding between the bars rather than from the tower.
Tower to one bar
A band from a fixed tower anchor to a point on one bar makes a triangle with that bar's pivot. As the bars swing, one corner moves, changing both the stretch and the leverage:
included angle φ = (bar angle + offset) − tower angle band span L = √(a² + b² − 2ab·cos φ) dL = a·b·sin φ ÷ L assist torque T = force(L − free span) × (−dL) × number of bandsHere the sign lives in sin φ, and it means the tower anchor has to sit above and behind the pivot. Anchored below the pivot, the bar anchor swings away from it as the lift rises, the band stretches on the way up, and you have built a spring that resists the lift. On a 4-bar this layout also has to reach the upper bar, because a band from the tower to the lower bar runs straight through the linkage.
What the parallel bars buy you
The two bars stay parallel, so the end effector never rotates. It translates along the arc the bar tip traces, and every point on it moves by exactly the same amount. That has a consequence worth knowing:
How far forward the load sits does not change the torque.A claw holding an object six inches out in front of the effector rises by the same amount as the effector itself, so it lifts through the bar length and nothing else. Only the bar length matters, which is why this page asks for that rather than for a distance to the object. It still moves your center of gravity, so it can still tip the robot; it just does not cost torque here.
With your numbers
The bars themselves do rotate, so they count at their own balance point, normally half their length. That is why bar weight costs about half what the same weight bolted to the effector would.
The goal is matching a shape, not adding force
Both terms carry the same cos θ, so gravity on the whole linkage is hardest with the bars level and nearly nothing with them vertical. That is the same curve theRequired Lift Torque page is built around.
So the job of the anchors is not to produce as much assist as possible. It is to produce assist shaped like that curve, so what is left for the motors is small and even across the whole sweep. Two setups with identical peak assist can leave very different amounts of work behind.
The classic failure
Bands tuned by feel usually end up heaving the lift off the bottom, because that is where it feels heaviest. The assist then peaks low and stays high as the bars rise, so near the top the bands pull harder than gravity and the motors have to fight them back down.
On the plot that shows as the assist line crossing above the gravity line. The residual goes negative, and holding a raised lift steady starts costing current for nothing.
Why measuring beats a spring constant
Rubber does not obey Hooke's law. It stiffens unevenly as it stretches, and the same nominal band varies with brand, batch, age and temperature. Published descriptions give one roughly linear region at low stretch and another with a different slope later, so a single number would be wrong across most of the range.
Measuring four or five points takes minutes and sidesteps all of it. This page interpolates what you measured, and past your last point it says so rather than extrapolating confidently into territory you never tested.
Do not run them near their limit
Fatigue life collapses long before a band breaks. The safe range shown here is 35% of the published breaking elongation, which is a conservative guide rather than a datasheet figure. A band that fails mid-match takes the lift down with it, usually at the worst moment.
Sources & assumptions
Band dimensions, breaking strength, elongation and tensile figures arepublished distributor specifications. The Alliance 37646 is 3.5" by 0.25" at a 0.04" gauge, non-latex synthetic, breaking at 24 lb and 720% elongation.
Worth knowing if you have read advice written for natural rubber bands: the Alliance band is thinner, 0.04" against roughly 1/16", so its cross section is about 64% as large and it pulls correspondingly less at the same stretch. Band counts suggested for natural rubber willoverestimate the assist you get from these.
No spring constant is published or assumed anywhere on this page. Force comes entirely from your own measurements. The safe working fraction isestimated, not taken from a datasheet.
Models one band path as a straight line between two anchors, in tension whenever stretched. It ignores friction, the band's own weight, any standoff or pulley it wraps around, and hysteresis, which is real and is why a banded lift is easier to raise than to lower.
- Alliance Rubber 37646 distributor specifications (size 64, 0.04" gauge, non-latex) — checked August 2026
- Standard #64 rubber band dimensions — checked August 2026
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Where this goes next
Explore further on the full mapWhere the answers on this page can be used, and which tools could have given you the numbers it asks for.
Comes after
DR4B Geometry Calculatorfills in your arm length hereRequired Lift Torquefills in your lift load hereComplete Lift Designerfills in your lift load hereTwo-Bar Liftfills in your arm length hereSix-Bar Liftfills in your lift load hereYou are here
Rubber Band Assist Calculator
Where your answer goes
Lift Speed & Gear Ratiogear the lift faster now the bands carry part of the loadbrings your lift load with itShaft & Structure Load Checkcheck the shaft survives the bands pulling and motors pushingCatapult & Puncher Energysee what those same bands store when you use them to launchuses your rubber band force againTwo-Bar Liftsee reach, height and torque for the same arm without the bandsbrings your arm length with ita number carries across the next question it raises