Robot Joint Cable Checker: Torsion, Bend Radius & Hollow-Shaft Fit
A cable through a robot joint is asked three things at once: to twist with the joint, to bend around it, and to fit through the actuator's hollow shaft with the other cables. Each has a rule an engineer can check on paper before a harness is drawn. This page does the three checks together, from the joint's rotation, the cable's rating and diameter, and the list of conductors, and shows the formula and the source behind every number.
The address bar holds every value you changed, so the link reproduces this result.
Estimates for early design. Torsion and bend ratings are the cable maker's for a specific construction, and the bundle diameter is a packing estimate that real harnesses beat or miss by a few percent. Confirm the cable's own datasheet figures, allow for the harness maker's shield and jacket, and validate the joint with life testing on the actual motion before the design is frozen. How it is calculated →
How it is calculated
1. Torsion
A cable through a rotating joint is twisted along the length that is free to twist: the length between the clamps on either side of the joint. The cable makers rate their torsion cables in degrees of twist per metre of that free length, either way from the position the cable was fitted in, so what counts is how far the joint turns from that position: half the range each way for a harness fitted at mid-travel, the whole range one way for one fitted at an end stop. That twist divided by the free length is checked against the rating, and the same twist over twice the length is half the rate.
twist (°) = half the joint's range, each way (fitted at mid-travel)
= the whole range, one way (fitted at an end of travel)
twist per metre = twist (°) ÷ free cable length (m)
pass if twist per metre ≤ the cable's torsion rating (± °/m)
tight if within 10 % of the rating
minimum free length = twist ÷ rating2. Bend radius
The minimum radius a cable may be bent to is quoted as a multiple of its outer diameter, and the multiple grows with how often and how fast it moves: a cable laid once can be bent tighter than one in a drag chain, and a cable that twists while it bends is treated like the drag-chain case or stricter. The radius is the inner radius of the bend, the way the makers define it.
minimum bend radius = multiple for the use × cable outer diameter pass if the actual radius (the inner radius of the bend) ≥ the minimum tight if within 10 % of it
3. Bundle and fit
Up to seven wires of one size, the smallest circle that holds them is exact geometry: two side by side are two diameters wide, three in a triangle 2.155, four in a square 2.414, a ring of six around one is three, and a laid-up cable achieves these. Any other bundle takes the sum-of-squares estimate connector makers use to size backshell entries: the packing factor times the root of the sum of the squared diameters, which is the same thing as the wires' total area divided by a packing density. The default factor is 1.25. Virginia Panel publishes 1.2, and Glenair's and NASA's count-factor tables work out to 1.20 to 1.25 from twenty wires up; 1.25 is the smallest round figure that stays above the proved tightest packing for every wire count checked, where 1.2 falls under it for two to six equal wires. Averaging diameters, as those tables do, under-sizes a bundle with one thick wire among thin ones, so the estimate also never goes below the two largest wires side by side. Shield and jacket add their thickness on each side. Fit is reckoned by area, as conduit fill is, and the limits are borrowed from the nearest moving cases, because no actuator or cable maker publishes one for a hollow shaft.
one size, up to 7 bundle core = circumscribed factor(N) × d
factor: 1 → 1, 2 → 2, 3 → 2.155, 4 → 2.414, 5 → 2.701, 6 and 7 → 3
otherwise bundle core = packing factor × √(Σ count × diameter²)
packing factor 1.25 by default,
never less than the two largest wires side by side
finished bundle = core + 2 × shield + 2 × jacket
fill = (finished bundle ÷ bore)² an area ratio
fits if fill ≤ recommended (36 % by default)
tight if fill ≤ 60 % and the bundle is narrower than the bore
won't fit beyond thatDefault values, and where each comes from
| Figure | Default | Basis | Source |
|---|---|---|---|
| ±360 °/m: the highest rating, unshielded robot cables | ±360 °/m | igus CFROBOT8.PLUS (to 5 million cycles), Lapp ÖLFLEX ROBOT 900 P (5 million) and ROBOT F1 (10 million), Helukabel ROBOFLEX unshielded (5 million; 10 million for the recycle grade). The highest figure any of them publishes. | [1][5][7][9][14] |
| ±180 °/m: the usual rating; shielded robot cables | ±180 °/m | igus CFROBOT2 to 9, Lapp ROBOT 900 DP and F1 (C), Helukabel ROBOFLEX-D: the shielded members of each family, and most of the unshielded ones at 10 million cycles. | [1][2][6][9][13] |
| ±90 °/m: a standard chainflex cable approved for torsion | ±90 °/m | igus approves some of its standard unshielded drag-chain cables (CF5, CF77.UL.D, CF9) for ±90° over 1 m. A drag-chain cable from another maker has no such figure unless its datasheet gives one. | [4] |
| Not torsion-rated: a flexing or fixed-installation cable | — | A cable rated for bending but not for twisting. Helukabel puts a standard cable at about ±30 °/m and warns that a cable not designed for torsion fails in several ways; without a published figure there is nothing to check against, so the check fails and the tool shows the rate the joint would need. | [10] |
| Bend radius, static: fixed once installed | 5 × OD | igus CFROBOT and Helukabel ROBOFLEX: 5 × OD fixed; Lapp's robot cables and igus CF77.UL.D allow 4 ×; DIN VDE 0298-3 gives 3 to 4 × for fixed power cables. | [1][9][5][12] |
| Bend radius, flexing: occasional movement, not in a carrier | 8 × OD | igus CFROBOT: 8 × OD for flexible use outside a cable carrier. | [1] |
| Bend radius, continuous flex: cable carrier, millions of cycles | 10 × OD | Helukabel's rule of 10 × the largest outer diameter, 12.5 × past 3 m of travel; igus's best classes manage 7.5 × in a carrier. | [11][9][3] |
| Bend radius, torsion and bending together: robot joint | 10 × OD | 10 × OD for every igus CFROBOT, Helukabel ROBOFLEX and Lapp ROBOT F1 when twisted; Lapp's ÖLFLEX ROBOT 900 P and DP ask 15 ×. | [1][9][7][5] |
| Packing factor | 1.25 | Bundle core = factor × √Σd² for any bundle but seven or fewer wires of one size. Virginia Panel publishes 1.2; Glenair's and NASA's count factors work out to 1.20 to 1.25; 1.25 stays above the proved tightest packing for every count checked. Never less than the two largest wires side by side. | [21][16][20][22] |
| Braid allowance | 0.32 mm per side | Glenair's 0.025 in on the diameter for an overall braid; the default shield thickness, to be replaced by the harness maker's figure. | [16] |
| Recommended fill | 36 % of the bore's area | A bundle 60 % of the bore's diameter: igus's rule for robot dress-pack carriers, the nearest published case to a bundle that twists; Tolerance Labs suggests about 35 %. No actuator or cable maker publishes a hollow-shaft figure. Tight at 60 % of the area, about the conduit rule's 40 % once the air between the wires is counted; Glenair allows 70 % in convoluted conduit, which does not twist. | [26][18][23][24][25] |
Typical wire diameters by gauge
For the conductor list when the datasheet is not to hand: the insulated outer diameter of two common constructions, PVC hook-up wire (UL1007, 300 V) and thin-wall XL-ETFE (M22759/32, 600 V), from their published tables. A robot cable's own conductors are usually finer-stranded and thinner-walled than these, and a finished multi-core cable goes in as one wire at its datasheet OD.
| Gauge | UL1007 PVC, strands | Insulated OD | M22759/32 XL-ETFE, strands | Insulated OD |
|---|---|---|---|---|
| 28 AWG | 7/36 | 1.17 mm | 7/36 | 0.69 mm |
| 26 AWG | 7/34 | 1.27 mm | 19/38 | 0.81 mm |
| 24 AWG | 7/32 | 1.42 mm | 19/36 | 0.94 mm |
| 22 AWG | 7/30 | 1.57 mm | 19/34 | 1.09 mm |
| 20 AWG | 10/30 | 1.78 mm | 19/32 | 1.27 mm |
| 18 AWG | 16/30 | 2.03 mm | 19/30 | 1.52 mm |
| 16 AWG | 26/30 | 2.39 mm | 19/29 | 1.73 mm |
| 14 AWG | 41/30 | 2.67 mm | 19/27 | 2.16 mm |
Disclaimer. Estimates for early design. Torsion and bend ratings are the cable maker's for a specific construction, and the bundle diameter is a packing estimate that real harnesses beat or miss by a few percent. Confirm the cable's own datasheet figures, allow for the harness maker's shield and jacket, and validate the joint with life testing on the actual motion before the design is frozen.
Through the shaft, around the joint, or across it
A cable on the axis of a hollow-shaft joint only ever twists, which is the loading a torsion cable is built for; a cable looped around the outside bends and rubs, and on a humanoid it snags on whatever the arm passes. So the first choice is to go through the shaft, and the smallest bore in the stack sets what can. The cable is clamped at both ends of the joint, and the length between those clamps is not packaging slack: it is the design parameter that sets the twist per metre, which is why the first check above returns a minimum free length rather than a yes or no. humanoid.guide puts the connector rule plainly: thread it first, join it second, because a terminated connector is wider than its cable and, as Tolerance Labs notes, connector size decides the bore more often than cable area does.
Where the free length cannot be had, two shapes take up rotation without twisting the cable to its limit. A service loop lets the cable swing around the joint; it has to cover the arc the cable travels, roughly the loop radius times the rotation in radians, and it bends every cycle, so the bend-radius check applies to it. A clock spring is a flat cable coiled in an annular drum around the axis, which absorbs a few turns in little height, and is how steering-wheel and some wrist joints are done. For continuous rotation nothing passive survives: that is a slip ring, with the shield given its own ring and the bus rate checked against what the ring passes.
The second and third checks follow from the first. A cable that twists also bends where it enters and leaves the bore, so the bend-radius multiple is the makers' torsion figure, 10 × the outer diameter, not the fixed-installation one. And the bundle that has to pass the bore is the whole stack: every conductor the joint carries plus the ones for the joints beyond it, which is why daisy-chaining the power and the bus from joint to joint keeps the bundle the same size down the limb while a star-wired limb grows a conductor pair per joint.
Choosing and rating the cable
A torsion rating is a construction, not a property of flexible cable in general. The makers build torsion cables with fine-stranded conductors laid at long lay lengths around a core that lets the layers slide, with a braided or wrapped screen designed to twist, and PUR or TPE jackets; Helukabel puts an ordinary cable at about ±30 °/m and warns that a braided screen built for bending fails under torsion. The rating is also a number with conditions: ±360 °/m is the ceiling any of them publishes, igus's own table takes its ±360 °/m cable to ±270 at 7.5 million cycles and ±180 at 10 million, and the shielded member of each family is rated half of its unshielded sibling. Take the figure for your cycle count and temperature from the datasheet, and expect the makers' motion limits, around 180 °/s and 60 °/s², to apply with it.
The arithmetic the checker does is the plain reading of the unit, not a formula the makers publish: they test with fixing points 1 m apart and quote the result per metre, and igus says outright that robot-cable stress usually cannot be determined by design in advance, which is why they rely on tests and guarantee cycle counts. The check is a screen for what is worth building, and the life test on the actual motion is what qualifies it.
A few rules from the guides and the datasheets travel well. Do not mix stiff and flexible cables in one bundle; the stiff one takes the load and the flexible one chafes against it. Cables in a motor bore run warm, so the temperature band of the rating matters. Keep the bend radius under torsion at 10 × the diameter, or 15 × where the maker asks for it. And when a design is near the limit, the cheapest margin is almost always free length: twice the length is half the twist.
What the harness maker controls
The checks above assume the cable is clamped where the drawing says. In the built harness that is the harness maker's work: a clamp or gland on both sides of every moving section, so the twist happens in the free length and not at a connector; no connector inside the moving section or the bend; strain relief that holds the jacket, not the conductors. The tightest bend in a joint is usually right at the clamp, so the clamp position and the bend radius are drawn together.
The bundle diameter is a drawing figure too. A braid adds twice its thickness, a jacket or sleeve twice its wall, and the conductors' own insulation is set by the wire specified; the estimate here errs a few percent on the large side for a well-laid bundle, and a sample measured with calipers settles it. In a humanoid, where the same limb harness is built dozens of times, consistency is the point: the same lay, the same clamp positions and the same free length on every unit, so a joint that passed its life test is the joint that ships. A drawing that gives the cable part number and its torsion rating, the free length between clamps, the minimum bend radius, the conductor list and the bore it has to pass is what lets a quotation say whether the design is buildable, and what it will be tested to.
Common questions
Where does twist per metre come from, and is the formula exact?
It is the plain reading of the unit the makers use. igus, Lapp and Helukabel rate a torsion cable at ± so many degrees per metre, each way, and test it with fixing points 1 m apart for a stated number of cycles. Dividing your twist by your free length gives the figure in the same unit; whether the rating scales exactly to other lengths is not something the makers state, so treat the result as a screen and the cycle test as the proof. The rating itself also falls with cycle count and temperature: read it from the datasheet at your numbers.
My joint moves ±90°. Do I enter 90 or 180?
Enter the whole range, 180°, and say where the cable is installed untwisted. Fitted at mid-travel it twists 90° each way, which is what a ± rating is compared with; fitted at an end of travel it twists the full 180° one way and needs twice the free length. A knee fitted straight is at an end of travel; a wrist fitted centred is at mid-travel.
What if my cable has no torsion rating?
Then there is nothing to check it against, and the checker says so and shows the rate the joint would need. Helukabel puts an ordinary cable at about ±30 °/m, and igus approves some of its standard drag-chain cables for ±90° over 1 m, but neither is a figure to design a joint around. Use a torsion-rated cable, add free length, route the cable as a service loop or a clock spring, or, for continuous rotation, a slip ring.
Why is the bend multiple 10 × here when my datasheet says 7.5 × or 15 ×?
Because the presets are the common steps and the datasheet is the authority. igus's CFROBOT cables, Helukabel's ROBOFLEX and Lapp's ROBOT F1 all ask 10 × the outer diameter under torsion; Lapp's ÖLFLEX ROBOT 900 P asks 15 ×; igus's best classes manage 7.5 × in a cable carrier. Type your cable's figure into the multiple field. The radius is the inner radius of the bend.
How accurate is the bundle diameter estimate?
Up to seven wires of one size it is exact geometry: two side by side are two diameters, seven in a hexagon are three, and a laid-up cable achieves that. Any other bundle is 1.25 × √Σd², the sum-of-squares estimate connector makers use to size backshell entries (Virginia Panel publishes 1.2; Glenair and NASA multiply the average diameter by a count factor that works out to 1.20 to 1.25 from twenty wires up), never less than the two largest wires side by side. 1.25 sits above the proved tightest packing for every count checked, so the estimate errs a few percent on the large side; a loosely laid bundle can be larger still. A braid adds about 0.6 mm to the diameter, a jacket twice its wall. For a go or no-go against a bore, build a short sample and measure it.
What fill ratio should I aim for in a hollow shaft?
No actuator or cable maker publishes one, so the default is borrowed from the nearest moving case: igus's rule for robot dress packs, where the cables must not exceed 60 % of the carrier's diameter, which is 36 % of its area. Tolerance Labs' guide suggests about 35 % and quotes a wrist at 17 % as leaving room to twist. The tight limit, 60 % of the area, is about where the conduit-fill rule lands once the air between the wires is counted (40 % of the bore filled by the conductors themselves, for cable pulled in once and never moved); Glenair allows 70 % for a harness in convoluted conduit, which flexes but does not twist. Two igus cautions travel: lay cables of very different diameters separately, and do not leave so much room that cables can cross and trap each other. The fill field takes your own rule, and the connector that has to pass the bore is usually the real limit.
Does a pass here replace life testing?
No. The torsion rating is a cycle-tested figure for one construction under the maker's conditions, the bend multiple likewise, and the bundle is an estimate. A pass means the design is worth building; the joint is qualified by running the actual harness through the actual motion for the cycles the product needs, which is also what the makers' guarantees are tied to.
Where the numbers come from
Each entry says what the checker takes from it. Torsion and bend figures are the cable makers' own, quoted from their catalogues and datasheets.
- [1]chainflex torsion cables catalogue — igus, 2023.The torsion classes: ±180° over 1 m of cable (class 3) for the CFROBOT families and ±360° (class 4) for CFROBOT8.PLUS; the fall in rating with cycle count (5, 7.5 and 10 million); the test with fixing points 1 m apart; bend radii of 5 × OD fixed, 8 × flexing and 10 × in a twisted cable carrier.
- [2]CFROBOT8 datasheet — igus, 2022.Torsion ±180 °/m tested over a 1 m three-dimensional cable carrier for at least 3 to 5 million cycles; the motion limits of 180 °/s and 60 °/s²; the guaranteed-life table at −15 to +60 °C.
- [3]chainflex cable classification — igus, 2026.How a torsion rating is stated, ±180° with 1 m cable length, and the cable-carrier bend radii by class, from 7.5 × OD.
- [4]Robot cables: overview — igus, 2026.Standard unshielded chainflex cables approved for ±90° over 1 m; the note that robot-cable stress usually cannot be determined by design in advance, which is why the makers rely on tests.
- [5]ÖLFLEX ROBOT 900 P datasheet — Lapp, 2026.Torsion ±360 °/m for 5 million cycles; 15 × OD when twisted and flexed, 4 × fixed.
- [6]ÖLFLEX ROBOT 900 DP datasheet — Lapp, 2026.The shielded sibling: ±180 °/m, half the unshielded rating.
- [7]ÖLFLEX ROBOT F1 datasheet — Lapp, 2026.Torsion ±360 °/m, designed for up to 10 million cycles; 10 × OD.
- [8]Technical tables T0: minimum bending radius — Lapp, 2026.The definition the checker uses: the minimum bending radius is the inner radius of the bend.
- [9]Robotics catalogue: ROBOFLEX cables — Helukabel, 2024.Torsion ±360 °/m for 5 million cycles and ±180 °/m for 10 million on the unshielded ROBOFLEX cables, ±180 °/m on the shielded -D; limits of 180 °/s and 60 °/s²; 10 × OD under torsion, 5 × fixed, 10 × in a carrier and 12.5 × past 3 m of travel.
- [10]How to choose the right robot cables — Helukabel, 2026.A standard cable tolerates only about ±30 °/m; a braided screen that works for bending fails under torsion; a cable not designed for torsion is damaged in several ways.
- [11]The meaning of bending radius — Helukabel, 2026.The rule of 10 × the largest outer diameter for cables in continuous motion.
- [12]Permissible minimum bending radius per DIN VDE 0298-3 (table as reproduced by a distributor) — HiTech Controls, 2026.The wiring standard's multiples for fixed power cables, 3 to 4 × OD by diameter band, and its ceiling of 6 × for moving uses, which the robot-cable makers' figures sit well above.
- [13]ÖLFLEX torsional robotic cable, catalogue section — LAPP USA, 2020.The shielded ROBOT F1 (C) at ±180 °/m, and 15 × OD for torsion and flexing on the 900 P.
- [14]CFROBOT8.PLUS product page — igus, 2026.The guarantee table by torsion and temperature: ±360 °/m to 5 million cycles, ±270 to 7.5 million and ±180 to 10 million between −15 and +60 °C, and ±330 / ±240 / ±150 outside that band.
- [15]Robot Harness and PCB Calculator — Robo2u, 2026.The closest existing tool: a wire-gauge and connector check per kinematic chain with bend and torsion flags against quoted maker rules. It has no bore or bundle check and gives no minimum free length.
- [16]Wire bundle diameter calculator (reference guide) — Glenair, 2022.A connector maker's bundle estimate for sizing backshell entries: the average wire diameter times a factor by wire count (2 → 2.0, 4 → 2.4, 7 → 3.0, 10 → 4.0, 20 → 5.6, 100 → 12.2), 0.025 in added to the diameter for an overall braid, twice the wall for a jacket. A table of count factors, not a sum-of-squares formula; from twenty wires up it works out to 1.20 to 1.25 × √N.
- [17]Hollow-shaft joints: how power and data get through every humanoid joint — humanoid.guide, 2026.Rules of thumb credited by name: route through the shaft so the cable only twists; the smallest hole in the stack sets the limit; clamp at both ends and treat the free length as a design parameter; thread the cable before terminating it; continuous rotation needs a slip ring. Its torsion arithmetic matches this checker's.
- [18]Hollow-shaft joints and cable routing through robot joints — Tolerance Labs, 2026.Rules of thumb credited by name: connector size decides the bore more often than cable area; a service loop must cover the arc the cable travels; a clock spring is a flat cable coiled in an annular drum; fine-stranded conductors and PUR or TPE jackets; do not mix stiff and flexible cables in one bundle; keep connectors out of the moving section. Its 35 % fill figure carries no source and is noted as such.
- [19]chainflex service-life calculator — igus, 2026.The maker's own life estimate for its cables from travel, temperature and bend radius: the tool to use once a chainflex cable is chosen.
- [20]MSFC-SPEC-494 Rev B, Table III: bundle size factor — NASA, 2009.The same count-factor table as Glenair's, applied to the average wire diameter, with a worked example (5 × 0.137 in and 17 × 0.098 in: 0.107 in × 5.8 = 0.621 in); the sum-of-squares form at 1.25 gives 0.634 in for the same bundle.
- [21]Calculating the maximum wire bundle diameter (tech tip) — Virginia Panel Corporation, 2021.The sum-of-squares form the checker uses, B = 1.2 × √(N₁d₁² + N₂d₂² + …); the checker's 1.25 is the next round figure up, because 1.2 falls under the proved tightest packing for two to six equal wires.
- [22]Circle packing in a circle — Wikipedia, 2026.The smallest enclosing circle for N equal circles: 2, 2.155, 2.414, 2.701, 3 and 3 diameters for two to seven (Graham, 1968, for five and six), 3.305 for eight, 3.813 for ten, 4.029 for twelve and 4.863 for nineteen: the figures the exact geometry and the 1.25 factor are checked against.
- [23]How to use Chapter 9 in your next design — EC&M, 2011.The NEC conduit-fill rule as the trade reads it: 53 % of the conduit's area for one conductor, 31 % for two, 40 % for more, counted as the conductors' own cross-sections, 60 % in a nipple up to 24 in. A rule for cable pulled in once; the tight limit here is about this rule once the air between the wires is counted.
- [24]Introduction to conduit interconnect technologies and packaging — Glenair, 2026.70 % fill recommended for a harness in convoluted conduit, reckoned as the bundle's envelope over the tubing bore: a case that flexes but does not twist.
- [25]Energy chain filling rule — igus, 2026.At least 10 % clearance all round an electrical cable; a compartment no more than one and a half times the cable's diameter, so cables cannot cross; cables of very different diameters laid separately.
- [26]Robot cable management: triflex R dress packs — igus, 2026.Total cable and hose diameters not to exceed 60 % of the carrier's diameter, and 10 % clearance between any two: the rule for cables that bend and twist on a robot arm, and the checker's default recommended fill (60 % of the diameter is 36 % of the area).
- [27]UL1007 hook-up wire data sheet — Remington Industries, 2026.Insulated outer diameters of PVC hook-up wire, 0.015 in wall, 28 to 14 AWG, for the wire table.
- [28]M22759/32 finished wire diameters — NASA NEPP, 2026.Insulated outer diameters of thin-wall XL-ETFE wire, 28 to 14 AWG, for the wire table.
igus, chainflex and CFROBOT, Lapp and ÖLFLEX, Helukabel and ROBOFLEX, Glenair, Robo2u, humanoid.guide and Tolerance Labs are names or trademarks of their respective owners, used here only to identify the sources quoted. Interconnix is not affiliated with, sponsored by or an authorized distributor of any of them; the cables named are examples of published ratings, not recommendations.
Designing a joint harness? Send your drawing to support@
The joint's rotation and free length, the conductor list, the connectors at each end and the bore it passes through are enough to start; a drawing is better. The quotation says which cable is proposed, what it is rated for and what is tested.