Cylinder Pivot & Lever Force
The torque a cylinder puts on a pivoting arm, through the whole sweep. Force is set by bore and pressure; how much of it becomes torque is set entirely by where you mount it.
Inputs
The cylinder
From the cylinder force tool. A single VEX cylinder at 100 psi gives 12.17 lbf extending.
How far the rod travels. This decides whether the geometry below is reachable at all.
Where it is mounted
Along the arm, from the pivot bolt to where the cylinder rod attaches.
The fixed end of the cylinder. Negative is behind the pivot, positive is in front.
Negative is below the pivot. Most cylinders anchor below and behind.
The sweep
From the lift torque tool, or weight times its distance from the pivot.
Results
Does it drive the load?
—
Torque at this angle
—lb·in
Moment arm at this angle
—in
Cylinder length here
—in
Best torque in the sweep
—lb·in
Worst torque in the sweep
—lb·in
Worst angle
—°
Stroke this geometry needs
—in
The linkage at this angle
Gray is the arm, red is the cylinder. The dashed line is the moment arm: the perpendicular from the pivot to the cylinder's line. Torque is force times that length and nothing else, so watch it shrink as the arm swings — where it reaches zero, so does the torque.
of the required torque, at the weakest point
How this is calculated
A force only produces torque about a pivot to the extent that it acts off that pivot. Push straight at a hinge and nothing turns, however hard you push. What matters is the perpendicular distance from the pivot to the line the force acts along.
torque = cylinder force × perpendicular distance to its lineThat distance is called the moment arm, and on a pivoting mechanism it is never constant. As the arm swings, the attachment point moves, the cylinder's angle changes, and the moment arm changes with it, which is why a mounting that feels strong at one end of the travel can be useless at the other.
With your numbers
Dead center
If the cylinder's line of action passes exactly through the pivot, the moment arm is zero and so is the torque. That point is called dead center, and a mechanism that passes through it during its travel will stop there and refuse to move, no matter what pressure you give it.
It is not a rare mistake. A cylinder anchored close to the pivot, or too nearly in line with the arm, produces a sweep that crosses dead center in the middle of its useful range. The fix is always geometry (move the anchor further from the pivot line), never more air.
Why the worst angle is the one that matters
A mechanism has to work everywhere in its range, so the number that decides whether it works is the smallest torque anywhere in the sweep, not the average and certainly not the best. This page reports the worst point and the angle it happens at, because that is the one that will stall.
Stroke has to reach
Separately from force, the cylinder has to physically span the distance at both ends of the travel. The page works out the difference between the longest and shortest cylinder length the geometry demands. If that exceeds your stroke, the arm cannot complete the sweep: it will run out of rod before it runs out of angle.
Torque and sweep are traded against each other
Those two are not independent, and what connects them is exact rather than a rule of thumb:
stroke used = average moment arm × sweep angle in radiansIt falls out of the geometry: the rate at which the cylinder lengthens as the arm turns is the moment arm. So the stroke a mechanism consumes is just the moment arm added up across the sweep.
The consequence is worth sitting with. Torque wants a large moment arm. Range wants a large angle. Their product is stroke, and stroke is a small fixed number that came in the bag. You cannot have a strong pivot and a wide sweep from one cylinder, not because it is hard, but because the arithmetic forbids it.
A worked case: 15 lb·in through 90°, with the rod attached 4 inches from the pivot. Checking every anchor position on a quarter-inch grid,not one of the 1,044 works. The mountings that make the torque need 3.75 inches of stroke against the 1.97 a 50 mm cylinder has; the ones that fit the stroke cannot make the torque. Narrow the same job to 45° and it becomes comfortable. The values this page opens with hold 21.8 lb·in at their weakest against 23.8 at their best, which is what good geometry looks like.
So when a pneumatic pivot will not do what you want, the useful move is usually to want less angle. If you do need 90°, that is a motor's job, or a linkage that multiplies the cylinder's travel. It is not a bigger bore.
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Sources & assumptions
No VEX data beyond the cylinder stroke lengths. The geometry is ordinary statics and applies to any linear actuator on a pivot, pneumatic or not.
Checked two ways. Torque is computed from the cross product of the attachment vector with the cylinder's direction. That was verified against virtual work (force multiplied by the rate the cylinder length changes with angle) at eight angles across the sweep. The two methods agree to about one part in a million, and the moment arm never exceeds the attachment radius, which is a bound it cannot physically pass.
- V5RC Override Game Manual v1.1 (2026-27) — checked August 2026
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
Cylinder Force Calculatorfills in your cylinder force hereCylinder Mount Finderfills in your cylinder stroke herePneumatic or Motor?fills in your cylinder stroke hereYou are here
Cylinder Pivot & Lever Force
Where your answer goes
Cylinder Mount Finderfind an anchor spot where the torque does not dip mid-swingbrings your lift torque with itCylinder Force Calculatorwork out the bore or pressure that covers the torque you lackuses your cylinder force againMatch Air Budget Calculatorsee what each swing of that stroke costs you in airuses your cylinder stroke againPneumatic or Motor?see whether a geared motor would drive this arm better than airbrings your cylinder stroke with ita number carries across the next question it raises