Hydraulic scissor lift table calculator: cylinder force, stroke and bore
This free calculator sizes the hydraulic cylinders of a single-scissor lift table: the cylinder force over the whole lift, the stroke, the bore and whether the cylinder fits, all computed from the pin positions. Change the geometry, drag the cylinder mounts on the diagram or load one of six examples from 500 kg to 3000 kg.
The calculator is a beta (Lite 0.9.0): the force model is checked by two independent methods, and the comparison with the kinematic model of a built 1200 kg table is in progress.
Key values at a glance
| Value | What it is | Why it matters |
|---|---|---|
| Max. cylinder force | Total force of all cylinders, maximum over the whole lift | Sets the bore and pressure; for most layouts it occurs at the bottom |
| Arm r | Distance from the centre pivot O to the cylinder axis | The force is inversely proportional to r |
| Collapsed leg angle αmin | Leg angle in the lowest position | A lower table costs a much higher force |
| Cylinder stroke | Change in pin distance over the lift | Needed to choose a cylinder from a catalogue |
| Retracted pin distance | Pin distance in the lowest position | Must be at least stroke + dead length of the cylinder |
| Force margin | Available cylinder force / required force | Covers friction, tolerances and start-up |
| Vertical clearance | Space left for the cylinder body and eyes when collapsed | Limits bracket offsets and the collapsed angle |
How to use the calculator
- Pick an example: 500, 1000, 1500, 2000 or 3000 kg, or 2000 kg with the cylinder mounted on the leg axes for comparison.
- Move the Position slider: the diagram, the readout and the force chart follow the lift from the bottom to the top.
- Change the geometry: type values in the form, press Show dimensions and click a boxed dimension on the diagram, or press Edit nodes E, F and drag the cylinder mounts.
- Read the checks: every check in Results and checks is marked OK, Note or Not OK; the headline shows the maximum force, stroke, heights and force margin.
- Print: Print / PDF gives a three-page A4 summary with the input data, diagram, checks, chart and stroke table.
All dimensions are in millimetres. The origin is on the axis of the fixed bottom pivot C, x to the right, y up.
Why the force is highest at the bottom
The two legs of a scissor rotate relative to each other about the centre pivot O. When the lift opens by an angle dα, the cylinder extends by ds = 2r · dα, where r is the distance from O to the cylinder axis. Virtual work then gives the total cylinder force:
Fs = L · cos α · ((Q + Q_platform) / 2 + Q_legs / 4) / r
where L is the leg length (pin to pin), α the leg angle, Q the load, Q_platform the platform weight and Q_legs the weight of all legs. For a cylinder mounted on the leg axes, r = z · sin(α + β), with z the distance of the upper mount from O and β the cylinder angle.
In the lowest position α is small, the cylinder lies almost flat and r is short, so the force peaks. In the 2000 kg example with mounts on the leg axes the force falls from 188 kN at the bottom to 53 kN at the top, a ratio of 3.5. On a rigid platform the force does not depend on where the load sits; the joint forces do.
The collapsed angle: the main trade-off
A lower table means a smaller collapsed leg angle, and the force grows quickly as the angle falls. For the 2000 kg table with mounts on the leg axes:
| Collapsed angle αmin | Collapsed height | Max. cylinder force |
|---|---|---|
| 6° | 338 mm | 248 kN |
| 8° | 401 mm | 188 kN |
| 10° | 463 mm | 153 kN |
The calculator treats 8° as the recommended minimum and 6° as a conditional limit: below 8° the result becomes very sensitive to pin clearance, roller friction, leg deflection and fabrication accuracy. Find the lowest αmin searches for the smallest angle at which the force margin, cylinder length and space checks still pass.
Offset mounts: half the force at the same height
Moving the upper cylinder mount E off the leg axis onto a plate bracket increases the arm r exactly where it is shortest, in the collapsed position. In the 2000 kg example a 75 mm bracket raises r at the bottom from 115 mm to 221 mm and cuts the maximum force from 188 kN to 98 kN at the same collapsed height.
The bracket has three costs:
- it needs vertical space under the platform when the lift is collapsed, which the calculator checks;
- it puts a bending moment on leg AC near the centre pivot, where the leg is already most loaded;
- if the upper mount is placed beyond O towards C, the cylinder axis can pass through O during the lift; there the arm r becomes zero and the force has no finite value (dead centre). The calculator reports the height at which this happens.
Fitting the cylinder
A cylinder fits when the retracted pin distance in the lowest position is at least the stroke plus the dead length of the cylinder (base, piston, guide and eyes, from the catalogue). Moving the upper mount E further from O gives a longer stroke but a shorter retracted pin distance, so the cylinder can stop fitting. The calculator also checks the vertical space for the cylinder body and eyes in the collapsed position and the lateral fit of all cylinders between the inner legs.
Worked example: 2000 kg table, 2000 × 2000 mm platform, 1210 mm lift
Leg length 1800 mm, collapsed angle 8°, two cylinders, 200 bar, required force margin 1.25.
| Result | Mounts on the leg axes | Upper mount on a 75 mm bracket |
|---|---|---|
| Max. cylinder force (total) | 188.4 kN | 98.0 kN |
| Force per cylinder | 94.2 kN | 49.0 kN |
| Bore used / margin | Ø90 / 1.35 | Ø70 / 1.57 |
| Cylinder stroke | 403 mm | 461 mm |
| Retracted pin distance | 626 mm | 642 mm |
| Collapsed / max. height | 401 / 1611 mm | 401 / 1611 mm |
Result: the bracket halves the cylinder force, so Ø70 cylinders replace Ø90 at the same collapsed height. Cost: a 58 mm longer stroke, a bracket that must be designed for bending, and less free space under the platform.
Limitations of the model
- Kinematics and cylinder force only: joint and pin forces, leg stresses, rod buckling, platform deflection and stability are not calculated.
- Single scissor, rigid members, rigid platform; no pin clearance or elastic deformation.
- Masses, cylinder dead lengths and outer diameters in the examples are estimates.
- Angle limits are design-practice values and can be edited.
- The requirements of EN 1570-1 (safety of lifting tables) are not checked.
FAQ
How much force does a scissor lift cylinder need?
The force is highest when the table is lowered and depends mainly on the leg angle and the distance from the centre pivot to the cylinder axis. For a 2000 kg table with a 1210 mm lift it ranges from about 98 kN with an offset mount to about 188 kN with mounts on the leg axes, for both cylinders together.
Why is the force so high when the scissor lift is lowered?
In the lowest position the cylinder lies almost flat and its axis passes close to the centre pivot, so its lever arm is short. The required force is inversely proportional to that arm.
What collapsed leg angle should a scissor lift have?
At least 8° is a common design rule. Going down to 6° is possible but at the limit: the force rises steeply and the result becomes sensitive to clearances, friction and fabrication accuracy.
Does the load position on the platform change the cylinder force?
No, on a rigid platform the total cylinder force depends only on the load, not on where it sits. The forces in the pins and rollers do change.
How do I choose the cylinder stroke and length?
The stroke is the change in pin distance from the bottom to the top. The cylinder fits if the retracted pin distance in the lowest position is at least the stroke plus the dead length from the cylinder catalogue.
Can I use the calculator for a double scissor lift?
No. It models a single scissor with the cylinder mounted between the legs.
Further reading
- R. C. Hibbeler, Engineering Mechanics: Statics: virtual work and the equilibrium of mechanisms.
- EN 1570-1, Safety requirements for lifting tables: requirements for design, safety devices and testing.
Need a lift table designed?
papacad.com offers ready-to-build CAD projects of hydraulic lift tables and other workshop equipment (Autodesk Inventor 3D assemblies, STEP files, 2D production drawings and BOMs) and takes custom engineering commissions. CAD projects · Contact