Pantograph luffing: from boom moment to cylinder force

Follow the load path through a pantograph arrangement and understand why counterweight changes affect more than cylinder force.

By Anthony Nguyen · ACE Engineering Group

General technical information. Obtain engineering advice for your machine before applying it. Read the article disclaimer.

All Technical Insights

Follow the load path, not just the cylinder force.

This symbolic example considers static gravity loads at one luff position. It is a teaching guide, not a project assessment.

A counterweight adjustment can restore the calculated cylinder force while the centre link and support loads remain different. Check those effects as part of the complete machine assessment.

Illustrative analysis

Pantograph reclaimer: luff cylinder force

Static balance at one luff position, with the cylinders connected to the counterweight assembly.

Pantograph arrangement, force directions and moment balances for centre link and luff cylinder forces — Open image 1 at full size ↗

Added counterweight calculation with force relationships, assumptions and checks — Open image 2 at full size ↗

Read the calculation steps and assumptions

A is the boom pivot and B is the pantograph pivot. C to F are the cylinder pins; D to E is the connecting rod or centre link. Clockwise moments are positive at both pivots.

W_b and d_b describe the complete boom side assembly. W_r includes the counterweight boom, pantograph frame, fitted ballast and associated rear equipment in this model; d_r locates that assembly’s combined centre of gravity behind B. Use weight and centre of gravity from the same configuration.

Boom balance about A
+W_bd_b − NL₁ = 0
N = M_b / L₁ = W_bd_b / L₁
N is the actual centre link axial force.
Pantograph balance about B
+NL₂ − W_rd_r − F_cL₃ = 0
F_c = (NL₂ − W_rd_r) / L₃
Positive N and F_c mean tension for the directions drawn; negative results mean compression. L₁, L₂ and L₃ are perpendicular distances to force lines, not member lengths. F_c is total cylinder force. Divide by cylinder count only for equal moment arms and equal load sharing.

Added counterweight to retain the original cylinder force

At the same stationary luff position, with unchanged geometry and other loads:

ΔM_b = M_b,new − M_b,old

ΔN = ΔM_b / L₁

Δm_cw = ΔNL₂ / (g d_cw)

Here d_cw is the horizontal distance from B to the added ballast’s centre of gravity. It is not the distance to the original combined rear centre of gravity. Added ballast is the only rear assembly change in this calculation. Recalculate the combined rear centre of gravity when checking the revised total balance.

Restoring the calculated cylinder force does not restore the original centre link force or supported weight.

Model assumptions

Two dimensional static weight balance with ideal pin joints at one luff position. Link and cylinder self weight, digging, wind, motion related forces and friction are excluded. The diagram is not to scale.

Use the actual geometry through the full luff range. Check connected members, connections, slew support and stability, including non luffing structure outside these balances. Assess the loads excluded from this model.

Moments are in N·m, forces in N, lengths in m and masses in kg; g = 9.81 m/s². The example uses symbols only, with no project specific values.

Apply the example within its limits.

The guide excludes digging, wind, inertia and friction. An actual machine requires its geometry, load cases, complete luff range and stability to be assessed.

Read about weight savings and counterweight
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Technical information and disclaimer

This article is published by ACE Engineering Group Pty Ltd (ACE) for general technical education. It is not engineering advice for a particular machine, site or project. Reading or downloading it does not, by itself, create an engineering engagement with ACE or the author.

The technical content is prepared in good faith and reflects the author’s knowledge and the information available when that content was prepared or substantively revised. Standards, requirements and engineering knowledge may change.

Examples, calculations and diagrams may use simplified assumptions. They do not establish the safety, fitness for service or compliance of any machine. Do not use this article as the sole basis for designing, modifying, repairing, operating or assessing a machine. Before applying its contents, obtain advice from a suitably qualified engineer based on an assessment of the actual equipment, its condition, operating duty and applicable requirements.

ACE and the author do not warrant that this article is complete, current or suitable for your intended use. To the extent permitted by law, ACE and the author exclude liability for loss, damage, injury, cost or expense arising from use of or reliance on this article, including errors or omissions in its preparation or publication, whether in negligence or otherwise.

Nothing in this notice excludes, restricts or modifies any right, remedy, guarantee or liability that cannot lawfully be excluded, restricted or modified, including under the Australian Consumer Law.

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