Boom Pin Reaction Calculator: Cylinder Force and Pivot Pin Load for an Excavator or Crane Arm
Find the force in the cylinder and the load on the pivot pin of an excavator boom, crane jib or any hinged arm.
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How this calculator works
Take the pivot pin as the origin and enter the coordinates of the pin where the cylinder joins the arm, the load point and the base of the cylinder. Enter the load, and the diameter of the pivot pin.
The calculator finds the direction of the cylinder, then takes moments about the pivot, which gives the cylinder force without needing the pin reaction. The two force equations then give the horizontal and vertical pin reactions.
It gives the pin reaction, its angle, how many times the load it is, and the shear stress in the pin for the number of shear planes. It checks that the forces add to zero.
Formulas used
- \sum M_A = 0\ \Rightarrow\ F_c = \frac{W B_x}{C_x u_y - C_y u_x}
- A_x = -F_c u_x,\quad A_y = W - F_c u_y
- R_A = \sqrt{A_x^2 + A_y^2}
- \tau = \frac{R_A}{n_s A_p}
Worked example
With the default numbers in the calculator above:
- Cylinder length and direction (from the base pin to the pin on the arm): Length 2.51 m, direction (0.4115, 0.9114)
- Perpendicular distance from the pivot to the line of the cylinder: 0.87 m
- Moments about the pivot A (sum is zero): Load moment 153.20 kN m
- Cylinder force (positive = pushing, negative = pulling): 176.67 kN
- Horizontal reaction at the pivot: -72.69 kN
- Vertical reaction at the pivot: -121.02 kN
- Pin reaction and its angle from the horizontal: 141.17 kN, acting about 59.01 degrees from the horizontal
- Pin reaction compared with the load: 3.53 times the load
- Shear stress in the pin: 14.04 MPa (pin area 5026.55 mm2)
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
Why is the pin load so much more than the load?
The cylinder joins the arm close to the pivot, so its lever arm is short compared with the load's. It has to push many times the load, and the pin carries both forces.
Is this a complete design?
No. It is a static check without the weight of the arm or friction. Digging and swinging add dynamic loads that are often much larger, so apply the factor from your standard.
Which way does the cylinder act?
It acts along the line between its two pins. A positive answer means it pushes (compression) and a negative answer means it pulls.
How do I find the pin shear stress?
The pin reaction divided by the pin area times the number of shear planes. A pin in a clevis is cut across two planes.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any statics text (Meriam and Kraige, Engineering Mechanics: Statics, equilibrium of a rigid body); AS 1418 Cranes, hoists and winches.
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