Four-bar linkage force calculations

For the past couple of years I see a lot of robots with pneumatic-actuated four bar linkages on their intakes (i.e. 3476 2019, 5460 2019, 2471 2020), and we wanted to make one too this year. We tried to calculate the amount of force required for actuating our fourbar linkage during the season, but after two days of unsuccessful calculations we resorted to using a motor.

Now that we’re in the offseason, we wanted to revisit this topic and to design a fourbar linkage based intake that’s pneumatically actuated. How can one calculate the amount of force required to lift a fourbar linkage?

I can not remember the exacts of it but it is roughly the same as how you would do a non 4 bar arm. You take the length of your lever arm(where the pneumatic is mounted) and calculate the torque on that axis. This might not be the best explanation and it might be wrong but this is just what I remember from when it was explained to me. Please correct me if I’m wrong.

Is your problem calculating how much force you need to raise your arm, or how much force the piston is capable of exerting, or both?

I would imagine the force needed to actuate a 4-bar linkage would be fairly trivial to determine, and be similar to that of a simple arm (if not identical). Someone else can help out here (or a quick google search on levers should help too).

As for the latter, you can calculate the amount of force being exerted by a piston rather easily. All you need is the formula F=P*A. Where F = force exerted, P = your air pressure, and A = the area of the piston bore. For example, a 3/4" bore cylinder operating at 60PSI would produce a force of roughly 26lbs. This is because F = 60 * (pi * 0.375 ^ 2). The two biggest things to remember however when working with pistons is one, the return stroke will have less force than the extend stroke, and two, in FRC you probably don’t want to rely on having exactly 60 psi of operating pressure.

The reason for the 1st is that the piston rod takes up some of the area that the pressurized air can act on, so if you’re needing to calculate the force the piston can retract with, don’t forget to subtract the piston rods area from the area of the cylinder bore. As for not relying on 60 psi, you may find depending on your situation that your compressor can’t keep up with the demands of your system, or perhaps you didn’t manage to re-charge your system fully before a match. It’s always a good idea to design with a little safety factor (IMO at least).

My problem is finding the force required for raising the arm. There are enough calculators like the AMB Design Spreadsheet that calculate the force exerted by a piston, which is already pretty easy to calculate.

Do you know how to draw a free body diagram?

Also, you can ignore the four bar part of it, treat it as a simple arm, to make it easier.

How about you provide a sketch of what you are considering? We can then mark it up for you, showing you what to do, in the process.


If you have relatively accurate masses in CAD it would be fairly trivial to someone familiar with forces and statics. Select all the components that are going to be rotating, put the system in the, “worst case,” position (COM horizontal from pivot point, or closest point to that) and determine the torque the system applies at the pivot point. Using that torque and pistons of various bores, calculate the minimum distance the piston needs to be from the pivot taking into account the angle at which the piston is applying the force.

Without accurate masses in CAD it just becomes a longer, more drawn out problem. You would need to determine the torque applied by each member and component when the system is in the worst case scenario (including rollers, motors, bearings, etc. depending on how accurate you want to be) to determine the torque on the pivot, and then follow the same process as above.

Arguably the most accurate method, assuming you are alright with not having everything figured out in CAD, is to measure the force it takes to lift/move the actual system from its worst case point (ideally tangentially to the point), calculate the torque that corresponds to the force at that distance, and solve for the minimum point of the cylinders again.

You can also simply overestimate the mass/torque of the system and size it that way which will likely be the quickest brute-force method. If you know your arm weighs roughly 10 lbs, and the COM can’t be further than 6" from the pivot, use something like 12 lbs and 7". Quick and dirty, but gets the job done.

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As long as you can easily find the COM of that arm/system, this is accurate.

Edit: It is likely the COM is not located on any of the arms, but between them in space.

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Another thing to consider: are you retracting the cylinder to retract the arm, or are you extending the cylinder to retract the arm? Since there is more force applied when cylinders are extending, it’s generally more efficient to set it up the latter way, but that often makes packaging a bit more difficult.

As a quick first approximation, calculate the weight of the arm, multiply by the change in the height of the arm’s CoG, and divide by the travel of the cylinder mount point. Then double that for a safety factor. Make sure the cylinder is pushing in the direction that cylinder mount point travels; if not, you’ll have to divide by the cosine of that angle.