Double Reverse Four Bar mathematical equations

For this year’s notebook, our team has decided that adding some math would help explain our design decisions better. I was wondering if anyone knew what the DR4B equation was for the torque needed to lift based on height, weight, angle, and motor stall torque and if there was an equation to determine speed at different points in the process of lifting. I’m also not much of an engineer so if you could add an explanation for the equations, that would be very helpful. Thanks for the help. By the way, we mounted the motor on the middle bar if that makes a difference.

Just to be clear, if you have decided on the design before you do the math, it is disingenuous to say that the math is part of your design decision.


I have made a simple spreadsheet you can use to calculate the height of any DR4B lift, you will be able to see the equation I used if you select the height cell. Link to spreadsheet


Kind of like treating CAD as “computer aided documentation” rather than "Computer Aided Design…


I may not know the exact math but when deciding between a scissor lift, cascade, and dr4b, it would be obvious that the dr4b would need the least torque.

To quibble, a (well-built) cascade lift requires the least torque. There is a rather incredible mechanical advantage inherent in your lever arm only being as long as a sprocket instead of as long as, well, an arm.

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“Obviously”, “Simply”, “Clearly” are some of the most irritating and infuriating words a person can use, because they are both condescending, and usually accompanied by being incorrect.

No geometry family inherently requires the least torque. Into any mechanical system, you put in a certain amount of power and you get out that same amount of power (minus losses to friction, noise, etc…) out the other side. Mechanical advantage determines whether your input and output have more, less, or the same torque. Whether that mechanical advantage comes from gears, pulleys, levers, or any other mechanism does not really matter (beyond the inherent friction due to surface contact and weight, and the incidental friction due to build quality).

So no, without doing the math first, you DO NOT know whether a DR4B requires the least torque of all possible lifting options in all possible scenarios.


First of all, I’d like to apologize for my use of “obvious”. I really didn’t mean to be offensive (just on my phone and being wordy can be annoying to type out) and truly am sorry. And to clarify my initial question, I was specifically trying to figure out the gear ratio necessary for a DR4B. And as for my last post, I guess what I should’ve said was that I think that with the ease of building and maintaining along with necessary torque ratio, the DR4B seems to be the best choice. To reiterate, I am sorry for my poor word choice.


Of course, another consideration for all these mechanisms is the amount of counterbalance applied (rubber bands or surgical tubing), potentially to the point where the motor is needed to lower the mechanism as well as raise it.


DR4B’s biggest advantages are being easy to build, having a high tolerance for build error, moving in a relatively straight line, and getting a LOT of mechanical advantage in a pretty compact area. That mechanical advantage means that between a single 4 bar and a DR4B with the same motor torque and RPM going in, the DR4B will be twice as fast and half as strong. Doubling it is effectively a gear ration of 2:1. They also loose a small amount to inefficiency because they are moving laterally in the middle while the End Effector goes straight up and down. As mentioned before, a cascade list may be the most efficient (barring friction and build quality) because there is minimal wasted motion laterally.


Speaking as a ref, don’t be this team. It means your robot usually won’t stay in size, and we all have to wait for you to pin it down so the match can start. If your arm is lifting without motor input, reduce the counter tension please :slight_smile: