Four-bar lift: Square vs. Rectangular

Recently, we attempted to increase the height of a “squarish” 4-bar lift, and it was less effective than the original. Intuition led us to think a “squarish” 4-bar lift (where the vertical and horizontal bars are of similar length) would work more effectively than a “rectangular” one (where the vertical bars are twice as long as the horizontal ones), and trial and error showed this to be true. But why? The length of the vertical torque arm alone doesn’t explain it, because our 3 models for comparison were:

  1. short height, short width (small square) – good lift
  2. tall height, short width (tall rectangle) – poor lift
  3. tall height, wide width (large square) – good lift

All 3 models used the same 2 motors and same gearing configuration.

I’m thinking there should be an explanation from physics, but it’s not coming to mind. Or did we just “get unlucky” and happen to have a poor friction situation for the 2nd model?

Watch the video labelled “The Mighty Four Bar” listed here: It’s made for FRC but the concepts apply to Vex. Pay attention to when kinematic equations are covered. Basically, the way such four bars work if I recall correctly is that for the same load, the only thing that changes the force necessary to lift is the length of the horizontal bars. Lengthening them increases the load, shortening them decreases the load. For normal arms, the distance of the center of mass at the end of the arm matters, but not for four bars.

I am sorry, I do not fully how understand how you changed the four bar configuration, I guess what I don’t understand is in which way is it square? Is the distance between the two pairs of the bars the same as the length of the bars?

And here’s where the physics comes into play. In physics, torque = F * radius. Where R is the radius at which the force is applied and the F is the component of the force that is tangential* to the radius/path. So as you raise your arm, the torque increases until you pass the mid-point, or the place where the arm is parallel to the ground.

  • Sunny

Are you driving both of the two “height” bars per side or only one of them on each side? I am guessing based on the results you provided that you are only driving one of the “height” bars per side, which may cause binding in the tall rectangle setup that does not occur when you have a square.


The top bar is anchored, both of the 2 side bars are driven. I would have expected that lengthening the 2 side bars would create more torque, as the length of the torque arm increases, especially as it approaches 90 degrees. What I didn’t expect was that increasing the length of the top bar (i.e., increasing the distance between the 2 pivots) would (seemingly) reduce the torque.

still a bit confused on what you are saying
do u have pics?
or just do a few simple sketches
our graduated team had some experience with 4 bar
but theirs was pretty crappy/ inefficient
(they had so much friction in their gearbox, that you cannot move a 1:5 (geared down) 4bar by hand…)

Search for 3bar.cdy to use a java 4 bar simulator that helps visualize how changing the relative lengths change the motions.

In my view, there is far greater value in changing the relative lengths to get the correct motions, than to improve torque characteristics.

With a parallelogram 4 bar, the easiest way to make a neutral or slight-positive lift arm is to add rubber bands between the arms. See any 4bar student desk lamp( ,or pixar film short) for an example.

See also “Spring Arm Cam design spreadsheet”, post from 12-02-2009.
This spreadsheet shows that the change in gravitational potential energy due to changing the arm position from high to low to high can be exactly (in theory) offset by the change in stored spring energy, and that the torques and forces at any intermediate positions can be balanced out by the correct cam radius for that position.
In the examples, the perfect cam shape is nearly same as an offset circle, so a HS sprocket would work nearly as well as the calculated cam shape, to give the effect of a “weightless arm”.

Thanks for the tip! We’ll have to try that!

I’m still trying to process the information from your power point and Chris is me’s video. I is a slow learner (& bad grammarian).

One of the things I love about paralellogram four bars is how easy it is to “balance” the arm. Simply add latex connecting the bars so that it stretches when fully “down” and is more relaxed when fully “up”. This gives you a simple arm that will hold position without power. It’s easier to balance a four bar with elastics than a conventional arm with elastics, which requires a “tie down” off the back of the arm.

Thanks for the tip - I didn’t know that! You are right though, it would be easier than a conventional arm which also requires more elastics.

As long as the horizontal bars (the ones you are driving) are kept the same length, there should be no difference between ‘square’ and ‘rectangular’ for lifting a load acting straight down on the coupler (the bar on the end that you mount your intake or whatever onto), so the most likely problem would be friction.

However, if you have any twisting force on your coupler, this does not hold true. This would happen in any situation where an load is applied out in front of the coupler. This would mean that the shorter the coupler and ground links are, the more force will be on them. This will result in much more friction in the joints.

Hope this helps