So, you have, say, an intake, and you want to actuate it with a piston. Its mounted with the fulcrum at the end of your bar, and you want to mount the end of the piston rod somewhere in between both ends of the bar, and the other end of the piston is mounted somewhere else on your robot superstructure. You know that it has to fit inside your frame perimeter, and you know that it has to actuate a certain distance down so that you get proper compression. How do you tackle this problem?

Oh hey, that exists, cool!

Solidworks configurations, or Inventor representations are your friend. You can very simply model the piston with 2 configurations: extended and retracted. You can even have it be a parametric part so all you have to do is change a few values and you get a new piston size (Piston throw, diameter, hole-to-hole distance should be all you need).

Place the piston in your assembly, constrain it onto the frame and the thing you are actuating, then change the piston configuration.

Does it go where it needs to go? If no, change where it is mounted. This is quite an iterative process, but it should be easy to get the motion you want.

If this is something that is already created with no CAD model, it will likely be even more iterative, but the same process should work just physically putting the piston in place.

Edit: Bimbaâ€™s site has an amazing CAD generating tool for their entire piston line. You can take this model and modify it to have another configuration for when it is extended based on the throw.

This can also be solved without CAD. You know the starting and ending angles your mechanism will make, as well as the compressed and extended length of the piston. In each position, the piston and mechanism make a triangle. As the mounting points donâ€™t change, you end up with 6 unknowns across the 2 triangles - the length of the other sides (2 unknowns, as the length is the same in both triangles) and the other 4 angles. You can then form some equations pretty easily, using the Law of Sines, Law of Cosines, and the fact that the angles in a triangle add up to 180 degrees. Then itâ€™s just a question of solving the equations for your unknowns. Personally, I find it a rather fun exercise in math! Who would have thought trig would come in so handy?

This is also how I would solve this during initial design, and not necessarily after the fact. Depending on the application you would have different unknowns, for example if you want there to be a 90 or 180 deg angle between the arm and the frame, or if you just want the mechanism to extend so far. It would be mostly a case-by-case basis depending on the constraints you give the system.

This would make a very fun calculatorâ€¦

The video mike linked above shows how to handle this.

Definitely wouldnâ€™t solve it iteratively.

Hereâ€™s a pdf that poorly attempts to illustrate the same thing.

If you have an in-plane mechanisms and all of the following parameters are knownâ€¦

â€“ the positions of your mechanism in both stowed and deployed states

â€“ cylinder retracted length and extended length

â€“ ONE of the two cylinder end mounting locations

â€¦Then the other cylinder end mounting location can be found by geometric construction alone, thereâ€™s no need for any calculation of any kind.

The 2nd cylinder end mounting location MUST exist at one of the two intersections between two different-sized overlapping circles. One of these two intersecting points will not make any sense and can be thrown out, leaving you with a single point where the cylinder end must attach.

From there, you can refine the geometry by changing any of the parameters you selected at the beginning.

linkage laverdure 24july17.pdf (94.6 KB)

Shouldâ€™ve been more clear. When I said this, I meant using law of sines/cosines or construction geometry to determine mounting locations.

I would only solve iteratively in extenuating circumstances (students have not taken trig yet for example).

Great little PDF Nate. Man, I miss blobs for things from school. Fluids textbooks were always fun to look at. I used to look at those blobs as if they were clouds and try to guess what they were.

Edit: BTW Adam, awesome set of videos. Just found these for the first time. What an incredible resource.

Definitely, hence my inquiry. I figured trying to solve this after the fact wouldâ€™ve been a waste of time, and that you can get exact numbers through cad. Thanks for making those videos man!

To add onto this, all the process shown in the video does is to essentially automate the work you would be doing by hand anyway. Why do a bunch of trig when every SolidWorks sketch is essentially a geometric constraint-solver? Especially because you will likely have to go back and revise, again and again, as your detailed design takes shape. Revising a Solidworks design sketch is much easier and more flexible than revising a bunch of hand-derived geometric calculations.

Agreedâ€¦ but at the same time, I would prefer to have my students do the trig, at least the first time. Iterating the calculations a dozen times is just busy work that can be left to your CAD package. But actually doing it once helps provide a link between what they learn in the classroom and the practical applications in the â€śreal worldâ€ť. Even if theyâ€™re always going to let the software figure it out for them after they graduate, at least theyâ€™ll have a better understanding of how that software works and how the problem is solved behind the scenes.

Any time you can use what your students learn in the classroom to inform your robot design, itâ€™s a win. Thereâ€™s just so little connection provided between that classroom learning and the real world applications, and thereâ€™s less every day as computer programs like CAD automate away the need to actually do the math yourself. Having that connection right in front of you is, I think, inspiring. Hopefully it helps students that are passionate about robotics and FIRST to extend that passion into the classroom a bit more. And itâ€™s not just with math! There are tons you can do with physics and chemistry as you build the robot too. If you do any award submissions or grant applications, you can add in writing classes too. Even if a student hasnâ€™t gotten to that point yet, exposing them to it is great, and gives them an â€śah-ha!â€ť moment when they do get to it in class.

I think itâ€™s a great idea to have students do the math by hand the first time around, but something to consider is that both â€śanalyticalâ€ť and â€śgraphical synthesisâ€ť are valid methods for designing mechanisms. At the very least, both methods are taught at Berkeleyâ€™s Planar Machinery class. Iâ€™d be willing to share some resources to anyone who PMâ€™s me. The graphical methods can both be done with just a ruler, protractor, and compass and can be directly ported to CAD.