Pneumatic Cylinder operating a jaw or gripper - need help with the math

Hi All,

Can someone share an Inventor drawing (.ipt) or any drawing that explains how to calculate the movement of a piston that can open and close an arm. Below is a sketch that fellow coach shared with me last spring but I can’t make sense of it.

Thanks in advance, Steve

The sketch:

This is what I want to do:

If you look at the sketch, the leftmost point where the 2 lines intersect, is the pivot point for your arm. The 2 circles in the middle represent the maximum and minimum extension of the pistons. When you add all the dimensions and constraints in Inventor, the distance between the 2 points on the circle where the arm is attached will give you the minimum required stroke length for your piston.

Thanks, but I’m still confused.I modified the pictures with letters for each point. Could you clarify what each point or circle represents?

thanks so much,

You could just make a simple sketch in CAD. The variable X is a variable that you can change (I’m lazy so they’re all named X but they don’t have to be the same). The variable Y is the length of the piston whether it’s retracted or extended. This can be seen in Base.


Now say we want a pneumatic for what’s shown in Closed. We can see that it needs to be about 10.5 inches extended. I hoped onto mcmaster and found the pneumatics page ( and found this pneumatic ( that fit the about 10.5 inches extended requirement (Whether it can actually do the job is not taken into account here. I just went for what fits). Then you can check out how it would look like if the grabber was open.



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This looks like it would be a good application for the now defunct ForceEffect app that was available from AutoDesk. Are there any other free-body diagram calculators out there?

I don’t exactly understand the problem at hand here, but it does sound like something that could benefit from the pneumatic linkage calculator in my design spreadsheet.

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I like to make a model out of cardboard, and see how things move around…

but I’m computer illiterate.

WOAH, that’s cool.

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Thanks, Ari. I’m going to have to play with that a bunch when I have some time.

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From what I see in the actual mechanism. I don’t think an L bracket would suffice. The rear of the cylinder appears to be hard mounted so it can’t swivel. Therefore when the cylinder would retract, the L bracket wouldn’t want to stay perpendicular relative to the shaft. You’d have to make the rear of the cylinder able to swivel and likely use a heim joint where the shaft connects to the actual claw

As I understand this sketch (it is not completely accurate and there appear to be some half drawn elements):
A is the pivot point of the arm
E is the fixed end of the pneumatic cylinder
(A and E are both attached to the same structural element and do not move relative to each other)
D is the other end of the cylinder when the cylinder is retracted (I believe the smaller circle should have been drawn with the distance from E to D as the radius of the circle rather than the diameter of the circle)
C is the other end of the cylinder when the cylinder is extended (same problem with the larger circle)
Therefore the line segment AD is the arm position when the cylinder is retracted and AC is the arm position when the cylinder is extended (thus the “X” motion off to the right hand side of the sketch).
It is not clear what the sketcher was attempting to draw with the lines originating at B. Perhaps the sketcher was attempting to show what happens when you shorten the length of the arm between the arm pivot and the cylinder attachment point. This part is not very clear and does not appear to be drawn correctly (BC is shorter than BD and since the two circles were drawn incorrectly, it made it hard to use those two circles to illustrate the point he was trying to make).

Anyway, I might be wrong with my interpretation of this drawing.

Basically, since the cylinder is pivotably attached at each end, the locus of points that define one end of the cylinder relative to the other is a circle around the fixed end. There are two circles, one for the retracted cylinder and one for the extended cylinder. The arm is a line of fixed length between the pivot of the arm and where it attaches to the cylinder. Since the pivot point of the arm is fixed, you can draw a circle around that fixed pivot point whose radius is the length of that arm. Where that circle defining the length of the arm intersects with the two circles for the cylinder lengths are the two positions of the arm. At least that is how i usually sketch this problem.

This isn’t exactly what you asked for, but here’s a talk I gave a few years back about how you can use CAD to select pneumatic cylinders to drive your mechanisms.