How do I calculate forces and moments for this gripper 1

[Nithin1313]

If I have a torque coming from the servo of 1.96 Nm, how do i calculate force of the gripper on the object as well as compressive, tensile, and bending stresses on the links? Thank you for anyone who can help me out, this is a project I'm doing as a Junior.

 

[3DDave]

One piece at a time.

For example, since the driven gear on the bottom link is the same size as the drive gear on the servo, the gear ratio is 1:1 and so the torque applied to the driven gear is the same as that applied to the drive gear, in the opposite direction.

If this load is evenly divided then the upper driven gear will see half the torque and the lower driven arm will get half the torque.

Since torque = tangential force * distance, the tangential force in this mechanism will use the above division on each driven arm to produce half the servo torque/ (distance between pivots)

After that it gets complicated with more geometry than I care to sketch out. See at the bottom about free-body diagrams.

If you have access to the model and can make the jaws move in coordination with the servo, then you can measure the force by examining the work transfer.

For example, if you push 1 Newton to lift a weight a distance one meter you will have put 1 N-m into that to be stored as potential energy. If you used a simple lever that you pushed down on one end to lift that same pound of weight the same one meter , but you moved your end of the lever down 2 meters, you put in the same amount of work to produce the same potential energy, but through twice the distance; the effort you put in will only be 1/2 N.

Notice that I didn't have to explain the exact configuration of the lever to do this? Ignoring the friction losses, whatever work goes in = the work that comes out.

In your case the work comes from the rotation of the servo and the torque of the servo. The rotation is measured in radians. If the servo turns pi/2 radians at 1.96Nm then 3 N-m of work is done.

To use this method, called "virtual work," make the gear in the CAD model turn a small amount and then measure the distance the jaws close. Multiply the 1.96N-m of torque by the tiny angle (in radians) it turns and divide by the distance the jaws close - that will be the force the jaws exert at that position over that distance.

For a longer explanation: https://en.wikipedia.org/wiki/Virtual_work

Here's a video that also explains it:

Skip to 10 minutes to see a mechanism after the beam bending part. It has a large number of pieces and analyzing each one by geometry is tiresome.

To find individual loads you need to use free-body diagrams, which are far too much to explain here - but there are videos:

 

[GregLocock]

Hopefully 3DDave has you on the right track, I'd just point out that there is NO definitive force split in this setup, it depends on the position of each jaw and the load on each jaw.

 

[3DDave]

If it's just grabbing something the jaws should be close enough to equal. If one jaw is lifting something, then ignore the movement of the other jaw as it does no virtual work.

Otherwise the jaws are supposed to be geared together to move in mirror symmetry.

 

[Nithin1313]

If it's just grabbing something the jaws should be close enough to equal. If one jaw is lifting something, then ignore the movement of the other jaw as it does no virtual work.

Otherwise the jaws are supposed to be geared together to move in mirror symmetry.

the gripper isnt lifting against gravity directly, it produces a force on the object which generates static friction which resists gravity, i thought you could solve it like a four link system, but i dont know how to do that, could you help me with what a fbd would look like, obviously it would be different for every aperature, but a general fbd would be good.

 

[Nithin1313]

The problem also is that if I were to solve this as a link system or something the finger part of the gripper is a bent link so I don’t know how to account for that

 

[mfgenggear]

I believe the link positions may cause interference. Generally there a central pivot point for mechanical advantage. I believe this not a good design. All the force should be on the two levers connected to the gears. But it appears awkward. I would think this should be calculated like a simple plyers.

 

[BrianE22]

If you want to make it more difficult, consider what happens if any moment arm gets small (shortens) during part of the stroke. You would want to make sure the tolerances were tight enough not to affect the moment arm lengths.

 

[mfgenggear]

https://homework.study.com/explanation/determine-the-mechanical-advantage-of-the-pliers-shown-show-the-fbd-clearly.html

 

[GregLocock]

draw an FBD for the upper jaw and post it here.

 

[3DDave]

This is high-school junior right? Not mechanical engineering degree 3rd year of college sort of junior?

I don't see it as reasonable to educate here on a subject that is normally covered over 20-40 hours in class and another 20-40 hours of homework.

If there was some part of the "how to do free-body diagrams" video that you did not understand, there are dozens more.

How far into the video did you get and what diagrams did you draw of the linkage parts?

 

[Nithin1313]

I am a college junior, I just don't know what to do for bended links like the gripper finger. This is a general free body diagram I made to simplify things these are not the exact values that apply to my gripper, but if I could figure out how to solve this I could figure it out for the gripper. I'm a little hazy on statics, but also we didn't do bended members so I don't know.
based on my knowledge I get that Fg is 0.57 N, Fb is 1.2 N, and Fa is -0.8N

 

[GregLocock]

Even back in the day when high school physics was a thing I doubt I would have been confident in an FBD more complex than an excavator (this gripper is more complex than an excavator). They were badly taught. We did do force polygons.

 

[3DDave]

Back in the day I didn't have 50,000,000 YouTube channels, access to college level lectures, on-line calculators, and so on.

FBDs are like accounting - the correct answer is always 0.

 

[mfgenggear]

View attachment 10224

If I have a torque coming from the servo of 1.96 Nm, how do i calculate force of the gripper on the object as well as compressive, tensile, and bending stresses on the links? Thank you for anyone who can help me out, this is a project I'm doing as a Junior.

https://www.assp.org/docs/default-source/psj-articles/mtricketts_1020.pdf

the gear is the force in torque.
break it down as a simple lever.
look at the examples

 

[rb1957]

(apologies to 3DDave ... TLDR)

the torque is creating a force on the driven gear ... can you calculate this ?

it makes sense to assume that the torque applied to the 2nd driven gear is 1/2 the applied torque ... can you figure this out ?

do you know what a free body diagram is ? there is no special FBD for a "bent arm".

The beige links are not 3 force members ... the 1st driven gear has an applied force from the drive gear, a load onto the 2nd gear and two unknown forces (so that means X- and Y- components) at the center and onto the arm (yes?).

It may be easier to work backwards ... assume a force (and an angle, of the link) for the jaw fttg. This is reasonably a 3 force body (figure out what this means) and I think you can define the direction of two of those forces, and so determine the direction of the 3rd force (onto the driving link). This helps with solving the driving link as you now have only 1 unknown force (at the center lug) ... yes ??