Finding out the forces acting on a finger tendon

[Iacob Sorin]

TL;DR Summary

How big is the pulling force acting on a finger tendon(doesn't matter which one, let's say the flexor)?

Summary: How big is the pulling force acting on a finger tendon(doesn't matter which one, let's say the flexor)?

Hello!
To get straight to the point, I'm planning on building the "ultimate" monitor stand, and the design I came up with has a part in which there are 3 metal rods, connected via bearings and a metal wire which is welded on one end, runs trough them ,goes out the other end, and then also welded on a disc. So it's basically a finger with only one tendon, and instead of a muscle, there is a disc.

I would have gone other routes but due to limited parts this is the best I can do.
I plan on slapping a brake on that disc which is permanently engaged, so I can easily modify the cable length , and voilà, a redneck mechanism.

Now, if my thinking is right, by having 3 rods connected via bearings with a cable running trough, i should be able to position the 3rd rod in pretty decent area, and then have it stay there, because of the cable.

So the questions that remain are:
1.How big is the force that pulls the cable.
2.What is the tension in the cable.

 

[sophiecentaur]

A diagram is essential because the radii of the joints where the wire passes affect the necessary tension.

 

[Iacob Sorin]

A diagram is essential because the radii of the joints where the wire passes affect the necessary tension.

At the moment I have no way of providing a diagram, but I have realized a flaw in the design. The cable will run over the rods. I will try to attach a very raw sketch, please bear with me.
I'm sorry this is all i can for the moment,
Green-Wire
Red-Bearing
Purple-Small tube trough which the cable can run, or a pulley.
Blue-Disc
Black-Iron Rod
Edit:Forgot to mention but feel free to make everything whatever dimensions are easier to calculate.

 

[sophiecentaur]

I'm not too familiar to this sort of problem but I think (pretty certain, in fact) that, if the wire is continuous and free to move over all the pulleys, the arrangement will not be stable unless all the dimensions are correct. This is because the tension along a single wire would be the same all along its length. The outermost section will have the full tension of the wire over its pulley. That tension has to be high enough to support the weight of all three arms so it can pull the outermost joint 'inside out'. To avoid this, for a start, the pulleys need to have radii which match their loads. Ignoring numbers, small diameter on outer pulley and large diameter on inside pulley would be needed but the angle of the outer arm has knock-ons on the load on the inner arms. You can possibly choose the right pulley diameters for a particular orientation of the arms but changing the angle of either of the outer arms would upset the equilibrium. The weight of the actual load also comes into it (you cannot assume the arms have no mass).

Your fingers have multiple tendons to allow them to articulate in the way that you want. In addition, they are servo'd. Even your finger system (at least mine, when I tested it) can fail and the finger tip joint can tend to bend backwards under heavy load. So it ain't easy!

You would need three separate wires here so that the tension at the far end is kept low enough etc.. OR, perhaps sprung levers or series springs, rather than simple pulleys, could reduce the tension further out on the wire. Friction clutches at the joints could help, too.

It may be possible to 'do the Math' but I would expect it to get pretty turgid. Perhaps someone else on PF would recognise the problem and come up with some ideas.

A good problem for PF, though!

 

[jrmichler]

You solve a problem like this in several steps:
1) Identify the boundary cases. Four boundary cases to start with are a 2 X 2 matrix: finger most flexed (curved) and least flexed, and finger most horizontal and most vertical.
2) Choose one boundary case. Make a free body diagram (FBD) of the endmost link, its pivot, and the cable up to the pivot. Calculate the cable tension.
3) Simplify for now by assuming the cable guides and pivots have zero friction.
4) Since the end link and cable tension are known and in equilibrium, make a FBD from the second pivot out to the end. The cable tension is known, the weights and lengths are known, so calculate a sum of moments about the second pivot. If the moments sum to zero, it is stable at the second pivot. If not, it will flop one way or the other. If it flops, it will not work. This is different from most FBD's in that the forces are given, and you are finding if the joint is stable.
5) If stable, make a new FBD from the base pivot.
6) If it is stable this far, pick a different boundary case, and repeat.
7) Take a close look at how your fingers function, and note that each finger has opposing tendons. Then think about adding opposing cables as needed to stabilize the mechanism.
8) Have fun, it's an interesting problem.

 

[sophiecentaur]

It is an interesting problem but I think it would need some servoing. That or plenty of friction at the joints.
I think that anglepoise lamps would be widely available with three arms if it were easy. They would have ‘cool value’ and cost a lot but I have never seen one. You could Google Images and see if you can find one?

 

[hutchphd]

I built a parallelogram version arm for a small TV that gave me a six foot cantilever. The spring-parallelogram combination is inherently stable (for perfect springs sized correctly) and has much to offer. You might get some good info from:

https://en.wikipedia.org/wiki/Balanced-arm_lamp

Hope it helps.

 

[sophiecentaur]

I built a parallelogram version arm for a small TV that gave me a six foot cantilever. The spring-parallelogram combination is inherently stable (for perfect springs sized correctly) and has much to offer. You might get some good info from:

https://en.wikipedia.org/wiki/Balanced-arm_lamp

Hope it helps.

How many sections in the system?

 

[hutchphd]

As I recall it was two, but I think that is not a limit. The parallelogram structure rigidly takes care of the moment of the forces while the springs counter the weight of the rest of the structure (outboard of the joint). Considering how quickly I made it the result of that design impressed me at least..

 

[sophiecentaur]

As I recall it was two, but I think that is not a limit. The parallelogram structure rigidly takes care of the moment of the forces while the springs counter the weight of the rest of the structure (outboard of the joint). Considering how quickly I made it the result of that design impressed me at least..

If you look at the simple, two-arm situations, anything mounted at the end tends to be tightly held by the 'adjusting nut' and there is no equivalent to the 'wire' in the OP. I think that makes it just a two arm system with a single force and no torque applied at the end. I know all the angle poise lamps I have used and seen are as I describe (I'm looking at one now) and the end joint is not really part of the situation. imo.
I think that your quick success was due to the high friction and the details of the joints. Anglepoise lamps tend to have a very limited range of articulation - so that they don't fall over. The three arm system, as described, is way different.

 

[hutchphd]

The success was not from friction at the joints. .There are diagonal springs on each parallelogram segment which, when properly sized, hold the force for ~any extension of the parallelogram. Thinner parallelograms require stronger springs. Each parallelogram segment is independent. I believe one could have an arbitrary number of segments because they are essentially independent. The OP is building a monitor stand so it is unclear to me what his end articulation requirements are. Seems similar to holding a TV.

 

[Tom.G]

The magnifying lamp next to the computer here is the two-armed parallelogram style with diagonal springs. The lamp head stays at the same angle to the lamp mounting surface (edge of desk) regardless of the arm positions. The head has its own pivot for up-down (angle with respect to mounting surface) and for twist.

There is a friction brake for up-down of the lamp head and another at the joint of the two arms.

Cheers,
Tom

irrelevant p.s.
I got this for $5 out of the Clearance box at a local office supply store, probably because the mounting clamp was missing. My wife picked up the mounting clamp from the adjacent Clearance box for $1. I think that makes it the cheapest lamp we've ever bought!

 

[hutchphd]

Yep that was my inspiration. But when I did the analysis I was surprised to see that a perfect spring exactly compensates at all angles. Rather than repeat my calculations (from 35yrs ago) I point to this interesting paper where they do it:

https://robomechjournal.springeropen.com/articles/10.1186/s40648-016-0051-5
I feel certain this is more than you wanted to know!

 

[kolleamm]

I feel such a pulley system may eventually fail due to friction. It may be a better idea to implement a system with all solid parts if possible similar to the way this robotic hand is built. Look at the fingers to see what I mean.

https://www.robotshop.com/en/bionic...PMkELUqw00n-2qGxADeS6h4GLpb5dugBoCkugQAvD_BwE