Predicting the vertical/horizontal/mediolateral force of a lungfish limb

[mgranatosky]

Hello

This may be an incredibly simple question, but I am looking for some help to clarify things for me.

I am a researcher interested in animal locomotion. Currently, I am working on a project collecting single limb force data (vertical, horizontal, and mediolateral substrate reaction force in a single limb) from a lungfish (a fish that walks along the bottom of rivers similar to a salamander).

I am hoping to do some modelling before we collect any data. I want to be able to predict approximately how much vertical, horizontal, and mediolateral force will be on each limb.

I believe that the static models I provided in the pictures attached should be some representation of the expected forces when the animal is walking on the ground. Essentially, use the static models to predict force across the stride. In the horizontal and mediolateral model you'll notice that there is an angle measurement involved. I believe that this angle should be relative to the center of mass, but is it actually at the hip/shoulder joint?

To make matters a little more complicated (maybe not) these animals only walk in the water. In our experiments we are planning to collect data while animals walking in a fish tank on a desk. This fish does not float (it sinks to the bottom), but does buoyancy play a factor in this scenario, and if so, how will this change calculations?

I appreciate your help so much, and welcome any edits or better suggestions.

 

[A.T.]

I believe that the static models I provided in the pictures attached should be some representation of the expected forces when the animal is walking on the ground.

Why are you assuming that the force from each leg acts through the COM? Is each leg force of a table acting through the tables COM?

I believe that this angle should be relative to the center of mass, but is it actually at the hip/shoulder joint?

Is see no reason to assume either one of these two. The latter would only be justified for a very unstable static case, with the joints completely passive, and limbs aligned to produce no external torque around the joints.

This fish does not float (it sinks to the bottom), but does buoyancy play a factor in this scenario, and if so, how will this change calculations?

For the static case:
total vertical ground reaction = weight - buoyancy

 

[Andy Resnick]

Hello

This may be an incredibly simple question, but I am looking for some help to clarify things for me.

This is assuredly not a simple question.

I was tempted to think of this as similar to a crab or lobster, in which case the only significant difference relates to overcoming viscous drag. Which isn't too hard.

However, the images you show made me think carefully about how the lungfish legs are jointed- how does the musculature of the lungfish act to generate forces on the riverbed? Being confused, I quickly checked the literature, and sure enough, there is data:

https://academic.oup.com/icb/article/53/2/283/806410/Propulsive-Forces-of-Mudskipper-Fins-and
https://www.nature.com/articles/srep33734
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4008594/
http://www.pnas.org/content/108/52/21146.full

I think that you can extract out forces and torques from those papers (and cited references).

 

[mgranatosky]

Hello,

Thank you so much for the reply. I have answered your questions to the best of my ability below.

Why are you assuming that the force from each leg acts through the COM? Is each leg force of a table acting through the tables COM?

That is the way I've always thought it about. It makes things easier to consider quadrupeds as tables. I am basing these models on previously published data (see below)

Is see no reason to assume either one of these two. The latter would only be justified for a very unstable static case, with the joints completely passive, and limbs aligned to produce no external torque around the joints.

Is there a different model I should be using instead?

For the static case:
total vertical ground reaction = weight - buoyancy

So in the models provided weight should be adjusted to W' = W - buoyancy?

Thank you so much for your help on this

 

[mgranatosky]

This is assuredly not a simple question.

I was tempted to think of this as similar to a crab or lobster, in which case the only significant difference relates to overcoming viscous drag. Which isn't too hard.

However, the images you show made me think carefully about how the lungfish legs are jointed- how does the musculature of the lungfish act to generate forces on the riverbed? Being confused, I quickly checked the literature, and sure enough, there is data:

https://academic.oup.com/icb/article/53/2/283/806410/Propulsive-Forces-of-Mudskipper-Fins-and
https://www.nature.com/articles/srep33734
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4008594/
http://www.pnas.org/content/108/52/21146.full

I think that you can extract out forces and torques from those papers (and cited references).

Thank you so much for looking into this for me. I am familiar with these papers, and they have gotten me really excited about the origins of quadrupedal locomotion in non-tetrapod species.

From a modelling perspective, I would like to predict forces as if the animal was a table (see below). This will serve as a null hypothesis, and the empirical data can be used to see where differences occur.

Thank you so much

 

[A.T.]

Why should there be any horizontal forces at the legs here?

 

[mgranatosky]

Why should there be any horizontal forces at the legs here?

Hello,

That view is meant to be a cross-section of the animal (see below). Anytime you have an animal with a sprawling limb posture (like the lungfish) mediolateral forces can be high. Sorry about the confusion

 

[A.T.]

Anytime you have an animal with a sprawling limb posture (like the lungfish) mediolateral forces can be high.

They can, but there is nothing in simple statics that says there must be any horizontal forces at all. It's all physiology and different optimization goals:

When standing on all legs, it makes sense to have the forces pass near the joints, so the muscles do not have to create much counter torque.

When the opposite leg is up, it makes sense to have the force pass near the COM to keep balance.

Locomotion is far more complex.

And the hydrodynamics of locomotion under water even more complex.