Force Transfer Between Body Segments - A Physics Question

[Sam Beckham]

I think stickmans ankles are going to get really sore doing that.

[hypertrophy]

In the diagram with the moments, why do all three joints have 4330 inch pounds of torque? Shouldn't the moment on the knee and the ankle be less than the hip?

[spacediver]

Assuming I understand hypertrophy's question, I don't have a full answer for it, but here are some thoughts. Hope I have this right. If not, someone with more experience please correct me, I'm still learning...

First, let's sharpen the question.



In the image above (which I've adapted from another image in this thread, so forgive the strange protuberances), assume that the green limbs are massless, and that G represents ground (imagine someone has no shanks and has their knee - point A - attached to G).

Points A and B are frictionless hinge joints. There are no muscles, and the only force in play is the force of gravity on point C (point C is directly above point A).

The question is, what happens to the system once we hit "start" on the simulation?

The answer is that the torso will rotate downwards around point B, and the femur will not move.

We know this because the horizontal distance between C and A is zero, and thus there is no torque around A (and since the limbs are massless they cannot impart a torque around A).

You are correct that forces are transmitted through matter (in this case, through the torso and femur). But the beauty of using the moment arm analysis is that we don't need to track the forces through the entire causal chain. We can skip directly from C to A and use the technology of moment arm analysis (it really is a technology) to simplify things. The simplification produces the correct answer, but can be misleading in terms of understanding causation.

If you were to indeed trace the forces at a more granular level, you would discover that the net torque of the femur around point A is zero, which explains why it doesn't move.

To really get deep, you'd want to understand how torque works in the first place. Why does a longer moment arm produce a greater turning force in the first place? There are cool thought experiments and proofs you can do to convince yourself that this relationship holds, but I'm curious if there's a way to understand it on a finer grained level (e.g. deriving the relationship by tracing the transmission of force from atom to atom along the lever).

Btw, once you add muscles into the equations, things are not as simple as the starting strength model makes it out to be (see the above linked thread). Yes, the torque of the system, due to the barbell, on the knee is minimized when it's directly over the knee joint. But the position of the barbell with respect to the hip joint changes the torque that the hamstrings have to generate to keep the barbell in position, and this torque generated by the hamstrings creates a torque on the knees. So there is no guarantee that minimizing the moment arm between barbell and the knee (or between barbell and shoulder during the press) will minimize the torque at the knee (and shoulder). The previous sentence is true when there is at least one joint linking the joint in question to the load (the hip is the linking joint between knee and barbell, and the elbow is the linking joint between shoulder and barbell). If there is no linking joint, then the torque will indeed be minimized when the moment arm between load and joint is minimized.

Finally, here's a question I asked on the physics stack exchange a couple years ago. Might be tangentially relevant.

[dshannon89]

Could you elaborate on this? I don't follow.

If you look at the femur in isolation as a simple lever, the moment is equal to the horizontal distance between the hip and knee. However, the human body is a compound lever system. As such, a moment force exists on the shank at the knee and so forth until the force meets the ground. If the system is stable, an equal amount of force from the ground pushing back will travel up the lever segments until it exerts a moment load on the femur at the knee. These forces create flexure that must be absorbed by the lever arm or the lever will fail in rupture. (that feeling of your femur bending in the middle as the squat drives up) The remaining difference between the upward and downward moment forces is the net moment, or net torque.

[WFB]

In the diagram with the moments, why do all three joints have 4330 inch pounds of torque? Shouldn't the moment on the knee and the ankle be less than the hip?

I don't think so - I think the moment is the same, but the force counter-acting the moment as a result of the moment is different based on the moment arm.
If some one sees it different, though, I'm open to their views.

[Sam Beckham]

The ankle and hip better have different moments. If that were the case I would have developed some semblence of a calf muscle, and I haven’t.

A moment applied to one end of a lever can be reacted by a force vector at the other end (and balanced by an additional force vector at the moment end).

Another angle: If you consider stickman a rigid body and balance the forces I think you will see. Since we are assuming stickman himself weightless the moment at the ankle will be just the horizontal offset of the bar and center of foot. I think, idealistically, this would be zero or very close to it.

[hypertrophy]

Spacediver, your explanation was great, and was pretty much exactly what I was looking for. I didn't realize the moment arm was just a mathematical innovation used to simplify the physics of what is actually happening. For weightlifting purposes I think this level of explanation satisfies my curiosity on the matter and I'll just accept that it works.