# Calculating joint reaction forces

• Haku
In summary, the conversation discusses a biomechanics class question regarding the direction of forces and the confusion over how to define the positive direction. One calculation uses the value of the force as positive while the other uses it as negative. Both calculations result in the same answer of +125N for Fkx. It is concluded that the direction of the force is not as important as the static nature of the forces in the given scenario.
Haku
Homework Statement
If the joint reaction force at the ankle in the x direction is -125N, calculate the joint reaction force at the knee in the x direction (assuming those are the only two horizontal forces acting on it)
Relevant Equations
Summation
I have this question in my biomechanics class, and the way the teacher has solved it raised some questions with me.
This is the snippet of work from the lecture slides:

But, if we see the red variables acting as 'placeholders' for the value of respective forces, and the value of the force at the ankle in x direction is -125N.
When summing all ankle forces in x direction it looks like the direction is accounted for twice, because what the summation is if you leave the variables as placeholders for the actual values is:

Fax + Fkx = 0.

=>

Fkx = -Fax = -(-125N) = 125N.

What I get from the calculation done in the picture is the following:

-Fax + Fkx = 0

<=>

-(-125N) + Fkx = 0

=>

Fkx = -125N

But in this case, you have applied the direction of the joint reaction force at the ankle twice right?
Which calculation is correct? Imo the former calculation is more mathematically sound, but I am not sure since it is contradictory to calculation given in class.

I would not describe it as having applied a force twice. Rather, it is a confusion over how the positive direction has been defined.
Where it is clear that two forces will act in opposite directions, it is not unusual to define each to be positive in the direction it will act. That would give the summation equation in the snippet, but in that model the value should have been inserted as +125N.

Since the given force is specified as negative, it is more natural to use the same direction as positive for all forces. That leads to Fax + Fkx = 0, so, again, an answer of +125N.

Haku
haruspex said:
I would not describe it as having applied a force twice. Rather, it is a confusion over how the positive direction has been defined.
Where it is clear that two forces will act in opposite directions, it is not unusual to define each to be positive in the direction it will act. That would give the summation equation in the snippet, but in that model the value should have been inserted as +125N.

Since the given force is specified as negative, it is more natural to use the same direction as positive for all forces. That leads to Fax + Fkx = 0, so, again, an answer of +125N.
Right, but we don't know the direction of force for Fkx. We just know that they are static, so ma = 0. Hence the sum of the forces is 0.
So should it just be Fax + Fkx = 0, then since we know Fax = -125N we can solve for Fkx right?

Haku said:
Right, but either way, with Fax defined as -125N, the resulting Fkx should be +125N right?
Yes.

Haku

## 1. What is the purpose of calculating joint reaction forces?

The purpose of calculating joint reaction forces is to determine the forces acting on a joint in a biomechanical system. This information is important for understanding the stress and strain placed on the joint and can help in designing effective treatments or interventions for injuries or conditions affecting the joint.

## 2. What factors are involved in calculating joint reaction forces?

The factors involved in calculating joint reaction forces include the external forces acting on the joint, the geometry and orientation of the joint, and the properties of the tissues and structures within the joint. These factors can vary depending on the specific joint and movement being analyzed.

## 3. How do you calculate joint reaction forces?

Joint reaction forces can be calculated using principles of statics and biomechanics, specifically by applying Newton's laws of motion. This involves breaking down the external forces acting on the joint into their components and balancing them with the internal forces generated by the joint structures and tissues.

## 4. Can joint reaction forces be measured directly?

While it is not possible to directly measure joint reaction forces, they can be estimated using various techniques such as motion analysis, force plates, and musculoskeletal modeling. These methods use mathematical models and algorithms to calculate the forces acting on the joint based on data collected from sensors and markers placed on the body.

## 5. How can calculating joint reaction forces be useful in sports and rehabilitation?

Calculating joint reaction forces can be useful in sports and rehabilitation by providing valuable information about the forces acting on a joint during specific movements or activities. This can help in identifying potential injury risks, improving performance, and designing effective rehabilitation programs tailored to an individual's needs and abilities.

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