Calculating torque of rotator cuff muscle

[James_The_Ern]

Homework Statement

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Rotator cuff strength test. Patient's elbow is flexed 90 deg. while the shoulder is abducted 90 deg. and externally rotated 90 deg. The therapist applies pressure to the dorsal surface of the hand/wrist. If this is the patient's dominant arm, and the length of her upper arm is 0.25 m and the distance from the elbow to the point the therapist applies the force is 0.20 m, answer the following: a) If the therapist is applying 40 N force, what is the internal moment this muscle group must generate to maintain a constant position / static equilibrium? b) If the muscle group can generate 14 Nm of torque when activated maximally, what is the greatest force the patient can resist before the arm starts to move? Assume z-axis runs through elbow / upper arm / shoulder.

Homework Equations

Torque = F * r.

The Attempt at a Solution

I have dealt with statics before usually in 2D. It seems more like a 3D problem and I'm a bit lost. The force is applied from the z-axis if we consider forearm be x-axis and lower arm be y-axis here. How do I project the forces and make the overall torque equal to 0 (since it's static equilibrium)?

 

[haruspex]

For those of us unversed in anatomy, it would help to provide a diagram.

 

[James_The_Ern]

https://s3.amazonaws.com/iedu-attachments-message/35d24530b326f0f94289c9fabe4dfc86_3c3d647d8dd92cd6a07f4de563fae997.pdf

Problem 6, this is the whole question with the picture. Thanks!

 

[haruspex]

https://s3.amazonaws.com/iedu-attachments-message/35d24530b326f0f94289c9fabe4dfc86_3c3d647d8dd92cd6a07f4de563fae997.pdf

Problem 6, this is the whole question with the picture. Thanks!

In general, given a force applied to a rigid body and a point about which the body may pivot, the magnitude of the torque about the point is given by the magnitude of the force multiplied by the perpendicular distance (that is, perpendicular to the line of action of the force) from the line of action of the force to the pivot. The direction of the torque, as a vector, is perpendicular to both the distance and the force.

For the torque about the shoulder, you can treat the elbow as rigid, so go directly from the applied force to its affect at the shoulder.

Thus, there will be a horizontal torque about the elbow, and a torque at some angle in the vertical plane about the shoulder.

 

[James_The_Ern]

For those of us unversed in anatomy, it would help to provide a diagram.

In general, given a force applied to a rigid body and a point about which the body may pivot, the magnitude of the torque about the point is given by the magnitude of the force multiplied by the perpendicular distance (that is, perpendicular to the line of action of the force) from the line of action of the force to the pivot. The direction of the torque, as a vector, is perpendicular to both the distance and the force.

For the torque about the shoulder, you can treat the elbow as rigid, so go directly from the applied force to its affect at the shoulder.

Thus, there will be a horizontal torque about the elbow, and a torque at some angle in the vertical plane about the shoulder.

So, I have to determine that angle using trigonometry for the lengths given, right? I could find that angle using tan here. Now, what about equilibrium problem? I need to find the opposite torque that has the same magnitude, but the opposite direction?

 

[haruspex]

So, I have to determine that angle using trigonometry for the lengths given, right?

Probably. It depends whether a single muscle group is responsible for opposing it or more than one. If more than one you might have to resolve the applied torque into components.

the opposite torque that has the same magnitude, but the opposite direction?

Yes.

 

[James_The_Ern]

Probably. It depends whether a single muscle group is responsible for opposing it or more than one. If more than one you might have to resolve the applied torque into components.

Yes.

Is there a way you could show me the solution? It's quite hard for me to understand, although I believed I got it right. I'm trying to look at the free body diagram and I'm lost. This problem is due soon and I just can't figure it out.

 

[haruspex]

Is there a way you could show me the solution? It's quite hard for me to understand, although I believed I got it right. I'm trying to look at the free body diagram and I'm lost. This problem is due soon and I just can't figure it out.

I can calculate the magnitude and direction of the torque about the shoulder, but I do not know enough anatomy to say which muscles have to counter it, and how they divide that up.
For the magnitude, just multiply the applied force by the distance from the point the force is applied to the shoulder.