# Find the forces and moments in a leg

nivek0078
Hello,
I'm very confused with this problem and need some help and direction on how to write dynamic equations of motion. The problem is as follows:
Write the dynamic equations of motion for muscle force Fm, hip force Fj in the normal direction n towards rotation center along the -r direction and in the tangential direction t perpendicular to that direction. The equations should be written in terms of weight of the leg W,Fm, Fj appropriate angles and distances. Assume the entire leg moves as a rigid body about hip O. Assume the muscle force acts at 2/3 of the length of the thigh on the axis, making 15 degree angle with axis shown. No initial conditions were given.

The rest of the information is in the attachment provided. Thank you in advance for your help.
-Nivek

#### Attachments

• leg.jpg
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## Answers and Replies

timthereaper
So where did you start with this problem? Give us your thought process.

nivek0078
Thanks timthereaper for your response. So first off i turned the image so that the x and y orientations were correct. Then i tried to sum the forces at point O in the image. For the forces i looked at the individual compontes in the normal n and tangential t directions. These are the equations that I got.

given:
sum Fn = m(an) , sum Ft = m(at)

sum of the forces:

sum Fn = -Fjn(sin(beta-theta)) + Fmn(sin(15)) + Wn(sin(sigma)) = m(an) Note: had to add theta and sigma for the angles not included in the image

sum Ft= Fjt(cos(90-beta) + Fmt(cos(90-15)) + Wt(cos(90-sigma)) = m(at)

sum of the moments at point O:

sum Mo = Wt(d1) + Fm(d2) - Wn(d3) = Io(angular acceleration) Note: Had to add d1,d2,d3 distances not included in the image.

Is this the correct approach, if not what is? How do I reduce this down.