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Math Help - Finding Forces in a leg

  1. #1
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    Finding Forces in a leg

    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.

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

    Finding Forces in a leg-leg-doc.jpg
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Finding Forces in a leg

    Quote Originally Posted by nivek0078 View Post
    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.

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

    Click image for larger version. 

Name:	leg DOC.jpg 
Views:	5 
Size:	279.5 KB 
ID:	29535
    I'm not certain what you mean by "dynamic" equations, but as a general approach you can do sum of forces in the "usual" x and y directions, then use the torque equations (are you calling them "moments"?) on as many axes as you need to get the right number of equations you need. In this case the point 0 at the top of the leg would be a good choice. It's messy to solve but conceptually no harder than that. Are you stuck at some point?

    -Dan
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  3. #3
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    Re: Finding Forces in a leg

    Hey Dan,
    Thanks for the response! The “dynamic equation’s” is just that it should be in symbolic form is all no numbers. I kind of figured it would be a messy equation. My confusion is in how to handle the angular acceleration and velocity when summing the forces and also how to determine the correct angles when doing so. Is there a simpler way of breaking all this down?
    -Nivek
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    Re: Finding Forces in a leg

    Quote Originally Posted by nivek0078 View Post
    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.

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

    Click image for larger version. 

Name:	leg DOC.jpg 
Views:	5 
Size:	279.5 KB 
ID:	29535
    If I understand you correctly you are asking for either Lagrangian of Hamiltonian dynamic equations. Lagrangian is one second order ODE in position as a function of time, or momentum as a fufnction of time. You will need initial conditions. The Hamiltonian is two first order equations, you still need initial conditions. Is this what you meant by dynamic equations, or you meant balance of mementa?
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  5. #5
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    Re: Finding Forces in a leg

    Thank you votan for your response. I thought it was the Lagrangian as well but no initial conditions are given so it must be balance of mementa. I am open to any information on how to solve this problem. Thank you again for your help.
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