Calculating Forces in a Leg: Gait Analysis and Joint Reaction Force

[By55]

Homework Statement

Already posted

Relevant Equations

Basic eq that states that for a stationary object the sum of forces is 0 and for a statinary object also the sum of moments is 0.

TL;DR Summary: I had this question in my voluntary homework, but I cant seem to get it done the right way. I have tried to make the balance equations for the x and z axis as well as one for the moment.

Full question here, also as a PNG below
Based on the gait analysis experiments, the following information is available: the vertical component of ground reaction force (GRF) is 67 N, the horizontal component of GRF is 15 N. The horizontal distance between the GRF and the ankle joint b = 3.2 cm, and the vertical distance d = 2.6 cm. The inclination of the tibia in the sagittal plane is 10° and the Achilles tendon force is assumed to be parallel to the tibial longitudinal axis and acting at a distance of 25.4 mm. Calculate the Achilles tendon force and the joint reaction force. (answers: Ft ≈ 776 N, Rx ≈ 67 N, Rz ≈ 1.4 kN).

Typo in the picture, vertical GRF is 67N)
My answer so far in the pdf, ask if (when) there is something you cant understand

 

[berkeman]

Welcome to PF. Can you please attach the problem and diagram instead of linking off-site? That would help a lot. Thanks.

 

[By55]

Welcome to PF. Can you please attach the problem and diagram instead of linking off-site? That would help a lot. Thanks.

Oh, yes of course. My bad for missing the button to add attachments

 

[haruspex]

I have tried to make the balance equations for the x and z axis as well as one for the moment.

Please also post your attempt, per forum rules.

 

[By55]

Sorry for al this hassle. Posting this here since it doesn't let me edit the OG post anymore. But here is my train of thought so far:

Firstly lets define the point of GRF as B and the joint as A. Now ##B_z = 76N,~B_x = 15N##. Also we can get the x and z components from the Achilles tendon force ##F_t##.
$$F_x = sin(10)*F_t, ~F_z = cos(10)*F_t$$.
Now the x-axis balance is ##-B_x-R_x+sin(10)*F_t=0##
And for z-axis ##B_z-R_z+cos(10)*F_t=0##
And the moment balance $$0.032m*B_z-0.026*B_x-0.025m*F_x+0.0044m*F_z=0$$, where the lengts of B_z and B_x are from the assignment and for F_x and F_z they are calculated usind sin- and cos-functions. When solving these three equations, I get these answers that aren't even close to the correct ones.
Also I tried to calculate the F_t from the moment equation, since it is the only variable there, but get something like ##2.18N*10^5##

 

[haruspex]

Sorry, it's there now

PDF is not a great choice. On my iPad I would have to download it.
Forum rules say you should type in your work, preferably using LaTeX.
Upload images for diagrams, of course, but images for equations are a pain, even if legible, because those responding cannot copy/paste. If you must upload images of your working, ensure they are clearly legible and number the equations.

 

[berkeman]

@By55 -- There is a "LaTeX Guide" link below the Edit window. I will send you some additional LaTeX tips now via Private Message (PM).

 

[By55]

Really appreciate your patience, I have a ton going at the moment and now realise that this was maybe not the best time to ask help for this problem, but here we are. Thank you for the PM!