Segment and joint angles problem.

[clokey34]

Homework Statement

Calculate the knee joint angle based on the XY coordinates of the hip, knee
and ankle joint centres.

Hip joint(x = 1.0183, y = 0.7959)
Knee joint(x = 1.1223, y = 0.5042)
Ankle joint(x = 1.0539, y = 0.1081)

Homework Equations

θjoint = θproximal −θdistal

The Attempt at a Solution

Biomechanics student here.
Not sure how to do this. I'm sure its a simple one just confused how to start. It is supposed to come out to 29.42 deg. Thanks for your help.

 

[tiny-tim]

Welcome to PF!

Hi clokey34! Welcome to PF!

Draw the graph, and use the letters H K and A.

Then the upper leg is KH, and the lower leg is KA, and you want the angle between KH and KA.

So use coordinates to write KH and KA as vectors: KH = H - K, KA = A - K,

Then there's two methods:

i] use tanθ = y/x to get θproximal and θdistal, and then use θjoint = θproximal −θdistal, or:

ii] dot-product KH and KA, and divide by their ordinary product: cosθ = KH.KA/|KH||KA|.

Can you do either of them, or do you need more help?

 

[clokey34]

Thank you very much. :)

tanθ = y/x was helpful! My answer came close within a degree, but I suppose there was issues rounding, I'll ask my teacher what he wants.