Polarity of a relative angle - Knee joint angle

Question

I'm wondering if it's correct to write:

$$ alpha = theta_{lg} - theta_{th} $$

EDIT: the theta angles are defined positive in counter-clock direcction, instead alpha in clockwise direction. My goal is to find a relationship between the three angles I wrote above (the relationship should be valid at any time istant).

Thank you for your time.

Phil Sweet · Answer

The short answer is don't. You might need two diagrams. One has the convenient or intuitive (to non engineers) angles for illustrative purposes. But the computational angles must all be RHR consistent. So define the computational alpha as CCW from the same axis as the other angles. The angle you show as alpha is fine for an illustration or input, but it must be converted to standard RHR conventions before any calcs are done. So take alpha as input. Convert it to a CCW angle as 360 - alpha. run your calcs. Then convert back if necessary.
Do not do any computations using ass backwards angles

Ali Haider Al-kutubi · Answer

$rm{alpha = theta K = theta th - theta lg}$
Your answer will give correct value, but with the wrong sign (it will give a false negative sign).
The proof of my answer is illustrated within the image:

kamran · Answer

As shown in your diagram.

$$alpha = suplement(theta_K )$$

therefore,

$$ alpha = 180- (theta_K)  = 180-(theta_{th}- theta{lg} )=180 +theta_{lg} -theta_{th}$$

So you need to add 180 to your answer.

Polarity of a relative angle - Knee joint angle

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