# Polarity of a relative angle - Knee joint angle

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.

As shown in your diagram.

$$\alpha = suplement(\theta_K )$$

therefore,

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

• Hello @kamran, I forgot to tell that the two absolute angles theta oscillate either side of 90°. In this case is my relashionship correct? – Gennaro Arguzzi Mar 6 '19 at 21:14
• @GennaroArguzzi, now you lost me. I would add arrow tips to the end of angles, then read and add them all as thetas, then multiply by minus one to get the a. – kamran Mar 7 '19 at 0:01
• Sorry @kamran, i have some difficult to visualize on a sketch your reply. Can you explain with other words the sentence please? – Gennaro Arguzzi Mar 7 '19 at 0:06
• @GennaroArguzzi, I am not remotely knowledgable in biology. But the way your diagram shows angles of limbs are denoted by drawing a line from the joint under consideration along their lengths and read from X axis, horizontal axis. I just suggest you draw a tip at the end of the angles to see more clearly. like the leg angle could be wrongly read from the knee down, but it is from the ankle up, which makes a 180-degree difference. – kamran Mar 7 '19 at 0:23
• Hi @kamran, thank you for your suggestion. I'm goint to try to do it. – Gennaro Arguzzi Mar 7 '19 at 6:59

$$\rm{\alpha = \theta K = \theta th - \theta lg}$$

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:

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