Thanks for the drawing. It helps me to understand where I was wrong.

I derived the transforming formulas based on your drawing, for the right
arm. However, I don't understand why there would be a difference between
positive and negative zb's?

Here are the formulas:

stc = sin(theta_central)
ctc = cos(theta_central)
sts = sin(theta)
cts = cos(theta)
tts = tan(theta)
sps = sin(phi)
cps = cos(phi)

xt = xb - (yb*sts*cps*stc + zb*sts*cps*ctc)/(cts*ctc + sts*sps*stc);
yt = (yb - zb*tts*sps)/(ctc + tts * sps * stc);

And they are the same for both positive and negative zb...
Do they look similar to yours, and what am I missing here?

Diancheng