Search code examples
mathvectorgeometryplane

Finding a vector with known 2 angles (1 of which lies on plane) and length

Sketch of the problem

Hi guys! I am preparing physical model of a robotic leg on my undergraduate studies and I have encountered a problem that I can not solve.

The problem is described in the picture. I have two angles, one of which is a angle between XZ plane and plane marked with a red color. The second angle lies on this plane as shown.

With the constant length AB and variable value of those two angles I want to find formula that describe position of point B in 3D Space.

Solution

  • Point A doesn't look as origin (0,0,0) as painted.

    In any case, you can find position of point in XZ plane as

     B'' = (lAB * Cos(Gamma), 0, lAB * Sin(Gamma))

    then rotate B'' about X-axis by beta angle (matrix (4) here).

    If A really is not origin, then shift coordinates by z-coordinate of A