your drawing is messed, but I think that I got the idea...


3 axis system

        Z

        I
        I
        I
        ---------> Y
       /
      /
     /
  X

(a) is fixed relative to the base. r1 is the hypothenusa (constant), z is the height (variable), so
a = asin (z/r1)

(c) is fixed relative to r1/r2 joint. r2 is the hypothenusa (constant), z' is the height (variable), so
c = asin (z'/r2)

z' is relative to the ground also, since it's measured after the tip z of r1

hth

orlando