Thanks for your continued help.Previously I just created a fairly low resolution plot and saw that there was a convergence in approximately the right area. I just tried to generate a numerical solution by setting up a search function with a resolution of 4d.p.
For the following parameters:
L21 = 302.7397; L3 = 245.4678;
I get q3=-3.577 and q4 = 32.2953
Interestingly this gives an (norm) error between desired and actual W of 0.0017. Though this sort of error would be perfectly acceptable in my application I can see why this non-zero solution would cause the solution to be unsolvable. Quite enlightening.
Someone also suggested that Maple may not be providing a solution as I have not constrained q3 and q4 to be between -360 to +360 degrees. I've tried to do this (using solve() assuming q3<2pi etc.) but I still get the same answer as before.
W = [Wx,Wy,Wz] = [-34.0053 37.9050 -524.3520]
q1 = -0.1870;q2 = 0.0584;