  Alkaline earth monoalkoxide free radicals (MORs) have molecular properties
conducive to direct laser cooling to sub-millikelvin temperatures. Using
dispersed laser induced fluorescence (DLIF) measurements from a pulsed
supersonic molecular beam source we determine vibrational branching ratios and
Franck-Condon factors for the MORs CaOH and CaOCH$_{3}$. With narrow linewidth
continuous-wave dye laser excitation, we precisely measure fluorescence
branching for both $\tilde{X}-\tilde{A}$ and $\tilde{X}-\tilde{B}$ electronic
systems in each molecule. Weak symmetry-forbidden decays to excited bending
states with non-zero vibrational angular momentum are observed. Normal mode
theoretical analysis combined with ab initio structural calculations are
performed and compared to experimental results. Our measurements and analysis
pave the way for direct laser cooling of these (and other) complex nonlinear
polyatomic molecules. We also describe a possible approach to laser cooling and
trapping of molecules with fewer symmetries like chiral species.
