Single bonds are generally rotatable and multiple bonds are not. Multiple bonds can twist somewhat but not by much before the pi bonds will break. 'Rigidity' is not a well-defined term and you won't get an answer to that question on this Forum unless you are a bit more specific. You can talk about certain bonds being 'stiffer' than other bonds. This is related to steric interactions, bond length and bond strength.
Most materials will be active in the infrared spectrum. The energy of the infrared band is the energy of bends, twists, rocks and other intramolecular motions (not spinning or translating). An examination of the infrared spectrum of the species of interest will give you some insight into the energies of these twisting, bending, rocking and stretching motions. The intensities will tell you about the likelihood of the absorption of these energies.
Molecular modelling programs can give you a calculated infrared spectrum if none exist or you can't find one for your specific compound. You can also wing it by examination of the bond length of the species in question, the mass of the substituents and the bonding energy. Shorter bonds are usually stiffer than longer bonds and higher bond energies usually infer the same.