The dynamics of the H-atom elimination reactions of C((3)P(J)) atoms with ethylene, allene, and methylacetylene have been investigated in experiments conducted with pulsed supersonic beams using a variable beam crossing angle configuration at relative translational energies, E(T), in the range of 0.7 to 5.5 kJ mol(-1). H((2)S(1/2)) atoms were detected by time-of-flight mass spectrometry after sequential excitation to the (2)P(o)(J) state using a laser beam tuned to the Lyman-alpha transition around 121.57 nm and ionization by a second laser beam at 364.7 nm. Doppler-Fizeau spectra of the recoiling H atoms were recorded in two configurations, with the Lyman-alpha laser beam oriented either parallel or perpendicular to the relative velocity vector of the reagents. A mathematical model developed to account for the density-to-flux transformation and to extract angular and recoil energy distribution functions from the experimental spectra by a forward convolution procedure is fully described. The model, applied to the C + C(2)H(4) reaction, gives an excellent agreement with differential cross sections already determined in a previous combined study, thus providing a good test for its validity. All three processes are seen to pass through single pathways, identified by the comparison of the recoil energy distribution functions with the calculated reaction enthalpies, yielding H(2)CCCH + H (for the C + ethylene reaction) and H(2)CCCCH + H (for the C + allene and methylacetylene reactions). These results are discussed in the context of earlier experimental measurements performed at much higher collision energies.