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Golovich et al. 2017b presents an optical imaging and spectroscopic survey of29 radio relic merging galaxy clusters. In this paper, we study this survey toidentify substructure and quantify the dynamics of the mergers. Using acombined photometric and spectroscopic approach, we identify the minimum numberof substructures in each system to describe the galaxy populations and estimatethe line of sight velocity difference between likely merging subclusters. Wefind that the line-of-sight velocity components of the mergers are typicallysmall compared with the maximum three dimensional relative velocity (usually$<1000$ km s$^{-1}$ and often consistent with zero). This suggests that themerger axes of these systems are generally in or near the plane of the skymatching findings in magneto-hydrodynamical simulations. In 28 of the 29systems we identify substructures in the galaxy population aligned with theradio relic(s) and presumed associated merger induced shock. From thisensemble, we identify eight systems to include in a `gold' sample that is primefor further observation, modeling, and simulation study. Additional papers willpresent weak lensing mass maps and dynamical modeling for each merging system,ultimately leading to new insight into a wide range of astrophysical phenomenaat some of the largest scales in the universe.

Merging Cluster Collaboration: A Panchromatic Atlas of Radio Relic Mergers