Conditions that give rise to phase shifts among the limbs when an animal changes gait are poorly understood. Often a "switch mechanism" is invoked that has a neural basis which remains speculative. Abrupt phase transitions also occur between the two hands in humans when movement-cycling frequency is continuously increased. The asymmetrical out-of-phase mode shifts suddenly to a symmetrical in-phase mode involving simultaneous activation of homologous muscle groups. The boundary between the two coordinative states is indexed by a dimensionless critical number, which remains constant regardless of whether the hands move freely or are subject to resistive loading. Coordinated shifts appear to arise because of continuous scaling influences that render the existing mode unstable. Then, at a critical point, bifurcation occurs and a new stable (and perhaps energetically more efficient) mode emerges.