Reconstructions of the past positions of the continents indicate that at least twice a supercontinent has formed and subsequently split and dispersed as smaller continents. This has led to speculation about the existence of a periodic cycle of supercontinent coalescence and breakup, for which various mechanisms involving mantle dynamics have been proposed. In this paper we investigate the plate-tectonic system by means of a simple kinematic model to determine to what extent its behavior results from geometric or kinematic factors as opposed to dynamic processes. Results from computer simulations show that the overall behavior of the system is determined by the dimensionless parameter T = Ωτ, where Ω is the mean relative angular speed of the continents and τ is the mean time interval between plumes. The results for T = 0.10 are in good agreement with observations and indicate that a supercontinent is unlikely to form at current plate speeds in the presence of steady-state plume fluxes; evidence of supercontinents therefore implies that plume fluxes and plate speeds have varied through time.