Cells adhered to an external solid substrate are observed to exhibit rich dynamics of 1 actin structures on the basal membrane, which are distinct from those observed on the dorsal (free) 2 membrane. Here we explore the dynamics of curved membrane proteins, or protein complexes, that 3 recruit actin polymerization when the membrane is confined by the solid substrate. Such curved 4 proteins can induce the spontaneous formation of membrane protrusions on the dorsal side of cells. 5 However, on the basal side of the cells, such protrusions can only extend as far as the solid substrate 6 and this constraint can convert such protrusions into propagating wave-like structures. We also 7 demonstrate that adhesion molecules can stabilize localized protrusions, that resemble some features 8 of podosomes. This coupling of curvature and actin forces may underlie the differences in the 9 observed actin-membrane dynamics between the basal and dorsal sides of adhered cells.10