A moveable machine to rapidly apply and cure thin layers of a UV curable coating on a surface such as a floor. The machine has an applicator to apply a thin curable coating in a path following the direction of motion of the machine. The machine also has UV lamps to cure the curable coating with a curing beam that overlaps newly applied coating. The UV lamps emit an intense UV radiation beam creating an annular cure zone around the applicator path. Movement of the machine along with the ensuing movement of the applicator and rotating UV lamps causes the applied curable coating to be exposed to the annular cure zone and cured. This rapid curing of applicator coating paths allows the machine to be immediately passed over the cured area multiple times and rapidly build up multiple thin cured layers to achieve a thick coating.