In this article, we give a mathematical framework to model the kinematics of the surface growth of objects such as some crustacean creatures. For this, a growth velocity in the direction of the Darboux vector field is defined at each point on a spatial generating curve. A local orthonormal frame (alternative moving frame) is added to each point of the generating curve and a velocity is given in terms of local coordinate directions to obtain a system of differential equations. Using the analytical solutions of this system, various surface examples, including some seashells are provided and the shapes of these surfaces are illustrated. (C) 2017 Elsevier Inc. All rights reserved.