This paper presents an optimization method to find link shapes for a dynamically balanced planar four-bar mechanism. The shaking force and shaking moment developed in the mechanism due to inertia are minimized by optimally distributing the link masses. The link shapes are then found using cubic B-spline curves and an optimization problem is formulated to minimize the percentage error in resulting links inertia values in which the control points of the B-spline curve are taken as the design variables. The effectiveness of the proposed method is shown by applying it to a numerical problem available in the literature.