The physical insight used in formulating a multi-criteria optimization problem for the synthesis of compliant mechanisms, is quickly lost if mathematical programming techniques (SLP, SQP etc.) are used to determine the optimal solution. As opposed to the previous works that relied upon mathematical programming search techniques to find the optimum solution, in this paper we present an alternative method of solution called the optimality criteria method. Optimality criteria methods have proven to be effective in structural optimization problems with a large number of variables, and very few constraints as is the case in the topology synthesis of compliant mechanisms. The important new results of this paper include: (i) the derivation of a physically insightful optimal property of compliant mechanisms which states that the ratio of the mutual potential energy density and the strain energy density is uniform throughout the continuum (ii) the development of the optimality criteria method of solution in the form of a simple update formula for the design variables by using the above property (iii) design parameterization using the frame finite-element based ground-structure that appropriately accounts for the requisite bending behavior in the continuum, and (iv) numerical implementation of previously reported density based design parameterization using bilinear plane-stress elements. In addition, a new energy based multi-criteria objective function is presented to maximize the useful output energy (which is equivalent to maximizing the mechanical advantage) while meeting the kinematic requirements. Several examples are included to demonstrate the validity of the optimal property, the optimality-criteria method of solution, and the improvements made possible by the new energy based objective function.