Engineering design is a highly integrated and integrating process This two-part paper describes an integrated computer-based platform for the development from first principles of design solutions to appropriately defined need, and the choice and quantification of the best forms of embodiment This second paper (Part II) concentrates on the use of mathematical techniques based on sophisticated simulation and symbolic manipulation in the development and quantification of the conceptual schemes generated by the use of Artificial Intelligence The methods of selecting the best embodiments of the required functions are described, together with the means of determining the best size of component The use of function maps relating function to cost, weight, limits on strength, efficiency of operation, etc , are shown Finally, details are given of the use of automatically generated simulations of chosen embodied schemes These simulations are used to confirm expected performance and as part of the procedure for optimising the design