This work is devoted to improving the form and method of designing a shoe last using modern computer technologies and advanced equipment. In order to obtain initial information about the shape and parameters of the foot, anthropometric studies of the feet have been carried out in the traditional manual way using a stop meter, a ruler and a measuring tape, and a non-contact 3D scanning method using a specialized FootIn 3D scanner. The results showed significant variation in circumferential measurements. Further, 8 test lasts were developed and manufactured for individual customers on the basis of anthropometric parameters obtained by 3D scanning. Trying on samples of shoes made on these lasts demonstrated the need to adjust the lasts, which was associated with excessive freedom of fitting of the foot: 7 out of 8 lasts turned out to be too wide in circumferential and latitude parameters. To develop an improved design method, the parameters of the necessary reduction in the circumferential-latitude parameters of the foot have been investigated by manually adjusting the manufactured lasts and re-testing. In addition, it has been proposed to use the contour of the last bottom, pre-designed based on the footprint. To develop a method for designing the contour of the lasts track of different styles, a study has been carried out as for the influence on its configuration and the main geometric parameters of such factors as the height of the heel and the toe shape. The proposed design method provides for the use of a 3D scanning of the foot and additional information in the form of manual measurements of the main circumferential parameters and bottom contours, developed on the basis of the footprint. Next, we tested samples made on lasts designed according to the proposed method. A comparative analysis of the shoe lasts developed using different methods has been carried out by assessing the customer's subjective omissions when trying on shoe samples made on these shoes. For this, we made shoe samples on a standard last of the corresponding style and size; on the last corresponding to the parameters of the 3D scan of the foot; and on a customized last designed according to an improved method. Comparative analysis has demonstrated the advantages of the improved shoe shape. When designing high-heeled lasts, the problem arises of the impossibility of matching the 3D model of the foot and the last. For this purpose, the work proposes the use of a foot model adapted to the last style, for which a mathematical model of the rapid deformation of the points of the rear part of the foot surface when raising the heel to the corresponding heel height is applied. At the same time, the anthropometry of the foot and the peculiarities of its work when lifting to the heel have been studied. The work has also developed practical recommendations for modelling the shape of a shoe last based on the results of 3D scanning of the foot with an atypical shape of individual areas, considering the necessary adjustments to the parameters and the main contours of the shoe surface. For this, graphical-analytical calculations of the change in the position of the nodal points of the transverse contours have been carried out with an increase in the perimeter of a separate section. For expanding the range of shoe styles, there has been proposed a method for creating a new shape based on the existing main back part by attaching a new toe part to it in a 3D graphic CAD environment using the Morphing function. To achieve the versatility of the method and the possibility of applying the same toe shapes to different back parts of the lasts, a study has been made of the parameters of the lasts shape of the same size-width interval. This made it possible to rationalize the cutting plane separating the main back part of the last from the toe. In this area, the last shapes are as close as possible in parameters, which made it possible to average the contours of the section. This makes it possible to develop interchangeable forms of the main and toe part of the last. Further, this method was implemented in practice by making lasts with a replaceable toe part, which can be used for various models of the main (rear) part of the last. The introduction of such last designs has cut the cost of purchasing new lasts in half, and has reduced the cost of maintaining storage facilities for storing lasts by almost the same amount. In order to develop an improved technology for finishing footwear, research has been carried out on the chemical composition and physical and mechanical properties of finishing compositions. It has been determined that finishing compositions improve the physical and mechanical properties of Crust leather for custom-made shoe uppers.
