Automation of the shoe last grading process according to international sizing systems

The last is the basic industrial component in footwear manufacturing, from which product development starts. Correct last grading ensures the best fit for the intended group of users of the footwear model to be produced. The size marked on the last should respect the specific intervals defined in the different international sizing systems, like the European, UK, US or Mondopoint systems, which are all described in international standards. New approaches in the field of CAD/CAM have emerged over recent years towards the automation of this process. However, these are partial approaches that neither address the grading process according to the different standards nor consider the various parts of the shoe that are not affected by size increments. This paper presents a new accurate and efficient technique for the automation of the shoe last grading process based on the conjugate gradient method. Through this method, it is possible to obtain a graded shoe last that conforms to the international standards in force relative to shoe sizing and allows for the shoe parts that are not affected by size increments. This technique is based on the target measures of length and perimeter of the last to be graded, and aims to minimise the quadratic difference between these values and those obtained from the graded last. This method has been evaluated through a battery of tests performed on a geometrically heterogeneous group of shoe lasts. The results obtained were accurate and the execution time was fast enough to be used for mass