A mathematical fit model of footwear

Pao Yue-kong Library Electronic Theses Database

A mathematical fit model of footwear


Author: Ma, Xiao
Title: A mathematical fit model of footwear
Degree: Ph.D.
Year: 2015
Subject: Footwear.
Hong Kong Polytechnic University -- Dissertations
Department: Institute of Textiles and Clothing
Pages: xviii, 160 leaves : illustrations (some color) ; 30 cm
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b2816381
URI: http://theses.lib.polyu.edu.hk/handle/200/8154
Abstract: With the rapid development of computers, CAD/CAM technologies, and information technologies, the footwear industry is being reshaped for online shopping.There are many parameters to evaluate how appropriate the footwear is for a person, such as the fit, comfort, materials, style, and design. Footwear fit is the foundation and undoubtedly the most important parameter since improper fit may lead to injuries. The shoe-last, many times referred to as the heart of the shoe-making process, is a reproduction of the approximate shape of the human foot vital to the manufacturing of shoes and controls the style, comfort and fit. In spite of numerous studies on feet and footwear, uncomfortable, ill-fitted, injury-prone and illness-inclined footwear are still common. One of the key reasons for this is neglect in the design of the shoe-last. Currently it is an art rather than a science to make a new shoe-last, where a skilled master uses manual techniques to sculpture a new shoe-last guided by only girth and length measures. Footwear production involves sample design, sample fit trials, and production runs. The shoe-last design and fit testing are obviously error prone, very subjective due to the limited number of shoe testers, time consuming and costly. Since the foot shape, the shoe-last shape and the corresponding shoe shape are different, careful study is required to make scientifically designed shoe-lasts for better fitting. Thus, the main objective of this research is to parameterize and quantify the space among the foot shapes, the shoe-last shapes and the inside shoe shapes to enhance the accuracy of the fitting evaluation during the shoe-last design and the shoe design. To begin, a predictive foot modeling method is presented. 80 Chinese male were selected as subjects for the development experiment and validation experiment of the modeling method. Their feet were scanned by accurate 3D laser scanner to be used as the reference foot models.50 subjects' data out of the 80 was used as the experimental data. The other 30 were used to validate the method. The normalized result was that the optimal key sections were at the 47% and 71% of the foot length for the right foot, while 48% and 72% for the left foot. Mean error between the modeled foot shape and scanned foot shape of the experiment data set were 0.74mm of the right foot and 0.73mm of the left foot. These values are approximate to the claimed error of commercialized laser scanners, which are between 0.5 to 1 mm. The mean errors of the validation data set of the right and left foot were 0.76mm and 0.75mm respectively, which were at the similar level of the accuracy with the experimental data set.Thus, the method can be applied during general foot modeling.Another experiment was then utilized to develop the fit model.Nine pairs of shoe-lasts with three different heel heights and three different toe shapes were designed. The corresponding shoes were used to explore the foot and shoe-last alignment model, the foot deformation model and the footwear fit model. The right feet of 50 subjects were scanned by Microsoft Kinect with the landmarks, defined on the transparent surface of the shoes.The scanned foot model was aligned with the shoe-last by the landmarks, then PCA axis of the foot was found then; and the angles between it and the shoe-last alignment axis (bottom center line) were calculated.The distribution of the angles by different styles of shoe-last illustrated that there is indeed an angle between the foot PCA axis and the shoe-last axis.The value of the angle is mainly affected by the toe shape design of the shoe-last, but little by the heel height. The shoe-last of the round and the square toe shape affects the angle less than the pointed one.A regression model was also given to calculate this angle.
The flat foot model was deformed to create foot shapes at different heel height and toe spring. This was called the Foot Deformed Model [FDM].The instep scaling factor curve was obtained to modify the height of the instep sections of the FDM, since differences between the FDM and the Scanned Deformed Model [SDM] in the instep region were found. Mean errors between the FDMs and the SDMs of 12 subjects were 2.77mm of the 10mm heel height shoe-last, 2.61mm of the 40mm heel height shoe-last and 3.42mm of the 70mm heel height shoe-last.After the foot registration and the foot deformation, the relationship between the foot model surface and the shoe-last model surface was analyzed entirely or regionally. Moreover, the shoe-last surface and the inside shoe shape were compared and analyzed. Twenty landmarks were defined on the transparent shoe upper, and then marked on the shoe-last and the subject's foot surface.The landmark fit model consists of the set of the foot landmarks, the set of the shoe-last landmarks and their vectors. The foot surface covered by the shoe upper was separated into 7 anatomical regions. A surface subdivision method based on the landmarks were proposed and used to extract the points of each region.The landmark regional fit model consists of the regional errors between the foot and the shoe-last and the mean error of each region. The regional fit model can give the error weight of each region of the shoe-last, which can be used in adjusting the overall average error so as to make the fit evaluation more accurate.Moreover, the deformation model for the change of the shoe-last shape into the inside shoe shape was proposed for shoe fit evaluation in shoes design. A number of issues in the shoe-last and shoe fit evaluation were solved in this research. The footwear fit model can provide a quantitative assessment on the shoe-last and predict the shoes' fitting, which will advances the CAD/CAM of the shoe-last and virtual footwear design, especially for customization.

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