## 4 Conclusions and Future Directions  
In this paper, a proposal for automating the 3D scanning of footwear used in indoor sports (handball) was presented, following a predefined trajectory based on a proposed mathematical model for a robotic arm with three actuated joints, which can be controlled by a simple controller.  
Digital 3D models of both sides of the shoes used in indoor sports were acquired and processed using VXelements software.  
The results demonstrated effectiveness and fast scanning technique compared to other types of scanning in terms of the accuracy of the results, the possibility to obtain a complete picture of the condition of outdoor sports shoes, and the possibility of an automatic scanning procedure based on inverse kinematics using a robotic arm.  
Figure 14: Time needed for automated scanning with 3D handle scanner for footwear type B.  
Figure 12: Time needed for automated scanning with 3D handle scanner for footwear type A.  
Figure 13: Virtual simulation for an automated scanning with 3D handle scanner for footwear type B.  
In fact, the presented inspection technique offers the possibility to study the condition of sports shoes as a whole and not only in specific points or target surfaces, in order to improve the data on their condition.  
Based on the original 3D models of footwear used in indoor sports, it is possible to superimpose the scanned model with the original one, in order to measure the geometrical discrepancies, representing wear and surface deterioration.  
Automated 3D scanning is a complex task that involves a combination of hardware and software, which saves time and increases the number of objects that can be scanned with a high degree of accuracy and precision.  
The mechanical arm would have a planar motion to follow the trajectory and to scan different parts of the object. The research in this paper is concerned with the optimization of the hand scanning method and the use of a mathematical model to generate 3D scanning strategies on equipment intended for indoor sports with a focus on shoes used in handball matches. However, few papers have dealt with the generation of scanning paths on indoor sports footwear.  
Direct kinematics is a mathematical technique used to determine the position and orientation of a 3D hand scanner given the joints and displacements of an automated arm.  
In the context of automated scanning, inverse kinematics can be used to determine the joint configurations required for the 3D hand scanner to reach a particular target point in space.  
In order to automate the scanning process using a 3D hand scanner using inverse kinematics, the chord system for each joint of the arm is defined, as well as the scanner.  
The novelty of this article consists of generating the direct and inverse kinematics of a robotic arm in order to optimize the scanning process for footwear used in indoor sports, based on which a simulation was performed to determine the minimum and maximum trajectory depending on the angles presented having the mathematical model as a source.  
The direct arm and the inverse kinematic model were defined taking into account the constraint that the last segment of the arm (\(\mathbb{I}_{3}\), represented in Figures 8 and 9) has to be perpendicular to the circular trajectory. The mathematical model was deduced based on the arm geometry completed with the constraint that the scanner has to face the scanned objects on the whole trajectory.