# Crouch Gait Analysis and Visualization Based on Gait Forward and Inverse Kinematics
## 5 Conclusions  
This paper presents a gait forward and inverse kinematics framework for modeling gait during walking for analysis and visualization purposes. Both methods are used to model an eight-DoF kinematic chain representing the lower limbs during the gait cycle. In addition, gait workspace and gait anatomical space analysis allows for establishing the normal gait ranges as the pattern to assess gait using objective metrics. We present an extended assessment for mild and severe crouch gaits in both the workspace and the anatomical space using statistical metrics, with the normal gait used as a reference. Depending on whether the aim of the analysis is diagnostic or rehabilitation assessment, any of these metrics could be used to classify gaits. The advantages of the proposed forward kinematics method using quaternions algebra is that is it scalable and useful for modeling kinematic chains, increasing the degrees of freedom, and avoiding gimbal lock and mathematical complexity. Reduction in mathematical and computational complexity as well as in the instrumentation required for data acquisition in the workspace is one of the main advantages of the approach for gait inverse kinematics presented here.  
A graphical comparison using the gait visualization framework for the seven events of the gait cycle for normal, mild, and severe crouch gaits was carried out. This is an important aspect for improving interpretation by specialists as well as the motivation of patients. The advantages of modeling and visualization following the approach proposed in this work as a future perspective offers an alternative approach to the development of a comprehensive exergaming rehabilitation platform. In addition, both virtual gaitvisualization feedback in real time for any patient and the anthropometry of the subject can be adjusted automatically.  
In future work, we intend to develop a three-DoF experimental platform to emulate and assess the gait cycle for different gaits in the sagittal plane. In addition, we plan to acquire the Cartesian coordinates for the eight degrees of freedom with a MoCap system for investigating real patients. Ultimately, we intend to develop a gait recognition framework based on the biomechanical modeling and metrics established in this paper.  
Conceptualization, J.-C.G.-I. and O.-A.D.-R.; methodology, J.-C.G.-I., O.-A.D.-R. and O.L.-O.; software, J.-C.G.-I. and O.-A.D.-R.; validation, O.-A.D.-R., O.L.-O. and J.-P.-O.-O.; formal analysis, J.P.-R. and F.M.G.; investigation, O.-A.D.-R.; resources, O.-A.D.-R.; data curation, J.-C.G.-I.; writing--original draft preparation, J.-C.G.-I. and O.-A.D.-R.; writing--review and editing, J.P.-R., [PERSON] and [PERSON]; visualization, [PERSON], [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data Availability Statement: Data available on request.  
The first author is grateful to CONACyT for granting the scholarship with application number: 2022-000002-01 NACF-07659. The second author thanks to the research direction of the Autonomous University of the State of Hidalgo.  
The authors declare no conflict of interest..