The Lateral Reaction of a Deformable Inclined Surface on a Wheel with an Elastic Trunk

Problem statement: This study is concerned with a very important problem belonging in the effects of deformable inclined surfaces on a wheel with an elastic trunk. These effects can be represented by two effects: A lateral withdrawal of the trunk and lateral shift of the ground. Also this study aims to study these effects and analyze them mathematically to find a mathematical relation describes them. Approach: A free body diagram of the wheel which represented all forces affected is drawn then starting with the lateral component all angles are calculated, then by building a relations between these different angles and forces, the final relation is derived mathematically which describes the total deformation of the trunk. Results: It was found that inclination angle of the wheel with inclined surface has a nonlinear positive relationship with both trunk deformation and the displacement in x-direction. On the other hand the relation between the inclination angles with both rigidity factor of the trunk and ground volumetric factor is a non-linear negative relationship. Conclusion/Recommendations: The inclination angle was decreasing as both rigidity and ground volumetric factors are increasing. Inclination angle was increasing with the increase in both displacement (x) and trunks' deformation values. The study of trunk deformation was very important since it will lead to reconstruct the wheel system in the future to get more efficient system, and the slipping phenomenon will be easily analyzed in the future.