Mathematical modelling of the elastic deformation of rimless wheels for a scout rover

Abstract

In the present thesis, the mathematical modelling of the elastic deformation of a rimless wheel for a scout rover is performed. Thereby, the focus is on the elastic deformation of a single spoke. This spoke is supposed to be curved and compliant, moreover an external force is expected to impact on the spoke. To satisfy all of this, an Euler-Bernoulli cantilever beam is considered. In chapter 2 some assumptions for the mathematical modelling are stated to frame the problem. After that, the static elastic deformation of an initially straight Euler-Bernoulli cantilever beam is studied for small and large deformations in chapter 3. Thereafter the governing equation for the dynamic deformation of the intitially straight beam is stated and solved: First for the case that no external force is impacting on the beam by the method of separation of variables and after that the entire equation by Laplace transformations. Finally, in chapter 4 the elastic deformation of a beam that is curved at rest is studied. Therefore, the governing equation is deduced again, this time considering the curvature of the beam. This leads to a partial differerential equation of order six. Another approach is finally made by conformal mappings.