RHex is an autonomous hexapedal robot capable of locomotion on rough terrain. Up to now, most modelling and simulation efforts on RHex were based on the linear leg assumption. These models disregarded what might be seen as the most characteristic feature of the latest iterations of this robot: the half circular legs. This thesis focuses on developing a more realistic model for this specially shaped compliant leg and studying its effects on the kinematics and dynamics of the resulting platform. One important consequence of the half circular compliant leg is the resulting rolling motion. Due to rolling, the rest length of the leg changes and the leg-ground contact point moves. Another consequence is the varying stiffness of the legs due to the changing rest length. These effect the resulting behaviour of any platform using these legs. In the first part of the thesis we are studying the effects of the half circular leg morphology on the kinematics of RHex using a simple planar model. The rest of the studies within the scope of this thesis focuses on the effect of the half circular compliant legs on the dynamics of a single legged hopping platform with a point mass. The formulation derived in this work is successfully integrated in a readily working but rather simple model of a single legged hopping system. We replace the equations of the straight leg in this model by the equations of the half circular compliant leg. Realistic results are obtained in the simulations and these results are compared to those obtained by the simpler constant stiffness straight leg model. This more realistic leg model brings us the opportunity to further study the effects of this leg morphology, in particular the positive effects of the resulting rolling motion on platform stability.