The load distribution among three legs on the wall: model predictions for cockroaches

摘要

In a former study on terrestrial locomotion of cockroaches in the sagittal plane, it was hypothesised that the ground reaction force distribution among three legs synchronously in contact with a substrate is predominantly explained by joint torque minimisation within all three legs. We verified this hypothesis with a simple mechanical model in two dimensions, consisting of one body and three mass-less legs. Hereto, we calculated force distributions resulting from different optimisation criteria for varying slope angles of the substrate. We compared these distributions to each other and the few experimental findings available. We found that, for any slope angle, the force distribution rather seems to be derived from the fundamental "table" solution, i.e. equalised vertical and vanishing horizontal components (equivalent to pure force minimisation at zero slope), than from pure torque minimisation. For cockroaches, the "table" solution is likely to be modified by torque minimisation within the leading and the trailing leg. We demonstrate that the minimisation of leg forces and of interaction forces is fully equivalent. Moreover, our model predicts the force distribution for arbitrary slope angles. Based on our model calculations, we speculate that in terrestrial locomotion, some animals may rely on spring-mass model dynamics whatever slope angle to be overcome. This might only become evident when focusing movement analyses strictly on a gravity rather than on a substrate-based coordinate system.