We present the continuum model of a robot inspired by organisms like centipedes and polychaete worms. The continuum model is obtained as the limit of a rigid body chain with pinned elements, which leads to a Timoshenko beam model that is described by a one dimensional continuum with local Euclideian structure. The local Euclideian structure models the cross sections that are kinematically described by their position and orientation. The leg structures in the biological systems are modeled in the continuum limit as a distribution of compliant elements. Modal properties of the system are investigated. The compliance of the legs can be exploited for sensing purposes with specific application to the reconstruction of the surrounding environment and to the estimation of physical properties. The class of models in this papers applies to the continuum description of several emerging robotic application that range from tools for exploration in hazardous or generally not accessible environments (to humans) to novel healthcare systems as for example endoscopic tools for diagnostic in the gastrointestinal tract.

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