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This paper deals with cable-based motor-to-joint transmissions of multi-link robots chain. Their effects on robots flexibility have to be taken into account for modeling and control design. More in details, slack cables do not provide any force during compression (unlike springs), may present an initial nonzero elongation (preload) and, depending on the material, could exhibit non-constant stiffness. Those features may lead to non-trivial piece-wise elastic torques in a mechanical transmission. In this context, we present a framework to generate a more general (piece-wise) elastic torque model which can be embedded in the classical flexible-joint robot model, coherently with the Lagrangian approach. Moreover, we propose a model based on polynomial stiffness, whose parameters can be identified with ordinary least-squares techniques. Experimental results conducted on a flexible transmission show the usage and the utility of this work.

Gait alterations are among the most disabling motor-symptoms associated with Parkinson's Disease (PD): reduced stride length, stride velocity and lower limb joint range of motion are hallmarks of parkinsonian gait. Research focusing on optimal functional rehabilitation methods has been directed towards powered lower-limb exoskeletons which combines the advantages delivered from the grounded robotic devices with the ability to train the patient in a real-world environment.As gait involves both central (CNS) and peripheral nervous systems (PNS), targeted rehabilitation must restore not only mechanics but also neurophysiological gait patterns.