Cable transmission has significant advantages in the development of a surgical robot which is fully magnetic resonance imaging (MRI) compatible and can work dexterously in the very limited space inside MRI core. However, apart from the nonlinearities due to friction and cable compliance present in the traditional steel cables, the MRI compatible polymeric cables also suffer from the significant viscoelastic behavior. Previous work in cable-conduit actuation modeling only addresses the transmission in elastic cables and ignores complex direction and time dependent nonlinear viscoelastic behavior of cable-conduits. These effects need to be characterized for system design and nonlinearity compensation. In this paper, an analytical model using standard linear solid model and Coulomb friction is developed to study the transmission characteristics of such a system. The model has been validated by experiments using dyneema cables passing through PEEK conduits, predicting motion and torque transmission with error levels of 3.38% and 16.16%, respectively. The effect of cable viscoelasticity is studied utilizing the model, and corresponding results are compared with that of an elastic cable.

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