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This article provides a tutorial on the dynamic modeling of continuum robots. Continuum robots (CRs) have gained popularity in recent years due to their flexible backbone structure. Modeling and control of CRs motivate accurate and efficient dynamic models. Such models will enable simulation of dynamic behavior, improved structural design, and the development of dynamics-based control systems for CRs. As a unified underlying approach, the Cosserat rod-based modeling of tendon-driven CRs is used as the basis of the modeling techniques discussed in this paper. In addition to conventional continuum robot assemblies, new and emerging assemblies such as tendon-bent concentric tube and co-operative robots are also considered. The governing equations of motion for conventional CRs are first summarized and then extended for other tendon-driven CRs. This tutorial also contributes to developing a MATLAB code package for simulation of the dynamic response of these robots. The presented method and codes provide a useful and compact resource for readers and can be used for further development of tendon-driven continuum robots.

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In this article, a novel bi-directional shear mode magneto-rheological elastomer–based vibration isolator has been designed, fabricated, and characterized to improve the dynamic response and identification of this class of “intellectual” mechanical devices. A heuristic embodiment has been realized in order to design such an isolator wherein both the vertical and horizontal directions can be operated only in the shear mode not only individually but also simultaneously. Two fixtures have been designed for performing the characterization of the magneto-mechanical behavior of the proposed magneto-rheological elastomer isolator in the vertical and horizontal shear modes under wide ranges of strain amplitude (4%–32%), excitation frequency (1–8 Hz), and magnetic flux density (0–220 mT). Experimental results revealed maximum relative magneto-rheological effects of 35% and 27 % in the vertical and horizontal shear modes, respectively. Furthermore, basic mathematical models of single-degree-of-freedom systems, employing the magneto-rheological elastomer–based isolator in the vertical and horizontal shear modes, have been established. The proposed magneto-rheological elastomer isolator in the vertical mode exhibited natural frequency shift of 6.1% by a small increment in the magnetic flux density which approves the potential of the proposed bi-directional shear mode magneto-rheological elastomer–based vibration isolator for vibration control applications, such as seat suspension systems.