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Accuracy and numerical calculation time are the two main challenges of continuum robots dynamics modeling. In fact, the numerical calculation times of exact models are so long, that they are not practical in applications such as real-time control. This paper presents a new method for dynamics modeling of continuum robot backbones. In this method, the backbone shape is considered as an arbitrary number of constant-curvature (circular arc) elements, and the dynamics model is derived using Lagrange energy methods. First, kinetics and kinematics of one element are derived. Then, the robot kinematics is derived, as a series of such elements. Finally, the robot dynamics model is derived, using Euler-Lagrange method. This paper is focused on dynamics of the flexible body of continuum robots, and the proposed model is independent of actuation systems. Besides, the numerical singularity of the constant-curvature elements is avoided, which occurs when an element is straight. The model is validated using experimental results. Comparison of simulation and experimental results shows the accuracy of the proposed method on dynamics modeling. Furthermore, the calculation time of the model is short enough to make it practical for applications such as real-time control.

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Origami, as a paper folding art and Japanese culture, has been utilized broadly in engineering areas. The exclusive features of origami such as negative Poisson’s ration, lightweight, deployable and so forth, can be considered in the design of deployable space structures, expandable shelters, drug delivery, and robots. In this study, firstly, the continuum robot with six serial modules of origami parallel structure as its skeleton and the helical springs as the compliant backbone is studied, and constant curvature kinematics was implemented in order to simplify and approximate the kinematic model. Accordingly, the kinematic model of one module was derived. Then, the robot kinematics was obtained as a series of mentioned modules. Furthermore, the proposed continuum robot was modeled by an equivalent mechanism, and a comparison was conducted between the methods to obtain a workspace. Based on the results, the modeling of the equivalent mechanism has an advantage in terms of calculation's volume compared to the constant curvature method and the workspace obtained from both methods was the same. The Jacobian matrix was obtained through the constant curvature approximation methods, which can be considered for singularity analysis in specific conditions and the analysis reveals that the singularities occur when the curve and radius are equal and symmetry is created and the other is when the radius is equivalent to zero. The paper concludes a perspective on several of the themes of current research that are shaping the future of origami-inspired robotics.