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In this study, a modified method has been introduced for forward dynamic analysis of fast parallel robots. For this purpose, inspired by the Lagrange-Virtual Spring (LVS) method, the Decoupled Natural Orthogonal Complement (DeNOC) method is modified which is a Newtonian based method. So far, virtual springs have been already used in energy based methods. However using the virtual springs in DeNOC method is a novel approach which is proposed in current study. In order to clarify the advantages of Modified Decoupled Natural Orthogonal Complement (MDeNOC) method, a planar 3RRR mechanism is chosen as case study. According to the results, the process of deriving the equations of motion is much less costly while the accuracy of MDeNOC is similar to the LVS and unlike the energy methods, the modified method is also able to calculate the constraint reactions, as well. On the other hand, the calculation time of MDeNOC is much more than the DeNOC and hence, is not suitable for real time calculations. Also, in closed loop systems, constraints must be defined in such a way that express the virtual springs’ longitudinal changes; otherwise, MDeNOC will not give proper results.

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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.