Grasping objects by continuum arms or fingers is a new field of interest in robotics. Continuum manipulators have the advantages of high adaptation and compatibility with respect to the object shape. However, due to their extremely nonlinear behavior and infinite degrees of freedom, continuum arms cannot be easily modeled. In fact, dynamics modeling of continuum robotic manipulators is state-of-the-art. Using the exact modeling approaches, such as theory of Cosserat rod, the resulting models are either too much time-taking for computation or numerically unstable. Thus, such models are not suitable for applications such as real-time control. However, based on realistic assumptions and using some approximations, these systems can be modeled with reasonable computational efforts. In this paper, a planar continuum robotic arm is modeled, considering its backbone as two circular arcs. In order to simulate finger grasping, the continuum arm experiences a point-force along its body. Finally, the results are validated using obtained experimental data. 1. Introduction Continuum robotic arms are typically made of a flexible backbone, which gives them infinite degrees of freedom. Thus, these robots are hyperredundant, compatible, and underactuated [1]. Continuum robots are inspired by biological manipulators, such as octopus arms, mammalian tongues, and elephant trunks [2] and are close to ordinary hyperredundant manipulators, such as snakes and spines [3–5]. Due to their special characteristics, continuum robots can perform a variety of tasks, such as dexterous manipulation [6, 7], whole arm grasping [8, 9], and ordinary underactuated grasp [10]. One of our continuum robots is depicted in Figure 1, as an example of continuum fingers. The finger consists of a flexible backbone and a tendon driven actuation system. The actuation system consists of the cable-guide disks and the tendons. When a tendon is pulled, the backbone is bent towards the tendon. Thus, using three cables, the backbone can be bent in any direction. Modeling the nonlinear dynamics of such continuum robots is essential for performing precise grasp analysis, optimization, and control. Besides accuracy, it is important that a model can be performed fast enough for real-time applications [4]. Figure 1: Object grasping by KNTU hand. Regarding continuum robots dynamics, the first work was presented by Chirikjian, using modal approach to model hyperredundant manipulators, considered as continuum arcs [11, 12]. The first exact continuous model for continuum robotic arms was introduced by Mochiyama and
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