Current trunk-like continuum robots face limitations in actuator capabilities, hindering the realization of adjustable multi-turn helical deformations. In our previous research [1], [2], we proposed the Twisted String and Spiral Hose (TSSH) mechanism, which utilizes both the tensile and torsional forces of twisted string actuators (TSAs) to generate helical deformations. However, the deformation principles of the TSSH mechanism remain not fully understood, motivating further investigation. The main contribution of this study is the analysis of TSSH deformation principles using a conventional mathematical model of twisted strings, supported by experimental validation. Building on this analysis, we developed a static simulation model based on potential energy minimization to predict TSSH deformation. The proposed model provides insights into the deformation behavior of the TSSH mechanism, enabling parameter optimization for enhanced performance. Furthermore, this static analysis can be extended to other TSA-based and tendon-driven systems, providing a valuable reference for string-actuated robotic mechanisms.

A method is proposed to predict the shape of a paper model of a three piece brassiere cup, which consists of several cloth and wire parts. Currently, the shape of each part is determined by creating a paper model and then refining the model. This process is repeated until the desired shape is achieved. However, predicting the 3D shape with a simulation would improve design efficiency. As a model is made of paper, each part is assumed to be inextensible and its surface is represented as combination of developable surfaces. The potential energy of a cup and geometric constraints imposed on the cup are formulated by use of the normal curvature and the direction of a generatrix of each developable surface. Minimizing the potential energy under geometric constraints derives a stable shape of the cup model. The computed and measured cup shapes coincided qualitatively.

A method to generate an appropriate path for manipulation of a belt object is proposed. It is important for automatic manipulation of a belt object such as a film/flexible circuit board to generate an appropriate path for a manipulator because such object is flexible in a certain direction but fragile in another direction and an inappropriate path which causes deformation in the fragile direction may lead to wiring disconnection. First, deformation of a rectangular belt object is modeled considering its bending and torsional deformation under the force of gravity. Next, a method to generate a path for belt object manipulation with quasi-static and non-excessive deformation is proposed. After that, deformation and loaded condition in the path generated by our proposed method and those in a common path based on linear interpolation are compared. Finally, the validity of our proposed method is verified by measuring the deformed shape of a polyethylene sheet during manipulation with the generated path.

A differential geometry based modeling of a belt object to represent its deformation path is proposed. Adequate deformation path of a belt object such as film circuit boards or flexible circuit boards must be generated for automatic manipulation and assembly. First, deformation of a belt object is described using the curvature of its central axis, torsion around the central axis and the curvature in the transverse direction. Second, a method to derive an adequate transition of the object shape from the initial state to the final state is proposed. It can be derived by minimizing the maximum of the local potential energy in the belt object during its manipulation. This is because locally excessive potential energy often leads to the excessive stress that makes fractures in the belt object. Finally, the validity of our proposed deformation path is verified by estimating the maximum local potential energy in a belt object.

A differential geometry based modeling to represent belt object deformation is proposed. Deformation of a belt object such as film circuit boards or flexible circuit boards must be estimated for automatic manipulation and assembly. First, the fishbone model to describe deformation of a rectangular belt object is explained. In this model, the object shape is represented by the curved ldquospine linerdquo and straight ldquorib linesrdquo. We can estimate deformation of the object by minimizing its potential energy under geometric constraints. Next, this model is modified to represent deformation in which the rib line at an endpoint does not coincide with the transverse edge. Moreover, the modified model is applied to a belt object with angles. The deformed shape of an angled object can be derived by separating it into rectangular parts and angled parts and by assuming that each angled part forms a part of a cylindrical surface. Finally, the validity of our proposed model is verified by comparing the computed shape of an L-shaped belt object with its measured shape.

This paper describes the dynamic modeling of linear object deformation considering geometrical constraints and contact with obstacles. Deformable linear objects such as cables and strings are widely used in our daily life, some industries, and medical operations. Modeling, control, and manipulation of deformable linear objects are keys to many applications. We have formulated the static deformation of a linear object using the differential geometry coordinates. In this paper, we apply differential geometry coordinates to the dynamic modeling of linear objects. First, we formulate dynamic 2D deformation of an inextensible linear object based on a differential geometry coordinate system. Second, we consider dynamic deformation of the linear object when forces/moments and geometrical constraints are imposed on the object. Third, we model contact of a linear object with a circular obstacle. It can be applied to self-contact of the linear object. Finally, we show simulation results using the proposed modeling technique

A planning method for unraveling manipulation of deformable linear objects is proposed. In manipulation of a linear object, its raveling must be avoided. It takes much time to unravel it once it is raveled. Therefore, it is important to generate unraveling plans efficiently. First, a manipulation process of a linear object including its unraveling is represented as a sequence of its crossing state transitions. Then, possible manipulation processes can be generated once the initial and the objective crossing states are given. Second, qualitative actions to realize manipulation processes are determined. Third, a method for unraveling a linear object as far as possible when its crossing state can not be identified completely is proposed. Finally, an example of unraveling process generation is demonstrated

A planning method for unraveling deformable linear objects based on 2D information about their crossing states is proposed. In manipulation of a linear object, its raveling must be avoided. It takes much time to unravel it once it is raveled. Therefore, it is important to generate unraveling plans efficiently. First, an unraveling process of a linear object is represented a sequence of crossing state transitions. It can be generated on a computer if 3D information about the current crossing state is given. Second, the crossing sequence of a linear object, which corresponds to its 2D information, is categorized into two types: unravelable and not-unravelable. Third, a procedure to generate efficient unraveling processes based on unravelability of the crossing sequence is explained. Finally, examples of unraveling process generation with our developed system are demonstrated

A planning method for knotting/unknotting and tightening manipulation of deformable linear objects is proposed. It is important for linear object manipulation in industrial/medical field to analyze knotting. Modeling of knotting/unknotting process is useful for design of knotting/unknotting system with different mechanism from human arms/hands and manipulation planning suitable for such system. Firstly, knotting/unknotting processes of a linear object is represented as a sequence of finite crossing state transitions. Secondly, grasping points and their moving direction to perform each state transition are defined. Then, possible qualitative manipulation plans can be generated on a computer system once the initial state and the objective state of a linear object are given. Thirdly, a planning method for tightly tying is proposed. Pulling parts for tightening knots can be determined by using this method. Finally, an experiment for tying an overhand knot by our developed system is shown.

This paper describes the dynamic modeling of linear object deformation based on differential geometry coordinates. Deformable linear objects such as cables and strings are widely used in our daily life, electric industries, medical operations. Modeling, control, and manipulation of deformable linear objects are keys to many applications. We have proposed the differential geometry coordinates to describe the 2D/3D deformation of a linear object with the minimum number of parameters. Based on this description, we have formulated the static deformation of a linear object using the differential geometry coordinates but the dynamic deformation has not been investigated yet. In this paper, we apply differential geometry coordinates to the dynamic modeling of linear objects. First, we formulate the dynamic 2D deformation of an inextensible linear object based on a differential geometry coordinate system. Second, we show simulation results using the proposed modeling technique. Next, we apply the proposed dynamic modeling to the control of a flexible link.

A planning method for linear object manipulation including knotting/unknotting by one hand is proposed. Firstly, topological states of a linear object are represented as finite permutations of crossing points. Secondly, transitions among topological states are defined. Then, we can generate possible sequences of state transitions, that is, possible manipulation processes from the initial state to a given objective state. Thirdly, a method for determination of grasping points and their moving direction is proposed in order to realize derived manipulation processes. Furthermore, a planning method for one-handed manipulation is proposed. Knotting by one hand is possible as any manipulation processes can be realized by iteration of one-handed operations. Finally, it is demonstrated that our developed system based on the above method can generate manipulation plans for raveling out of an overhand knot.

A planning method for linear object manipulation including knotting/raveling in the three-dimensional space is proposed. Firstly, topological states of a linear object are represented as finite permutations of crossing points including the crossing type of each crossing point. Secondly, transitions among the topological states are defined. They correspond to operations that change the number of crossing points or crossing point permutation. Then, we can generate possible sequences of crossing state transitions, that is, possible manipulation processes from an initial state to a given objective state. Thirdly, a method for determination of grasping points and their moving direction is proposed in order to realize derived manipulation processes. Furthermore, criteria for evaluation of manipulation processes are introduced in order to reduce the candidates of manipulation plans. Finally, it is demonstrated that our developed system based on the above method can generate manipulation plans for raveling from an overhand knot.

A systematic approach to the modeling of deformable rodlike objects is presented. Various rodlike objects such as cords and wires are manipulated in many manufacturing processes. In such processes, it is important for successful manipulation to evaluate their shapes on a computer in advance because their shapes can be changed easily and their deformation often shows hysteresis properties. In this paper, we develop an analytical method to model the shape of deformable rodlike objects including hysteresis properties. First, we investigate the mechanism of hysteresis. Second, the potential energy of a rodlike object and the geometric constraints imposed on it are formulated. The shape of the object can be derived by minimizing the potential energy under the geometric constraints. Thirdly, a procedure to compute the shape of a deformed rodlike object is developed by applying a non-linear programming technique. Finally, we show some numerical examples with hysteresis using our proposed method.

In manufacturing processes, there are many manipulative operations which deal with deformable objects. In this paper we analyse the dynamic motion analysis of deformable rodlike objects. First, a geometric representation to describe the shape of a rodlike object with dynamic deformation is introduced. The potential and kinetic energy of the object and the geometric constraints imposed on it are then formulated. The shape of the dynamically deforming object can be derived by minimizing the difference between the kinetic energy and potential energy under the geometric constraints. Next, a procedure to compute the deformed shape is developed by use of Euler's approach. Finally, some numerical examples are shown in order to demonstrate how the proposed approach computes the shapes of deformed rodlike objects.

A static analysis of deformable object grasping based on bounded force closure is presented. There are many manipulative operations that deal with deformable objects in manufacturing processes. Manipulative operations for these objects are often performed by utilizing their deformation actively while the operations may result in failure because of unexpected deformation of the objects during the manipulation process. In order to perform the manipulative operations for deformable objects successfully, it is necessary to evaluate their deformation by building object models and to derive task strategies by analyzing manipulation processes using the object models. In this paper, we will analyze stable grasping of deformable objects based on the concept of bounded force closure. Firstly, we will introduce the concept of bounded force closure, which is an extension of force closure condition. Secondly, we will investigate the necessary condition for bounded force closure in order to derive the properties of bounded force closure grasping. Thirdly, we will formulate the deformation of linear objects as an example of deformable objects and we will propose a procedure to evaluate stability of deformable object grasping. Finally, some numerical examples will be shown in order to demonstrate the effectiveness of our proposed method.

Various deformable objects are manipulated in many manufacturing processes. Deformation of these objects is often utilized in order to manipulate them successfully while the manipulation sometimes fails because of unexpected deformation of the objects. Modeling of deformable objects is thus required so that the shape of the objects can be evaluated on a computer in advance. In this paper, we develop an analytical method to model the shape of a deformable linear object such as cords and tubes. First, a geometric representation to describe the shape of a linear object with bending and torsional deformation is introduced. The potential energy of the object and the geometric constraints imposed on it are then formulated. The shape of the object in the stable state can be derived by minimizing the potential energy under the geometric constraints. Next, procedure to compute the deformed shape is developed by applying a nonlinear programming technique. Finally, some numerical examples are shown in order to demonstrate how deformed shapes of linear objects are computed using the proposed approach.

Various deformable parts such as cords, leather products, and sheet metals are manipulated and are handled in many manufacturing processes. Deformation of these parts is often utilized in order to manipulate them successfully while the manipulation sometimes fails because of unexpected deformation of the parts. Modeling of deformable objects is thus required so that the shape of the soft parts can be analyzed and evaluated on a computer. In this paper, we develop an analytical method to model the shape of a deformable object. Especially, we deal with deformation of a bendable thin object. The process of manipulating a deformable object is analyzed with regard to how the object interacts with other objects around it. The model of a bendable thin object is formulated according to the principle that the potential energy of the object reaches the minimum at its stable shape. An algorithm to compute the deformed shape of the object is developed by applying a nonlinear programming technique. Finally, a simple experiment is done to demonstrate the validity of the modeling method proposed in this paper.>