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.

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.

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.