geometrical constraint
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2022 ◽  
pp. 1-10
Author(s):  
Yohei Yamamoto ◽  
Jun Mitani

Abstract Origami techniques, as folding and unfolding, can be utilized in shrinkable structures. Especially when the crease pattern is rigid foldable, it can be treated as a mechanical linkage of rigid panels connected by hinges. Since rigid foldable crease patterns have the strong geometrical constraint of the facets not being able to stretch or bend, it is difficult to design new crease patterns, and variations of existing patterns are limited. However, it is known that there are cases where crease patterns can be made rigid foldable by adding some slits. This paper proposes a mechanical linkage that folds into a similar flat shape by adding slits. A method is presented of generating rigid foldable crease patterns in arbitrary polygons that fold smaller, and it is confirmed that structures that have a mechanism for shrinking can be generated from these crease patterns by using rigid thick panels and hinges.


2021 ◽  
Author(s):  
Takayuki Yamada ◽  
Yuki Noguchi

Abstract This paper proposes a topology optimization method that considers the geometrical constraint of a non-closed hole for additive manufacturing based on the fictitious physical model concept. First, the basic topology optimization concept and level set-based method are introduced. Second, the concept of a fictitious physical model for geometrical constraint in the topology optimization framework is discussed. Then, the model for the geometrical constraint of a non-closed hole for additive manufacturing is proposed. Numerical examples are provided to validate the proposed model. In addition, topology optimization considering this geometrical constraint is formulated, and topology optimization algorithms are constructed using the finite element method. Finally, optimization examples are provided to validate the proposed topology optimization method.


2021 ◽  
Author(s):  
Yohei Yamamoto ◽  
Jun Mitani

Abstract Origami techniques, as folding and unfolding, can be utilized in shrinkable structures. Especially when the crease pattern is rigid foldable, it can be treated as a mechanical linkage of rigid panels connected by hinges. Since rigid foldable crease patterns have the strong geometrical constraint of the facets not being able to stretch or bend, it is difficult to design new crease patterns, and variations of existing patterns are limited. However, it is known that there are cases where crease patterns can be made rigid foldable by adding some slits. This paper proposes a mechanical linkage that folds into a similar flat shape by adding slits. A method is presented of generating rigid foldable crease patterns in arbitrary polygons that fold smaller, and it is confirmed that structures that have a mechanism for shrinking can be generated from these crease patterns by using rigid thick panels and hinges.


Author(s):  
Hao Wu ◽  
Rong Yu ◽  
Jing Zhu ◽  
Wei Chen ◽  
Yadong Li ◽  
...  

Multiple twinned structures are common in low-dimensional materials. They are intrinsically strained due to the geometrical constraint imposed by the non-crystallographic fivefold symmetry. In this study, the strain distributions in sub-10 nm fivefold twins of gold have been analyzed by combining aberration-corrected transmission electron microscopy and first-principles calculations. Bending of atomic planes has been measured by both experiments and calculations, and its contribution to the filling of the angular gap was shown to be size-dependent.


2020 ◽  
Vol 54 (5) ◽  
pp. 1369-1384
Author(s):  
Xiangkai Sun ◽  
Xian-Jun Long ◽  
Liping Tang

This paper deals with some new versions of Farkas-type results for a system involving cone convex constraint, a geometrical constraint as well as a fractional function. We first introduce some new notions of regularity conditions in terms of the epigraphs of the conjugate functions. By using these regularity conditions, we obtain some new Farkas-type results for this system using an approach based on the theory of conjugate duality for convex or DC optimization problems. Moreover, we also show that some recently obtained results in the literature can be rediscovered as special cases of our main results.


2019 ◽  
Vol 9 (21) ◽  
pp. 4491 ◽  
Author(s):  
Xu Liang ◽  
Tingting Su

A new trajectory planning approach on the basis of the quintic Pythagorean–Hodograph (PH) curve is presented and applied to Delta robot for implementing pick-and-place operation (PPO). To satisfy a prescribed geometrical constraint, which indicates the distance between the transition segment curve and right angle of PPO trajectory is no greater than a prescribed value, the quintic PH curve is used to produce a connection segment path for collision avoidance. The relationship between the PH curve and constraint is analyzed, based on which PH curve is calculated simply. Afterwards, the trajectory is planned in different phases with different motion laws, i.e. polynomial motion laws and PH curve parameter-dependent motion laws, to obtain a smooth performance both in Cartesian and joint space. The relationship between the PH curve and constraint is also used to improve the efficiency of calculation, and the trajectory symmetry is used to reduce calculation time by direct symmetric transformation. Thus, real-time performance is improved. The results of simulations and experiments indicate that the approach in this paper can provide smooth motion and meet the real-time requirement under the prescribed geometrical constraint.


Sensors ◽  
2019 ◽  
Vol 19 (16) ◽  
pp. 3517
Author(s):  
Zheng Ji ◽  
Yifan Liao ◽  
Li Zheng ◽  
Liang Wu ◽  
Manzhu Yu ◽  
...  

The intelligent inspection of power lines and other difficult-to-access structures and facilities has been greatly enhanced by the use of Unmanned Aerial Vehicles (UAVs), which allow inspection in a safe, efficient, and high-quality fashion. This paper analyzes the characteristics of a scene containing power equipment and the operation mode of UAVs. A low-cost virtual scene is created, and a training sample for the power-line components is generated quickly. Taking a vibration-damper as the main object, an assembled detector based on geometrical constraint (ADGC) is proposed and is used to analyze the virtual dataset. The geometric positional relationship is used as the constraint, and the Faster Region with Convolutional Neural Network (R-CNN), Deformable Part Model (DPM), and Haar cascade classifiers are combined, which allows the features of different classifiers, such as contour, shape, and texture to be fully used. By combining the characteristics of virtual data and real data using UAV images, the power components are detected by the ADGC. The result produced by the detector with relatively good performance can help expand the training set and achieve a better detection model. Moreover, this method can be smoothly transferred to other power-line facilities and other power-line scenarios.


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