A geometric constraint solver for 3-D assembly modeling

In this paper, we propose a geometric constraint solver for 3-D assembly applications. First, we give a new geometry and constraint expression based on Euler parameters, which can avoid singular points during the solving process and simplify constraint types. Then we present a directed graph based constructive method to geometric constraint system solving that can handle well-, over- and under-constrained systems efficiently. The basic idea of this method is that it first simplifies the constraint graph by pruning those vertices which have only in-arcs from the graph and then reduces the size of strongly connected components (SCCs) left in the graph by DOF-based analysis. The method can solve all kinds of configurations including closed-loops. After that, we apply a hybrid numerical method of Newton–Raphson and Homotopy to solve under-constrained systems. The hybrid method makes use of the high efficiency of the Newton–Raphson method as well as the outstanding convergence of the Homotopy method. Finally, we give a practical example and conclusion.     

Solving 3D Geometric Constraints for Assembly Modelling

A geometric constraint solving method is presented that takes well-constrained mating conditions between a base and a mating component and directly transforms them into a 4 × 4 matrix that determines the relative orientation and location of the mating component with respect to the base component. In the proposed procedure, the 4 × 4 transformation matrix is determined by directly computing a rotation matrix TR and a translation matrix TL that define the relative orientation and location of the mating component, respectively. Thus, first, the rotation matrix is computed by solving a set of linear constraint equations associated with the orientation of two mating components. After repositioning the mating component by applying the rotation matrix TR, the translation matrix is calculated by solving a set of linear constraint equations associated with location. This new method is computationally very effective, since the transformation matrix for relative orientation and location of the mating component is algebraically derived directly from the linear equations associated with the mating conditions.     

Singularity analysis of parallel manipulators using constraint plane method

One of the most challenging problems in dealing with parallel manipulators is identifying their forward singular configurations. In such configurations these mechanisms become uncontrollable and cannot tolerate any external force. In this article a geometrical method, namely Constraint Plane Method (CPM), is introduced with the use of which one can easily obtain the singular configurations in many parallel manipulators. CPM is a methodical technique based on the famous Ceva plane geometry theorem. It is interesting to note that CPM involves no calculations and yields te result quickly. In addition, some of the previous geometrical methods led to many separate singular configurations; however, CPM yields the answer in just one phrase. In this article we have obtained singular configurations of some parallel manipulators. Moreover, a comparison is made between CPM and the previous methods to show the advantages of CPM.     

The comparison of joint kinematic error using the absolute and relative coordinate systems for human gait

Minimizing artifacts from skin movement is vital for acquiring more accurate kinematic data in human movement analysis. There are several stages that cause skin movement artifacts and these stages depend on the selection of the reference system, the error reduction method and the coordinate system in clinical gait analysis. Due to residual errors, which are applied to the Euler and Bryant angle methods in each stage, significant cumulative errors are generated in the motion analysis procedure. Thus, there is currently a great deal of research focusing on reducing kinematic errors through error reduction methods and kinematic error estimations in relation to the reference system. However, there have been no studies that have systematically examined the effects of the selected coordinate system on the estimation of kinematic errors, because most of these previous studies have been mainly concerned with the analysis of human movement using only the human models that are provided in the commercial 3D motion capture systems. Therefore, we have estimated the differences between the results of human movement analyses using an absolute coordinate system and a relative coordinate system during a gait, in order to establish which system provides a more accurate kinematic analysis at the ankle joint. Six normal adult subjects with no neurological or orthopedic conditions, lower extremity injuries, or recent history of lower extremity surgery were used in this study. The analysis was conducted at a walking speed of 1.35m/s. For the clinical estimation, we used a cardinal plane based on the segmental reference system and the differences were plotted on the planes. From this analysis, when a relative coordinate system was in the gait analysis, the average kinematic error occurring during the gait was determined to be 13.58mm, which was significantly higher than the error generated with an absolute coordinate system. Therefore, although the relative coordinate system can also be used to calculate the ankle joint center during the clinical gait analysis, the absolute coordinate system should be employed in order to obtain more accurate joint kinematic data. In addition, the results from this study can be used as a basis to select an appropriate coordinate system with regards to the diagnostic accuracy level required for various kinds of gait disorders. This paper was recommended for publication in revised form by Associate Editor Hong Hee Yoo Yong Hoon Rim received his B.S. and M.S degrees in Bio-Mechatronic engineering from Sungkyunkwan University in 2002 and 2004, respectively. Yong Hoon Rim is currently a Researcher at the Bio-Mechatronics center and also a candidate in the biomedical Ph.D. program at Sungkyunkwan University, Korea. His research interests are in the area of digital human modeling, workspace optimization and ergonomics in digital factory. Ahn Ryul Choi received his B.S. and M.S. degrees in Bio-Mechatronic engineering from Sungkyunkwan Univer-sity in 2005 and 2007, respectively. Ahn-Ryul Choi is curr-ently a Researcher at the Bio-Mechatronics center and also a candidate in the biomedical Ph.D. program at Sungkyunkwan University, Korea. His research interests are in the area of digital human modeling and simulation. Sang Sik Lee received his Ph.D. degree from Sungkyun-kwan Universi-ty in 2000. He is currently serving as a research professor at the Bio-Mechatronics center in Sungkyunkwan University. His research interests are in the area of digital human modeling and industrial ergonomics. Kyoung Kee Min received his Ph.D degree Sungkyunkwan University in 2008. Dr. Min is currently a researcher at the Bio-Mechatronics Center in Sungkyunkwan University. Dr. Min’s research interests are in the area of disease classification using artificial neural network, digital human modeling & control. Dong Hyuk Keum received his Ph.D. degree from Seoul National University in 1979. Dr. Keum is currently a Professor at the Department of Bio-Mechat- ronic engineering at Sungkyun-kwan University, Korea. He is currently serving as the chief of an evaluation committee of the Rural Development Administrator. Dr. Keum’s research interests are in the area of simulation of post-harvest systems, quality evaluation of food materials and the processing technology. Chang Hyun Choi received his Ph.D. degree from Iowa State University in 1988. Dr. Choi is currently a Professor at the Department of Bio-Mechatronic Engineering at Sungkyunkwan University, Korea. He is currently serving as an evaluation committee of the Rural Development Administration, Korea and Korea Industrial Technology Foundation. Dr. Choi’s research interests are in the area of nondestructive quality evaluation of foods, and automatic control of off-road machinery. Joung Hwan Mun received his Ph.D. degree majoring in mechanical engineering from the University of Iowa in 1998. Dr. Mun is currently a Professor at the Department of Bio-Mechat-ronic engineering at Sungkyun-kwan University in Suwon, Korea. He is currently serving as a director of the Bio-Mechatronics center with regard to an international IMS project. Dr. Mun’s research interests are in the area of digital human modeling, sports biomechanics, bio-electronics and digital factory for human oriented production system.     

Geometric non-linear analysis of thin flat plates under end shortening, using different versions of the finite strip method

Two finite strip methods are developed for predicting the geometrically non-linear response of rectangular thin plates with simply supported ends when subjected to uniform end shortening in their plane. Although the formulations of both finite strip methods are based on the concept of the principle of minimum potential energy, the first finite strip method utilizes a semi-energy finite strip, whereas in the second finite strip method (which is designated by the name full-energy finite strip method) all the displacements are postulated by the appropriate shape functions. It is noted that in the semi-energy finite strip approach, the out-of-plane displacement of the finite strip is the only displacement which is postulated by a deflected form while the von Kármán's compatibility equation is solved to obtain the corresponding in-plane displacement forms. The developed finite strip methods are then applied to analyze the post-local-buckling behavior of some representative thin flat plates for which the results are also obtained through the application of finite element method, employing general purpose MSC/NASTRAN package. Through the comparison of results and the appropriate discussion, the knowledge of the level of capability of different versions of finite strip method is significantly promoted.     

Analysis of the three-dimensional lymphatic architecture of the periodontal tissue using a new 3D reconstruction method.

Few studies of lymphatic vessels have been reported because diacrisis of this vascular system is rare. A complete examination of diacrisis of venula is not yet possible even using recent enzyme-histochemical or immunohistochemical techniques. In this study, we examined a lymphatic vessel by serial sectioning from the afferent lymphatic of the lymph node to the periphery by three-dimensional observation using a three-dimensional reconstitution method. This method was conventional and accurate, and the time required for processing was markedly reduced by using a computer. Reconstitution of the vasculature became possible utilizing the entire section instead of a portion of a parenchymatous organ. We examined the lymphatic vessel architecture of various oral regions, including gingiva, tongue, and the floor of the mouth, using this method. In the future, using this method, we plan to investigate the alteration of lymphatic vessel architecture in a pathological region, and correlate these changes with the dynamics of lymphatic vessel absorption.     

A family of non-conforming crack front elements of quadrilateral and triangular types for 3D crack problems using the boundary element method

This study focuses on establishing non- conforming crack front elements of quadrilateral and triangular types for 3D crack problems when the dual boundary element method is applied. The asymptotic behavior of the physical variables in the area near the crack front is fully considered in the construction of the shape function. In the developed quadrilateral and triangular crack front elements, the asymptotic term, which captures the asymptotic behavior of the physical variable, is multiplied directly by the conventional Lagrange shape function to form a new crack front shape function. Several benchmark numerical examples that consider penny-shaped cracks and straight-edge crack problems are presented to illustrate the validity and efficiency of the developed crack front elements.