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.     

Generation of assembly models from kinematic constraints

In this paper, we propose a new joint-based assembly modeling method. In joint-based assembly modeling, the assembly constraints are specified on the components, but not on the geometric elements of the components. The proposed method generates assembly models from kinematic joint constraints by applying three procedures (1) to extract all feasible JMFs (Joint Mating Feature) for each mating component using information on joint constraints, (2) to derive mating alternatives for each pair of mating components after reducing the number of JMFs using the pruning criteria, and (3) to generate an assembly model by choosing the intended one from the mating alternatives for each pair of mating components and solving the JMF constraints. Since the joint constraints are expressed in terms of the relations between components rather than relations between geometric elements, the proposed method is more intuitive and natural for assembly modeling and supports modeling activities effectively by minimizing user interactions. By using joint mating constraints for assembly modeling, moreover, the kinematic behaviors of assemblies determined in the conceptual design stage can be directly applied and consistently maintained up to the detailed design stage. In the proposed method, it is also not necessary to re-input the mating constraints even when the component topology is changed.     

基于几何约束的平面连杆机构通用仿真软件设计

把平面连杆机构用"基本坐标"和"连杆约束"表达为最小二乘问题,通过求解非线性方程组的形式对连杆机构的几何约束进行求解,并采用可视化搭建结果和仿真状态结果作为迭代初值,很好的解决了一般方法对迭代初值的敏感性.最后在Matlab/GUI平台上开发出通用的仿真软件,并给出了几种常见连杆机构的仿真结果.     

基于计算几何的曲面造型方法研究

以Pro/Engineer和UGNX为代表的计算机辅助设计和辅助制造软件,在制造行业已经成为产品设计和产品制造工程师的重要工具。这些CAD/CAM软件都必须能够胜任曲面造型的功能,它是产品三维设计的必然前提,因此曲面造型成为计算机辅助几何设计和计算机图形学的一项研究重要内容,而计算几何正是对曲面造型进行研究的数学方法。通过对曲面造型和计算几何的相关概念的介绍,详细阐述了基于计算几何方法建立曲面参数曲线的各种数学建模过程。这些数学建模方法能为各种CAD/CAM系统实现曲面功能提供理论指导。     

基于多色集合的装配序列形式化推理方法

为减小装配序列的求解空间,提出了一种基于多色集合理论的装配序列的形式化推理方法,并建立了零件基本配合约束与自由度之间关系的多色集合矩阵.采用多色集合中的体与元素之间的模块布尔矩阵,描述产品的零件组与装配约束的对应关系,建立装配约束关系的方程组和联接件的装配数学模型,并给出求取约束关系方程组的算法.以装配约束关系方程组作为筛选可行装配序列的充要条件,提出可行装配序列的推理算法.最后以实例对该算法进行了说明.     

Effect of the specimen geometry on wear - combination of polyacetal (POM) and carbon steel for machine structures

Engineering plastics which have been shown to have good mechanical properties are now frequently used as materials for various machine elements. Engineering plastics are combined with other engineering plastics and metallic materials for machine construction. These machine elements are fabricated with contact surface forms, such as convex, concave, and plane surfaces. Therefore, when designing machines with a combination of materials containing engineering plastics, it is useful to know the wear and friction characteristics for various contact surface forms. In the present research, polyacetal (POM), an engineering plastic, and carbon steel, a metal often used for machine structures, were chosen as materials to study wear and friction. Wear tests were performed in the combination of a convex surface and a plane, and in the combination of a plane and a plane. As a result, some features of the wear and friction characteristic are clarified. (1) The worn mass when the flat specimen made of POM is rubbed by the POM pin specimen is larger than when with the pin specimen made of carbon steel. (2) When the flat specimen made of POM is rubbed by the POM or the carbon steel pin specimen, the same grade of wear is observed regardless of the pin specimen material. (3) The worn length of the steel spherical pin specimen on the steel flat specimen becomes close to the initial radius of the curvature of the pin specimen when the sliding distance is large. The initial condition of the spherical tip pin specimen on the flat specimen evolves toward a condition of the flat tip pin specimen on the flat specimen. So, the comparison between the two geometries is non-relevant. Such problem did not occur in POM pin specimen.