Terms Of Surface Patches Research Articles

Three dimensional modeling and finite element simulation of a generic end mill

The geometry of cutting flutes and the surfaces of end mills is one of the crucial parameters affecting the quality of the machining in the case of end milling. These are usually represented by two-dimensional models. This paper describes in detail the methodology to model the geometry of a flat end mill in terms of three-dimensional parameters. The geometric definition of the end mill is developed in terms of surface patches; flutes as helicoidal surfaces, the shank as a surface of revolution and the blending surfaces as bicubic Bezier and biparametric sweep surfaces. The proposed model defines the end mill in terms of three-dimensional rotational angles rather than the conventional two dimensional angles. To validate the methodology, the flat end milling cutter is directly rendered in OpenGL environment in terms of three-dimensional parameters. Further, an interface is developed that directly pulls the proposed three-dimensional model defined with the help of parametric equations into a commercial CAD modeling environment. This facilitates a wide range of downstream technological applications. The modeled tool is used for finite element simulations to study the cutting flutes under static and transient dynamic load conditions. The results of stress distribution (von mises stress), translational displacement and deformation are presented for static and transient dynamic analysis for the end mill cutter flute and its body. The method described in this paper offers a simple and intuitive way of generating high-quality end mill models for use in machining process simulations. It can be easily extended to generate other tools without relying on analytical or numerical formulations.

On the placement of open-loop robotic manipulators for reachability

Abstract Criteria for and implementation of the placement of robot manipulators with the objective of reaching specified target points are herein addressed. Placement of an open-loop robotic manipulator in a working environment is characterized by defining the position and orientation of the manipulator’s base with respect to a fixed reference frame. The problem has become important in both the medical and manufacturing fields, where a robot arm must be appropriately placed with respect to targets (tasks) that cannot be moved. An applicable numerical formulation is presented. While other methods have used inverse kinematics solutions in their formulation for defining a locality for the manipulator base, this type of solution is difficult to implement because of the inherent complexities in determining all inverse kinematic solutions. The approach used in this work is based on characterizing the placement, forcing a cost function to impel the workspace envelope in terms of surface patches towards the target points and subject to functionality constraints, but not requiring the computation of inverse kinematics. The formulation and experimental code are demonstrated using a number of examples.

On the determination of boundaries to manipulator workspaces

The accumulation of two independent, broadly applicable formulations for determining the boundary to manipulator workspaces, presented elsewhere, are compared in this paper. Insights gained from one method are used to explain behavior exhibited in the other. Results are also compared and validated. A numerical formulation based on continuation methods is used to map curves that are on the boundary of a manipulator workspace. Analytical criteria based on row rank deficiency criteria of the manipulator's analytical Jacobian are used to map a family of one-dimensional solution curves on the boundary. The other formulation, based on a similar rank-deficiency criteria, yields analytic boundaries parametrized in terms of surface patches on the boundary. Results concerning the applicability of the numerical method to open- and closed-loop systems are compared with those limited to the open-loop for the analytical method. Conclusions regarding the behavior of the manipulator on geometric entities characterized by singular curves, higher-order bifurcation points, and surfaces inside the workspace are drawn. Applicability of both methods and their limitations are also addressed.

Protection of reservoirs

The geometry of cutting flutes and the surfaces of end mills is one of the crucial parameters affecting the quality of the machining in the case of end milling. These are usually represented by two-dimensional models. This paper describes in detail the methodology to model the geometry of a flat end mill in terms of three-dimensional parameters. The geometric definition of the end mill is developed in terms of surface patches; flutes as helicoidal surfaces, the shank as a surface of revolution and the blending surfaces as bicubic Bezier and biparametric sweep surfaces. The proposed model defines the end mill in terms of three-dimensional rotational angles rather than the conventional two dimensional angles. To validate the methodology, the flat end milling cutter is directly rendered in OpenGL environment in terms of three-dimensional parameters. Further, an interface is developed that directly pulls the proposed three-dimensional model defined with the help of parametric equations into a commercial CAD modeling environment. This facilitates a wide range of downstream technological applications. The modeled tool is used for finite element simulations to study the cutting flutes under static and transient dynamic load conditions. The results of stress distribution (von mises stress), translational displacement and deformation are presented for static and transient dynamic analysis for the end mill cutter flute and its body. The method described in this paper offers a simple and intuitive way of generating high-quality end mill models for use in machining process simulations. It can be easily extended to generate other tools without relying on analytical or numerical formulations.