CONTINUOUS PATH VERIFICATION IN MULTI-AXIS NC-MACHINING

2005 ◽  
Vol 15 (04) ◽  
pp. 351-377 ◽  
Author(s):  
RON WEIN ◽  
OLEG ILUSHIN ◽  
GERSHON ELBER ◽  
DAN HALPERIN
Keyword(s):  
Collision Detection ◽  
Translational Motion ◽  
Lower Envelope ◽  
Critical Surface ◽  
Efficient Computation ◽  
Detection Problem ◽  
Surface Patches ◽  
Radial Projection ◽  
Tool Axis ◽  
Nc Machine

We introduce a new approach to the problem of collision detection between a rotating milling-cutter of an NC-machine and a model of a solid workpiece, as the rotating cutter continuously moves near the workpiece. Having five degrees of motion freedom, this problem is hard to solve exactly and we approximate the motion of the tool by a sequence of sub-paths of pure translations interleaved with pure rotations. The collision-detection problem along each sub-path is then solved by using radial projection of the obstacles (the workpiece and the static parts of the NC-machine) around the tool axis to obtain a collection of critical surface patches in ℝ3, and by examining planar silhouettes of these surface patches. We thus reduce the problem to successive computations of the lower envelope of a set of planar curves, which we intersect with the profile of the tool. Our reduction is exact, and incurs no loss of accuracy. We have implemented our algorithm in the IRIT environment for solid modeling, using an extension package of the CGAL library for computing envelopes. The algorithm, combined with the proper data structures, solves the collision detection problem in a robust manner, yet it yields efficient computation times as our experiments show. Our approach produces exact results in case of purely translational motion, and provides guaranteed (and good) approximation bounds in case the motion includes rotation.

Efficient computation of one-electron two-centre exchange integrals in ion–atom collisions

1976 ◽  
Vol 54 (9) ◽  
pp. 944-949 ◽  
Author(s):  
Alfred Msezane
Keyword(s):  
Principal Quantum Number ◽  
Computing Time ◽  
Translational Motion ◽  
Matrix Elements ◽  
Efficient Computation ◽  
Close Coupling ◽  
One Dimensional ◽  
State Approximation ◽  
The Matrix ◽  
Exchange Matrix

A scheme is presented for the reduction to one-dimensional integrals of any one-electron two-centre exchange matrix elements which incorporate the momentum associated with the translational motion of the electron. These elements are of the types occurring in close coupling-based treatments of ion–atom collisions. It is shown in a six state approximation, by coupling both eigenstates and pseudostates for the asymmetric He2+–H collision process, that computing time for the evaluation of the matrix elements is determined mainly by the number of different exponents in the matrix elements. The coupling of additional states with the same principal quantum number as the already coupled ones alters computing time insignificantly.

ON THE COLLISION DETECTION PROBLEM FOR ROBOT MANIPULATORS

1995 ◽  
Vol 26 (2) ◽  
pp. 189-210 ◽  
Author(s):  
Mark Gill ◽  
Albert Zomaya
Keyword(s):  
Collision Detection ◽  
Robot Manipulators ◽  
Detection Problem

A Collision Detection Algorithm in Virtual Assembly Technology

2015 ◽  
Vol 713-715 ◽  
pp. 411-414
Author(s):  
He Qun Qiang ◽  
Chun Hua Qian
Keyword(s):  
Collision Detection ◽  
Classical Problem ◽  
Virtual Assembly ◽  
Detection Algorithm ◽  
Research Field ◽  
Component Model ◽  
Detection Problem ◽  
Tree Algorithm ◽  
Assembly Technology ◽  
Shape Characteristics

The collision detection problem is a classical problem in computer graphics research field. It has become a hot topic in recent years with the development of virtual assembly technology. And accurate collision detection is crucial to improve the reliability and authenticity of virtual assembly. In this paper, we designed a collision detection algorithm with a pre-segment strategy based on OBB-Tree algorithm, took advantage of the shape characteristics of component model, used a smaller bounding box for operation. Experimental results showed that the efficiency of the algorithm is about 10% higher than that of traditional OBB-Tree algorithm.

3D Collision-Free Trajectory Planning for Mobile Robot Based on Quadric Modeling

1998 ◽  
Author(s):  
Kao-Shing Hwang ◽  
Ming-Dar Tsai ◽  
Ming-Yi Ju
Keyword(s):  
Mobile Robot ◽  
Objective Function ◽  
Trajectory Planning ◽  
Collision Detection ◽  
Optimal Path ◽  
Collision Probability ◽  
Mathematical Representation ◽  
Coordinate Transformations ◽  
Detection Problem ◽  
Geometric Approximation

Abstract A 3-D collision-free trajectory planning method for a mobile robot is proposed in the paper. The geometric shapes of the objects in the workspace are modeled as ellipsoids of 3-D quadric model for simple mathematical representation and easy geometric approximation. By a series of coordinate transformations between the mobile robot and obstacles, the collision detection problem in trajectory planning is reduced to test a point falling outside or inside the transformed ellipsoids, which models obstacles geometrically. Finally, the collision probability, which is defined by projecting the quadric ellipsoid onto a 3-D Gaussian distribution contour, plays a very significant role in search the optimal path through the defined objective function.

Tool Path Planning for Five-Axis NC Machining of Implant Shaping Mold for Cranioplasty

2011 ◽  
Vol 697-698 ◽  
pp. 292-296
Author(s):  
Liang Zhang ◽  
J. Li ◽  
B.C. Lou
Keyword(s):  
Path Planning ◽  
Tool Path ◽  
Nc Machining ◽  
Normal Curvature ◽  
Tool Path Planning ◽  
Lead Angle ◽  
Tool Axis ◽  
Nc Machine ◽  
Five Axis ◽  
Tool Axis Vector

The necessity for skull patch surface for cranioplasty was introduced and it was divided according to maximum normal curvature in the discrete points after skull patch surface dispersed. Then the tool axis vector was determined by the lead angle of the tool, corresponding to generating the tool path in each area; At last, the implant shaping mold for cranioplasty was produced by five-axis NC machine.

Batch Process and Sensitivity Analysis of Collision Detection of Planar Convex Polygons in Motion

2013 ◽  
Vol 13 (4) ◽  
Author(s):  
Cheng-fu Chen
Keyword(s):  
Sensitivity Analysis ◽  
Programming Problem ◽  
Collision Detection ◽  
Parametric Programming ◽  
Batch Process ◽  
Detection Problem ◽  
Convex Polygons ◽  
Parametric Problem ◽  
Decomposition Procedure ◽  
Two Parameters

A new method for formulation, solution, and sensitivity analysis of collision detection of convex objects in motion is presented. The collision detection problem is formulated as a parametric programming problem governed by the changes in the relative translation and relative rotation between the two objects considered. The two parameters together determine all the possible relative configurations between two moving convex objects. Therefore, solving this parametric problem allows for knowing the proximity information for all the possible configurations of the objects. We develop a two-step decomposition procedure to solve this parametric programming problem, and show that the solution is a convex function of the two parameters. This convexity feature enables an archive of the proximity information and sensitivity analysis for the collision detection problem.

Solving the collision detection problem

1994 ◽  
Vol 14 (3) ◽  
pp. 36-43 ◽  
Author(s):  
A. Garcia-Alonso ◽  
N. Serrano ◽  
J. Flaquer
Keyword(s):  
Collision Detection ◽  
Detection Problem

A Linear Programming Solution for Exact Collision Detection

2005 ◽  
Vol 5 (1) ◽  
pp. 48-55 ◽  
Author(s):  
Ali Akgunduz ◽  
Prashant Banerjee ◽  
Sanjay Mehrotra
Keyword(s):  
Collision Detection ◽  
High Speed ◽  
Performance Testing ◽  
Detection Problem ◽  
Detection Algorithms ◽  
Contact Information ◽  
Polyhedral Objects ◽  
Ergonomic Analysis ◽  
Programming Solution ◽  
Assembly Analysis

This paper addresses the issue of real-time collision detection between pairs of convex polyhedral objects undergoing fast rotational and translational motions. Accurate contact information between objects in virtual reality based simulations such as product design, assembly analysis, performance testing and ergonomic analysis of products are critical factors to explore when desired realism is to be achieved. For this purpose, fast, accurate and robust collision detection algorithms are required. The method described in the text models the exact collision detection problem between convex objects as a linear program. One of the strengths of the proposed methodology is its capability of addressing high speed interframe collision. In addition to the interframe collision detection, experimental data demonstrate that mathematical programming approaches offer promising results in terms of speed and robustness as well.

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