Generation of non-degenerate meshes
USSR Computational Mathematics and Mathematical Physics
A variational form of the Winslow grid generator
Journal of Computational Physics
ACM Transactions on Graphics (TOG)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
On the tool-path optimization of a milling robot
Computers and Industrial Engineering
Adaptive restoration of complex geometry parts through reverse engineering application
Advances in Engineering Software
Optimization and correction of the tool path of the five-axis milling machine
Mathematics and Computers in Simulation
Curvilinear space-filling curves for five-axis machining
Computer-Aided Design
Non-existence of rational arc length parameterizations for curves in Rn
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
This paper presents a new grid generation method for tool path planning for five-axis machining based on minimization of the kinematics error. First, the procedure constructs a space-filling curve so that the scallops between the resulting tracks of the tool do not exceed a prescribed tolerance. At the second stage (which is the subject of this paper) a one-dimensional grid along the space-filling curve is generated using direct minimization of the kinematics error. A closed form representation of the kinematics error as a function of locations cutter contact points is derived from the inverse kinematics transformations associated with a particular five-axis machine and obtained through automatic symbolic calculations. The grid of cutter location points is generated so that it minimizes the kinematics error. Numerical and cutting experiments demonstrate that the proposed procedure outperforms distribution of points based on the equi-arc-length principle. Finally, we show that our optimization routine requires less points than that based on sequential point insertion and numerical evaluation of the cost function, such as bisection.