C-shaped Hermite interpolation with circular precision based on cubic PH curve interpolation

2012 ◽  
Vol 44 (11) ◽  
pp. 1056-1061 ◽  
Author(s):  
Yajuan Li ◽  
Chongyang Deng
Keyword(s):  
Hermite Interpolation ◽  
Curve Interpolation ◽  
Ph Curve

Design of Pythagorean Hodograph Curve Interpolator Based on NiosII Embedded Processor and FPGA

2011 ◽  
Vol 383-390 ◽  
pp. 6868-6872
Author(s):  
Jing Jie Guo ◽  
Wei Tang
Keyword(s):  
High Speed ◽  
Precision Machining ◽  
Interpolation Algorithm ◽  
Interpolation Scheme ◽  
Embedded Processor ◽  
Computational Burden ◽  
Curve Interpolation ◽  
Pythagorean Hodograph ◽  
Fpga Chip ◽  
Ph Curve

In this paper, a novel architecture of Pythagorean Hodograph (PH) curve interpolator based on Nios Ⅱ embedded processor and FPGA is proposed. The whole interpolator including NiosⅡ processor is built in a single FPGA chip. The interpolator uses a two-stage interpolation scheme to reduce the computational burden of PH curve interpolator. The Nios Ⅱ embedded processor implements 1st-stage interpolation, the FPGA receives the command from the Nios Ⅱ processor and implements 2nd-stage interpolation simultaneously. Therefore, the interpolator can implement the real-time PH curve interpolation algorithm steadily to meet the needs of high-speed and high-precision machining.

Rounding Spatial G-Code Tool Paths Using Pythagorean Hodograph Curves

2007 ◽  
Vol 7 (3) ◽  
pp. 186-191 ◽  
Author(s):  
Zbyněk Šír ◽  
Elmar Wings ◽  
Bert Jüttler
Keyword(s):  
Hermite Interpolation ◽  
Second Order ◽  
Peak Acceleration ◽  
Curve Segment ◽  
Industrial Environment ◽  
Tool Paths ◽  
Pythagorean Hodograph ◽  
G Code ◽  
Linear Elements ◽  
Ph Curve

We describe and analyze a new algorithm for rounding standard G-code tool paths. The joints of circular/linear elements are replaced by small segments of Pythagorean hodograph (PH) curves so that the final curve is globally C2 continuous. The PH segments are produced via a second order Hermite interpolation. We discuss some implementation details and investigate the error introduced by replacing a part of G-code by a PH curve segment. We also report results of tests within an industrial environment that demonstrate an increase in path velocity while decreasing peak acceleration.

Design and Implementation of Real-Time CNC Interpolation ASIC for Pythagorean Hodograph Curve Based on FPGA

2011 ◽  
Vol 130-134 ◽  
pp. 3998-4001
Author(s):  
Jing Jie Guo ◽  
Wei Tang ◽  
Xue Ling Wang
Keyword(s):  
Real Time ◽  
Motion Control ◽  
Interpolation Scheme ◽  
Design And Implementation ◽  
Curve Interpolation ◽  
Pythagorean Hodograph ◽  
Stepper Motors ◽  
Cnc Interpolation ◽  
Fpga Chip ◽  
Ph Curve

In this paper, a novel architecture of a real-time CNC interpolation ASIC for Pythagorean Hodograph curve based on FPGA is proposed. The ASIC built on a single FPGA chip contains a NikosⅡprocessor core. It uses a two-stage interpolation scheme to reduce the computational burden of PH curve interpolation. Firstly, the 1st-stage interpolation program is operated on the NikosⅡprocessor. The FPGA hardware logic performs the 2nd-stage interpolation and outputs two groups of pulses for the motion control of actuators (two stepper motors)

On the Hermite interpolation

2007 ◽  
Vol 50 (11) ◽  
pp. 1651-1660 ◽  
Author(s):  
Xing-hua Wang
Keyword(s):  
Hermite Interpolation

Algorithm 211: Hermite interpolation

1963 ◽  
Vol 6 (10) ◽  
pp. 617 ◽  
Author(s):  
George R. Schubert
Keyword(s):  
Hermite Interpolation

Wavelet Finite Element Method Analysis of Bending Plate Based on Hermite Interpolation

2013 ◽  
Vol 389 ◽  
pp. 267-272 ◽  
Author(s):  
Peng Shen ◽  
Yu Min He ◽  
Zhi Shan Duan ◽  
Zhong Bin Wei ◽  
Pan Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thin Plate ◽  
Hermite Interpolation ◽  
Energy Functional ◽  
Field Function ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Crack Problems ◽  
Element Method

In this paper, a new kind of finite element method (FEM) is proposed, which use the two-dimensional Hermite interpolation scaling function constructed by tensor product as the basis interpolation function of field function, and then combine with the energy functional with related mechanics and variational principle, the wavelet finite element equations for solving elastic thin plate unit that constructed in this paper are derived. Then the bending problem of thin plate is solved very quickly and availably through the matlab program. The numerical example in this paper indicates the correctness and validity of this method, and has high calculation precision and convergence speed. Moreover, it also provides a reliable method to solve the free vibration problem of thin plate and the pipe crack problems.

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