Back to Search
Start Over
Efficient high-speed cornering motions based on continuously-variable feedrates. I. Real-time interpolator algorithms
- Source :
- International Journal of Advanced Manufacturing Technology, vol 87, iss 9-12, The International Journal of Advanced Manufacturing Technology, vol 87, iss 9-12, Farouki, RT; & Nittler, KM. (2016). Efficient high-speed cornering motions based on continuously-variable feedrates. I. Real-time interpolator algorithms. International Journal of Advanced Manufacturing Technology, 87(9-12), 3557-3568. doi: 10.1007/s00170-016-8740-z. UC Davis: Retrieved from: http://www.escholarship.org/uc/item/2v5420wr
- Publication Year :
- 2016
- Publisher :
- eScholarship, University of California, 2016.
-
Abstract
- The problem of high-speed traversal of sharp toolpath corners, within a prescribed geometrical tolerance 𝜖, is addressed. Each sharp corner is replaced by a quintic Pythagorean–hodograph (PH) curve that meets the incoming/outgoing path segments with G 2 continuity, and deviates from the exact corner by no more than the prescribed tolerance 𝜖. The deviation and extremum curvature admit closed-form expressions in terms of the corner angle 𝜃 and side-length L, allowing precise control over these quantities. The PH curves also permit a smooth modulation of feedrate around the corner by analytic reduction of the interpolation integral. To demonstrate this, real-time interpolator algorithms are developed for three model feedrate functions. Specifying the feedrate as a quintic polynomial in the curve parameter accommodates precise acceleration continuity, but has no obvious geometrical interpretation. An inverse linear dependence on curvature offers a purely geometrical specification, but incurs slight initial and final tangential acceleration discontinuities. As an alternative, a hybrid form that incorporates the main advantages of these two approaches is proposed. In each case, the ratio $f=V_{\min }/V_{0}$ of the minimum and nominal feedrates is a free parameter, and the improved cornering time is analyzed. This paper develops the basic cornering algorithms—their implementation and performance analysis are described in detail in a companion paper.
- Subjects :
- CNC machines
0209 industrial biotechnology
Real-time interpolator algorithm
Inverse
02 engineering and technology
Classification of discontinuities
Curvature
Industrial and Manufacturing Engineering
Mathematical Sciences
Acceleration
020901 industrial engineering & automation
Engineering
Information and Computing Sciences
0202 electrical engineering, electronic engineering, information engineering
Mathematics
Mechanical Engineering
020207 software engineering
Toolpath corner rounding
Computer Science Applications
Quintic function
Industrial Engineering & Automation
Control and Systems Engineering
Continuously-variable feedrate
Pythagoreanhodograph curves
Reduction (mathematics)
Algorithm
Software
Free parameter
Interpolation
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- International Journal of Advanced Manufacturing Technology, vol 87, iss 9-12, The International Journal of Advanced Manufacturing Technology, vol 87, iss 9-12, Farouki, RT; & Nittler, KM. (2016). Efficient high-speed cornering motions based on continuously-variable feedrates. I. Real-time interpolator algorithms. International Journal of Advanced Manufacturing Technology, 87(9-12), 3557-3568. doi: 10.1007/s00170-016-8740-z. UC Davis: Retrieved from: http://www.escholarship.org/uc/item/2v5420wr
- Accession number :
- edsair.doi.dedup.....0f352ee3236231a0672539f68df6b7e0