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Jerk Limited Feedrate Profile Optimization for Nurbs Toolpaths in Cnc Machines with H-Bot Kinematics Cover

Jerk Limited Feedrate Profile Optimization for Nurbs Toolpaths in Cnc Machines with H-Bot Kinematics

Open Access
|Dec 2025

Figures & Tables

Fig. 1.

Schematic of Cartesian gantry (a) and H-Bot gantry (b) CNC machines (M – motor, P-passive pulley, q1,q2 – H-bot motors, X1,X2,Y – cartesian gantry motors, X,Y-Cartesian axes)
Schematic of Cartesian gantry (a) and H-Bot gantry (b) CNC machines (M – motor, P-passive pulley, q1,q2 – H-bot motors, X1,X2,Y – cartesian gantry motors, X,Y-Cartesian axes)

Fig. 2.

NURBS toolpath (blue) with control points (red circles) and control polygon (red dashed)
NURBS toolpath (blue) with control points (red circles) and control polygon (red dashed)

Fig. 3.

NURBS toolpath interpolation process
NURBS toolpath interpolation process

Fig. 4.

Block schematic of the feedrate optimization algorithm
Block schematic of the feedrate optimization algorithm

Fig. 5.

S-curve jerk limited feedrate profile (T1-T7 – durations of each profile segment)
S-curve jerk limited feedrate profile (T1-T7 – durations of each profile segment)

Fig. 6.

Picture of the experimental setup with the H-Bot CNC machine
Picture of the experimental setup with the H-Bot CNC machine

Fig. 7.

Block schematic of the H-Bot control system
Block schematic of the H-Bot control system

Fig. 8.

Initial S-curve Feedrate profile with chord error feedrate limit (dashed line) and axial velocity, acceleration and jerk profiles for both axes - “flower” NURBS toolpath
Initial S-curve Feedrate profile with chord error feedrate limit (dashed line) and axial velocity, acceleration and jerk profiles for both axes - “flower” NURBS toolpath

Fig. 9.

“Flower” NURBS toolpath. The curve color indicates the feedrate in mm/s
“Flower” NURBS toolpath. The curve color indicates the feedrate in mm/s

Fig. 10.

Feedrate profile and axial velocity, acceleration and jerk profiles for both axes - “flower” NURBS toolpath
Feedrate profile and axial velocity, acceleration and jerk profiles for both axes - “flower” NURBS toolpath

Fig. 11.

Drive current and following error in X and Y axes.
Drive current and following error in X and Y axes.
DOI: https://doi.org/10.2478/ama-2025-0075 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
Language: English
Page range: 665 - 672
Submitted on: Jul 17, 2025
Accepted on: Nov 24, 2025
Published on: Dec 19, 2025
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2025 Krystian ERWIŃSKI, Patryk USTASZEWSKI, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.