In this paper, an NC interpolation algorithm for a tripod-based parallel kinematic machine is investigated. The algorithm can be implemented in two steps, the rough interpolation in the Cartesian space and the precise interpolation in the actuator space. The upper bound of the theoretical interpolation error due to the interpolation algorithm in the precise interpolation and nonlinear mapping is analyzed. The representation of the interpolation error distribution within the Cartesian space is depicted in terms of the variations of the interpolation period and the programming velocity. It was concluded that this error is sufficiently small and may be neglected.
Issue Section:Technical Brief
Keywords:machine theory, numerical control, kinematics, interpolation
Topics:Errors, Interpolation, Kinematics, Machinery, Algorithms
C. C., and
Geometric Algorithms for Kinematic Calibration of Robots Containing Closed Loops,”
ASME J. Mech. Des.,
Merlet, J. P., 2002, “An Initiative for the Kinematics Study of Parallel Manipulators,” Proc. of the Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Quebec, Canada, Oct. 3–4, pp. 2–9.
Merlet, J. P., 1989, “Parallel Manipulators, Part 1: Theory, Design, Kinematics, Dynamics and Control,” Technical Report, #646 INRIA, France.
Luc, R., 2001, “Introduction to Algebraic Methods for Solving the Forward Kinematics Problem of Parallel Robots Applied to High Throughput and High Accuracy,” Proc. of the 3rd European-Asian Congress on Mechatronics, Besancon, Oct. 9–11.
A Generic Trajectory Verifier for the Motion Planning of Parallel Robots,”
ASME J. Mech. Des.,
Nenchev, D. N., and Uchiyama, M., 1996, “Singularity-Consistent Path Planning and Control of Parallel Robot Motion Through Instantaneous-Self-Motion Type,” IEEE Int. Conf. On Robotics and Automation, pp. 1864–1870.
Y. B., and
Kinematic Design of 3-HSS Parallel Machine Tool,”
China Manufacturing Tech. and Mach. Tool,
Wang, Y., 2002, “Development of Open Architecture Numerical Control System for Parallel Machine Tool,” Ph.D. dissertation, Tianjin University.
Five-Axis Surface Interpolators,”
Zhang, Q. G., and Greenway, R. B., 1997, “Real-Time NURBS Trajectory Generation for a Robot Using an Open-Architecture Controller,” MIM’97, pp. 862–866.
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