A real-time scheme of cubic parametric curve interpolations for CNC systems

Bahr, Behnam; Xiao, Xiaomao; Krishnan, Krishnan

doi:10.1016/s0166-3615(01)00087-2

Cited by 40 publications

(15 citation statements)

References 13 publications

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“…The main reason lies in that most NC systems only have the function of second curve interpolation, such as straight line, arc and parabola interpolation, and the solution is that the computer aided manufacturing (CAM) system could handle the complex curve and surface generated by CAD system with off-line interpolation, and use a large number of small line segments to approximate the original complex curve, and then the CAM system begins to compile NC machining program and finish NC machining. However, this approach will bring some shortcomings [2,3] ,such as huge program files , low machining precision and feeding speed. Therefore, it becomes a key problem to develop real-time interpolation of NURBS curve techniques for high precision computerized numerical control (CNC) at high speed.…”

Section: Introductionmentioning

confidence: 99%

Study on the Algorithm for Real-Time Interpolation of NURBS Curve

Hui

Liu

2011

AEF

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Abstract. In order to meet the needs of high speed and high precision computerized numerical control machining, a calculation based on the control of contour error and feeding acceleration for the real-time interpolation of Non-uniform rational B-spline (NURBS) curves was presented in this paper. On the premise of meeting the error requirement, machine can process parts with the highest feeding speed to achieve interpolation precision and interpolation speed optimization, and improve processing quality and efficiency.

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Section: Introductionmentioning

confidence: 99%

Study on the Algorithm for Real-Time Interpolation of NURBS Curve

Hui

Liu

2011

AEF

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“…There have been attempts to regulate the feedrate in parametric interpolation [5][6][7][8]. Yeh and Hsu [5] proposed speedcontrolled interpolators that regulate the feedrate using compensatory parameters.…”

Section: Introductionmentioning

confidence: 99%

Development of a real-time trajectory generator for NURBS interpolation based on the two-stage interpolation method

Park

Nam

Yang

2004

Int J Adv Manuf Technol

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This paper deals with the real-time NURBS interpolation method in which the interpolation error between the ideal curve and the interpolated curve is compensated within the machine basic length unit (BLU). Parametric curve interpolation methods are based on the Taylor series expansion of curve parameters and an approximation. This approach enables effective feed command generation following the target curve. However, the interpolation error caused by the curve segmentation cannot be controlled.In this research, a two-stage interpolation method that compensates for interpolation errors within machine BLU is proposed. The interpolation result was filtered by an acceleration/jerk limitation equation. Through this two-stage interpolation, both the interpolation error condition and the motion dynamics can be satisfied.Using computer simulations in which interpolation results are revaluated by a numerical iteration method, it is shown that the two-stage interpolation algorithm can interpolate target curves precisely with geometric and dynamic contentment. The proposed algorithm was implemented in the CNC simulator system and an experimental run was conducted to identify the real-time adaptation.

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“…However, free-form design and machining have become important in a variety of applications in the automotive, aerospace, and ship-building industries. Speciÿc examples are the design and machining of dies and molds, as well as propeller and impeller blades [7]. The consensus seems to be that free-form surfaces can easily be modelled in 3D space, but that the manufacturing of free-form surfaces has been a major di culty up to now.…”

Section: Introductionmentioning

confidence: 99%

“…The di erence between various representational schemes with which free-form surfaces are modelled in 3D space, lies in the utilization of di erent geometrical and polynomial properties required to control and modify the desired geometrical shapes [7]. More speciÿcally, non-uniform rational B-splines (NURBS) have long been favoured in computer-aided design (CAD) systems, since 'they o er exact uniform representation of both analytical and free-form parametric curves' [6].…”

Section: Introductionmentioning

confidence: 99%

“…Bahr et al [7] explain that a typical way to machine parts with spline surfaces (including NURBS) on a CNC machine tool is by converting or transforming the surfaces to linear or circular segments according to a prescribed error tolerance, so that the CNC machines can reproduce the parts. For many applications, these conversions or transformations will produce a large amount of data.…”

Section: Introductionmentioning

confidence: 99%

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Trajectory‐planning through interpolation by overlapping cubic arcs and cubic splines

Plessis

Snyman

2003

Numerical Meth Engineering

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SUMMARYA new path-planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar industrial robot. The user prescribes a set of nodal points along a general curve to be followed by the chosen working point on the end-e ector of the mechanism. Given these speciÿed points along the path and additional prescribed kinematical requirements, Overlapping Cubic Arcs are ÿtted in the Cartesian domain and a cubic Spline interpolation curve is ÿtted in the time-domain. Further user-speciÿed information is used to determine how the end-e ector orientation angle should vary along the speciÿed curve. The proposed trajectory-planning methodology is embodied in a computer-algorithm (OCAS), which outputs continuous graphs for positions, velocities and accelerations in the time-domain. If a varying end-e ector orientation angle is speciÿed, the OCAS-algorithm also generates continuous orientation angle, orientation angular velocity and orientation angular acceleration curves in the time-domain. The trajectory-planning capabilities of the OCAS-algorithm are tested for cases where the prescribed nodal points lie along curves deÿned by analytically known non-linear functions, as well as for nodal points speciÿed along a non-analytical (free-form) test-curve. The proposed trajectory-planner may be implemented as part of kinematic and kinetic simulation software, and it also has the potential application for controlling machine tools in cutting along free-form curves.

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A real-time scheme of cubic parametric curve interpolations for CNC systems

Cited by 40 publications

References 13 publications

Study on the Algorithm for Real-Time Interpolation of NURBS Curve

Study on the Algorithm for Real-Time Interpolation of NURBS Curve

Development of a real-time trajectory generator for NURBS interpolation based on the two-stage interpolation method

Trajectory‐planning through interpolation by overlapping cubic arcs and cubic splines

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