An airthoid curve and a smooth method for motion planning based on the airthoid curve

Abstract

The invention discloses an Airthoid curve and a motion planning smoothing method based on the Airthoid curve, comprising the following steps: Step 1: Obtain the smooth length of the smooth curve corresponding to a given approximation error; Step 2: According to the length of the straight line segment and the step 1. Determine the actual smooth length by the obtained smooth length of the smooth curve; Step 3: Determine the smooth curve according to the actual smooth length determined in Step 2; Step 4: Analytical calculation of the smooth curve based on the smooth curve determined in Step 3 Arc length and curvature extremes. The method of the present invention smooths the processing path based on the Airthoid curve to realize the smooth movement speed, and has the advantages of expressing the smooth curve based on the arc length parameter, C3 continuity, controllable contour error, and analytical expression of the extreme value of the curvature and the arc length. The invention has the advantages of high calculation efficiency, high contour accuracy and high flexible motion capability, and is more suitable for online application of local smoothing.

Description

technical field [0001] The invention belongs to the field of motion planning, and in particular relates to an Airthoid curve and a smooth method for motion planning based on the Airthoid curve. Background technique [0002] Complex space surfaces usually generate 3D design files in the form of NURBS curves. Considering that it is difficult for most CNC systems to directly interpolate parameter curves, computer-aided systems usually discretize the NURBS curve tool paths into continuous small line segments and input them to the CNC unit for processing. However, there is a discontinuity in the velocity direction and curvature at the first connecting point between the small line segments, requiring the machine tool to reduce the velocity to zero at this point. This frequent acceleration and deceleration not only reduces the processing efficiency, but also produces shock and vibration due to the friction or clearance of the feed system. Therefore, realizing local smoothing of c...

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Problems solved by technology

[0004] Document 2 "Tulsyan S, Altintas Y. Local toolpath smoothing for five-axis machine tools [J]. International Journal of Machine Tools and Manufacture, 2015, 96: 15-26." discloses a C3 continuous local smoothing method, which The method inserts a quintic B-spline curve at the corner. Although the approximation error is controllable and the jump of the velocity curve is continuous, the arc length of the smooth curve cannot be calculated by Newton-Simpson iteration.

[0005] Document 3 "Shahzadeh A, Khosravi A, Robinette T, et al. Smooth path planning using biclothoid fillets for high speed CNC machines [J]. International Journal of Machine Tools and Manufacture, 2018, 132:36-49." discloses a C2 Continuous local smoothing method, this method inserts a clothhoid curve based on the arc length parameter at the corner to achieve a smooth transition of the machining trajectory. The arc length of the smoothing curve can be calculated analytically, but the speed curve has a jerk discontinuity

[0006] The typical characteristics of the above literature are: although the smoothing curve can realize the smooth transition of the processing path composed of continuous small line segments, the smoothing method in the literature cannot simultaneously have controllable approximation error, continuous jerk and analytical calculation of arc length. Continuous is easy to cause vibration of the control system and reduce the surface processing quality of the workpiece. The iterative calculation of the arc length prolongs the time of the forward-looking process, which limits the online application of the fairing algorithm

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