Circular Arc Interpolation Research Articles

Trajectory planning and motion control of full-row seedling pick-up arm

Frequent start-stops of automatic seedling transplanters would lengthen the seedling picking time due to alternating movement of the motor, and cause positioning errors and frequent motor vibrations when starting the machine. To solve these problems and ensure the pick-up continuity of automatic transplanters, in this study the smooth circular arc interpolation algorithm and the least square method for multinomial curve fitting were used to conduct the trajectory planning of automatic transplanter based on the movement of the pick-up arm of the transplanter. Velocity and time curves were fitted in segments to acquire motion control parameters and further tracking control was conducted. The mathematical model of the control system was established using Simulink, and simulation analysis and system debugging test were performed. Experiments show that the trajectory curves obtained by MATLAB’s data processing can realize the continual and smooth motion trajectory of the pick-up arm; stepper motor velocity control can effectively track the planning curve and improve the seedling pick-up efficiency. The pick-up and pushing time of each motion of the planned plug seedling transplanter reduced by 1.0678 s and the start-stop times reduced from 6 to 1, which solved the frequent motor vibrations when starting the machine and improved the stability of the system. In addition, overstep and out-of-step of the motor at the start-stop moment were avoided and displacement error was reduced. Keywords: trajectory planning, motion control, motion trajectory simulation, transplanter, stepper positioning DOI: 10.25165/j.ijabe.20201303.5264 Citation: Ren L, Wang N, Cao W B, Li J Q, Ye X C. Trajectory planning and motion control of full-row seedling pick-up arm. Int J Agric & Biol Eng, 2020; 13(3): 41–51.

Trajectory planning and motion control of full-row seedling pick-up arm

Frequent start-stops of automatic seedling transplanters would lengthen the seedling picking time due to alternating movement of the motor, and cause positioning errors and frequent motor vibrations when starting the machine. To solve these problems and ensure the pick-up continuity of automatic transplanters, in this study the smooth circular arc interpolation algorithm and the least square method for multinomial curve fitting were used to conduct the trajectory planning of automatic transplanter based on the movement of the pick-up arm of the transplanter. Velocity and time curves were fitted in segments to acquire motion control parameters and further tracking control was conducted. The mathematical model of the control system was established using Simulink, and simulation analysis and system debugging test were performed. Experiments show that the trajectory curves obtained by MATLAB’s data processing can realize the continual and smooth motion trajectory of the pick-up arm; stepper motor velocity control can effectively track the planning curve and improve the seedling pick-up efficiency. The pick-up and pushing time of each motion of the planned plug seedling transplanter reduced by 1.0678 s and the start-stop times reduced from 6 to 1, which solved the frequent motor vibrations when starting the machine and improved the stability of the system. In addition, overstep and out-of-step of the motor at the start-stop moment were avoided and displacement error was reduced. Keywords: trajectory planning, motion control, motion trajectory simulation, transplanter, stepper positioning DOI: 10.25165/j.ijabe.20201303.5264 Citation: Ren L, Wang N, Cao W B, Li J Q, Ye X C. Trajectory planning and motion control of full-row seedling pick-up arm. Int J Agric & Biol Eng, 2020; 13(3): 41–51.

Trajectory error estimation to circular arc interpolation cutter path of machining center due to acceleration/deceleration motions of interpolation segments

Trajectory error estimation to circular arc interpolation cutter path of machining center due to acceleration/deceleration motions of interpolation segments

Error Estimation to Circular Arc Interpolation Cutter Path of Machining Center due to Acceleration/Deceleration Motions between Two Interpolation Segments

Error Estimation to Circular Arc Interpolation Cutter Path of Machining Center due to Acceleration/Deceleration Motions between Two Interpolation Segments

The Method of Fillet Contour Error Compensation Applied in End Cylindrical Crankshaft Grinder

The Contour accuracy of a crankshaft transition fillet is important for the crankshaft working reliability. The front end surface, cylindrical surface and the transition fillet of a crankshaft are grinded by an end cylindrical grinder. During this machining, due to the roller’s shape error and other factors, the contour error of the fillet cannot be guaranteed while 90 degree circular arc interpolation was taken. In this paper, a fillet contour error compensation model was established, the appropriate compensation macro program was designed, and the radical contour error compensation was implemented through 9 circular arcs approaching. The practical application is shown that the satisfactory result is achieved and this method can also be applied in the fillet compensation for wheel dressing when applying diamond disk or stylus.

Simulation and Implementation of an Improved Inscribed Chord Interpolation Algorithm

In order to improve the shortcomings of the realization of the traditional quadratic curve interpolation inscribed chord method, this paper proposes an improved internal chord interpolation algorithm. The program flow chart of the algorithm achievement and the interpolation method of circular arc interpolation and linear interpolation of a detailed operation process is given in this paper. Finally through a calculation example the simulation is conducted, and the point by point comparison method were compared. The simulation results show the improvement on the quadratic curve interpolation in the inner string interpolation speed, good flexibility, and it worth popularizing in the interpolation algorithm for real time interpolation.

A Practical Evaluation Approach to Form Deviation for Surface of Revolution Based on Discrete Point Coordinate Data

This paper proposes a practical evaluation approach to form deviation for surface of revolution based on discrete point coordinate data. An approximate curve composed of circular arc segments decided from an optimal interpolation process is accepted for computing the form deviation at measured points instead of the generating line of the surface to be inspected. This operation significantly simplifies the algorithm and improves the efficiency in the evaluation calculation. At the same time, it is also guaranteed that the difference of both form deviation values relative to the approximate surface or to the original surface is restricted within the specified accuracy in the circular arc interpolation operation. The effectiveness and efficiency of the approach are verified through a practical example of the surface of revolution with a generating line in the form of cubic Bézier curve.

Generation of NC Program for Realizing High Speed Feed Rate of Cutting Tool

As the feed rate of cutting tools is influenced by the quality of NC programs, this causes two problems when cutting freeform surfaces using NC machine tools, one is the feed rate does not reach the specified value, and the other is the quality of the machined surface decreases due to the large acceleration and deceleration of the control axes. One reason for these problems is that the method to generate cutter location data does not take into consideration the sampling time of the NC controller. To improve these problems, the approximation of offset curves with a series of circular arcs has generally been proposed. But conventionally, circular arc interpolation algorithms are complicated and not rational. So, in this study, we proposed two simple NC program generation methods. (1) Approximate the offset form with circular arcs based on the location of the center of curvature. (2) Make the distance between the cutter location points of the NC data an integral multiple of the “feed rate command F × sampling time T”. We also confirm the effectiveness of the proposed methods by simulations and experiments.

I11 インボリュート曲線の最適円弧補間の簡易方法(I1 加工・生産システム1(マイクロ技術の高度化))

I11 インボリュート曲線の最適円弧補間の簡易方法(I1 加工・生産システム1(マイクロ技術の高度化))

Efficient circular arc interpolation based on active tolerance control

In this paper, we present an efficient sub-optimal algorithm for fitting smooth planar parametric curves by G 1 arc splines. To fit a parametric curve by an arc spline within a prescribed tolerance, we first sample a set of points and tangents on the curve adaptively as well as with enough density, so that an interpolation biarc spline curve can be with any desired high accuracy. Then, we construct new biarc curves interpolating local triarc spirals explicitly based on the control of permitted tolerances. To reduce the segment number of fitting arc spline as much as possible, we replace the corresponding parts of the spline by the new biarc curves and compute active tolerances for new interpolation steps. By applying the local biarc curve interpolation procedure recursively and sequentially, the result circular arcs with no radius extreme are minimax-like approximation to the original curve while the arcs with radius extreme approximate the curve parts with curvature extreme well too, and we obtain a near optimal fitting arc spline in the end. Even more, the fitting arc spline has the same end points and end tangents with the original curve, and the arcs will be jointed smoothly if the original curve is composed of several smooth connected pieces. The algorithm is easy to be implemented and generally applicable to circular arc interpolation problem of all kinds of smooth parametric curves. The method can be used in wide fields such as geometric modeling, tool path generation for NC machining and robot path planning, etc. Several numerical examples are given to show the effectiveness and efficiency of the method.

A practical evaluation approach towards form deviation for two-dimensional contours based on coordinate measurement data

A precise evaluation of the form deviations of two-dimensional (2D) engineering contours is of essential importance in precision manufacturing. In this paper, we propose a practical approach towards evaluating form deviations of 2D contour profiles based on coordinate measurement data. Using this approach, a 2D contour is divided into straight and curved parts. Each straight part is directly presented by the original definition of the part; and each curved part is further represented by its optimal interpolation circular arc segments whose interpolation accuracy can be specified arbitrarily. The approximate contour curve consisting of the straight and circular arc segments has the fewest interpolation segments under the condition of satisfying the pre-specified interpolation accuracy. The form deviation of a measured point is defined as the distance from the point to its corresponding straight or circular segment. The geometrical form deviation of the contour profile is evaluated using the least square method. It has been demonstrated that the difference between the deviation definitions, relative to the original contour or to the approximate contour, is not larger than the pre-specified accuracy value for circular arc interpolation. Therefore, the evaluation precision of the form deviation can be sufficiently guaranteed. The approach is easy and convenient for engineering applications. The effectiveness and the efficiency of the approach are verified with a practical example of a planar cam contour in the paper.

Smooth circular arc interpolation for planar free curves with tolerance control

Several circular arc curve-fitting methods have been proposed to overcome the drawbacks caused by a series of short linear movements in planar curve contouring machining. Almost all the previous circular arc curve-fitting methods assume that overcut and undercut allowances are the same. This assumption is not practical in industry since the allowances can vary according to the characteristic of the part to be machined. The objective of this paper is to develop an enhanced circular arc interpolation algorithm for planar free curves including tolerance control, which is easy and robust in practical implementation. An important property of the circular arc curve is that its offset curve is also another circular arc curve and can be calculated analytically. Using this property, the tolerance factors can be taken into account effectively in the present algorithm.

Creation of a Digital Database for XXth Century Historical Earthquakes Occurred in the Iberian Area

—The problems of recovering the seismic information contained in the old seismograms through their digitization and processing by computer methods are discussed. We present the main principles of a simple manual technique for digitization of early seismic records of the Wiechert seismograph. Detrending of the zero-line slope, circular arc removal, smoothing and interpolation treatment of the digital data are made. The accuracy of the digitizing process is assessed and its reliability is tested by a comparison with automatically obtained digital data and their spectral amplitudes. The deconvolution of the seismograph response has allowed us to obtain the time variation of ground motion which is then contrasted with direct measurements of ground motion displacement amplitudes given in the old-time bulletins. We have created a digital database for historical earthquakes which occurred in the Iberian area during the period 1912–1940 and recorded by the Wiechert seismograph at the Geophysical Observatory of Toledo, Spain. It contains the following output data the digitized original records; the geometrically corrected and interpolated data; the time variation of ground motion; maximum amplitudes and corresponding periods; total duration of the seismic oscillations and amplitude spectra. We carry out magnitude estimates and give formulae for magnitude classification based on the signal duration and on the maximum ground displacement amplitude. We also perform seismic moment determinations by spectral analysis of waveforms and propose a new seismic moment-magnitude relation.

Optimal circular arc interpolation for NC tool path generation in curve contour manufacturing

Circular arc interpolation is essential in manufacturing of curve contours. However, the problems of how to determine the parameters of the circular arcs and how to minimize the number of arcs according to desired interpolation accuracy have not been completely solved. This paper presents a new algorithm of circular arc interpolation for planar curves. It is based on the principle of minimax approximation. The algorithm has three features which include: (1) the interpolation error is minimax in any spiral segment of the curve, tangent-continuous at the joints of two spiral segments and satisfies the desired accuracy; (2) the parameters of the circular arcs depend on the desired accuracy and the number of arcs is fewest; (3) the circular arcs are compatible with the curve in concavity and convexity, and have almost the same radius of curvature, in other words, the interpolation looks very smooth and natural. Experimental trials show the algorithm is simple and robust for the application to NC contour manufacturing. The trials are carried out on producing the contour of a planar cam and a quadratic NURBS curve.

Curved surface machining through circular arc interpolation

In curved surface machining it is customary to represent and to generate the surface as a sequence of short linearly interpolated moves. Experimental measurements of such stop-start motion shows that full cutting speed is achieved typically for only ten percent of the machining time: the remaining time is spent in accelerating, decelerating, or pausing between instructions. An algorithm is presented which uses a recursive approach to maximize the number of circularly interpolated moves for surface generation. A reduction in machining time of up to 5:1 is demonstrated using this approach.

クロソイド補間によるコーナ軌跡制御

In the continuous path (CP) controlling robots such as welding, painting, sealing and bonding robots, the circular arc interpolation is usually adopted to the rounding of the sharp edges of corners. However, by the discontinuity of curvature at the points connecting lines and arcs, it tends to cause vibration at the points. For the purpose, the authors developed a new method of corner interpola-tion which uses Clothoid curve. The curve has a continuously changing curvature which is proportional to the length of the curve. This report describes the basic theory and the computing method of the curve and gives the practical data for Clothoidal interpolation.