Research On Efficient NURBS Curve Velocity Planning Algorithm For The S-type Series

In t he devel opment of high-grade CNC machine tools, NURBS, with its strong free curve and surface modeling abilit y, has becom e an im portant indicators of the evaluation for CNC. The probl em of motion cont rol of NURBS curve in CNC modeling is studied in the paper, mainly include the following as pects:The second chapter introduces the related defini tions and three kinds of the equival ent repres entation of NURBS curves, and accordingly discus ses the advantages and disadvantages of this method. De Boor ’s algorithm and vector recursive method are us ed i n the formula of comput ing which lays a solid foundation for t he theory of NURBS curves to curvature and program designing.In the third chapter, for inconsi stencies of discrete speed requireme nt with continuous vel ocit y planning in NURBS curve interpolation, a S-typ e series velocity planning algorithm was proposed for NURBS curves, which was entirely designed by the discrete met hod to meet t he discret e requirem ents of uniform speed within the interpolation cycl e and it s step changes between i nterpolation cycle in actual interpolations. According to the known conditi ons to calculate the number of interpolation cycle, S-type series velocity curve was planned for t his reason. At the end of the accel erat ion phase, when the actual speed reaches the maximum allowable speed, uniform speed phase is entered, otherwise t he acce leration margin factor is increa sed, so t hat the speed is acce lerat ed to the maximum allowable speed. At the end of the dece lera tion phase, when actual speed reaches the end speed, the deceleration phase is finis hed, otherwis e the deceleration margin factor is increased,so that the speed is decelerated t o the end speed. S-typ e series velocity planning algorithm was consistent with the actual interpolation speed requirements, and the speed margin factor compensat ed for speed losses caused by the rounding algorit hm.In the fourth chapter, for i naccuracies wi th 17 kinds of acceleration-deceleration modes j udgment when NURBS curve interpolation and using the S-typ e series veloci ty planning al gorithm, the judgm ent method of S-type series acceleration and deceleration mode is proposed for NURBS curve, which is based on the di screte requirements of the uniform speed. The resul ts are suitable for the selection of the acceleration and deceleration m odes based on the comparison with the displ acement,veloci ty and the number of interpolat ion cycl e. To st art with, according to the curvature t o divi de the curve and get the speed at the point of subsection and thelength of the curve,and comparing with the maximum al lowable speed and the full length of accelerati on and decele ration phase, the modes are scree ned out. Then accordi ng to the series form ula to calculat e the number of interpolat ion cyc le, the 17 kinds of acceleration-decel erat ion modes can be accurately judged.,which attains the discrete requirements when performing actual i nterpolations, and gives the corresponding 17 kinds of modes of the serial formulas and judges flowcha rt, to ensure that the speci fic acceleration-dec eleration mode is applied to the corre sponding S-type velocity planning.Finally, the effectiveness of the algorit hm is verified and analyz ed by t he digital simul ati on exper iment of M ATLAB and phys ical simul ation exper im ent of HNC808.