# The midpoint differentiate law of circular arc interpolation

• Time:
• Click:160
On the foundation that compares law and DDA law principle in pointwise, a kind of when the article put forward circular arc interpolation new algorithm, midpoint differentiate law. One, the relation between feed direction and coordinate dot with I quadrant anticlockwise interpolation is a specification to concern this kind. See a picture 1, set bit of Pi(xi, yi) edge circular arc is anticlockwise direction moves, when Xi>yi, vy>vx, when Pi accordingly the dot is inside circular arc when, should be in fore-and-aft feed; When Pi the dot is outside circular arc when, should be in on vertical, horizontal direction in the meantime feed. And when Xi function of the differentiate that select a site reachs coordinate feed direction to be in graph 1 in, be in along round equation X2+y2-Rx2=0 I quadrant arrives by A B interpolation, set dot of interpolation of I pace to be Pi(xi, yi) . Function of the differentiate that select a site is: Fi=(xi-½)2+(yi+½)2-R2=xi2+yi2-xi+yi+½-R2 (1) is like A(xo, yo) is on circular arc, criterion: Fo=-xo+yo+0.

5 be like Fi<0 when Xi>yi, criterion up make a move, namely: Xi+1=xi, yi+1=yi+1 is like Fi ≥ 0, vertical, transverse at the same time make a move, namely: Xi+1=xi-1, yi+1=yi+1 is like Fi<0 when Xi ≤ Yi, vertical, transverse at the same time make a move, namely: Xi+1=xi-1, yi+1=yi+1 is like Fi ≥ 0, unexpected inward make a move, namely: Xi+1=xi-1, computation of deviation of dot of Yi+1=yi new differentiate if up make a move, xi+1=xi, yi+1=yi+1, analogy type (1) , criterion right now discriminate is: If Fi+1=(xi+1-½)2+(yi+1+½)2-R2=Fi+2yi+2 (2) is inclined up make a move, xi+1=xi-1, yi+1=yi+1, right now discriminate is: Fi+1=(xi+1-½)2+(yi+1+½)2-R2=Fi-2xi+2yi+4 (3) is like unexpected inward make a move, xi+1=xi-1, yi+1=yi, right now discriminate is: Interpolation of Fi+1=(xi+1-½)2+(yi+1+½)2-R2=Fi-2xi+2 (4) circular arc still involves quadrant and suitable, anticlockwise issue, these can apply coordinate commutation to try to solve. Graph the main measure when procedure of algorithm of interpolation of flow chart of 2 interpolation program has interpolation operation with midpoint differentiate law is: 1) coordinate is compared; 2) feed differentiate; 3) coordinate feed; 4) new deviation is calculated; 5) terminal differentiate. Its flow block diagram sees a picture 2. 3, 3 interpolation error analyses interpolation precision drawing for estimate to nod Pi to lie near Xi=yi when interpolation, and when Xi>yi, if the graph is shown 3 times, it is by this program perpendicular up interpolation, apparent, right now error is the biggest, but won't exceed √ 0.

5d(d is pulse equivalent) , the interpolation error that this error is more than way of the smallest error slightly (0.

5d) . Midpoint differentiate law, algorithm is relatively simple, precision is taller, interpolation error is more than half pulse equivalent slightly. Because it compares pointwise to compare a standard only much one pace coordinate is compared, and sometimes two coordinate at the same time feed, executive rate is accordingly rapidder. CNC Milling CNC Machining