Galil Motion Control DMC-21 5 Series User Manual page 58

Vector Mode - Mathematical Analysis
The terms of coordinated motion are best explained in terms of the vector motion. The vector velocity, VS, which is
also known as the feed rate, is the vector sum of the velocities along the A and B axes, VA and VB.
√
2
VS= VA
+VB
The vector distance is the integral of VS, or the total distance traveled along the path. To illustrate this further,
suppose that a string was placed along the path in the X-Y plane. The length of that string represents the distance
traveled by the vector motion.
The vector velocity is specified independently of the path to allow continuous motion. The path is specified as a
collection of segments. For the purpose of specifying the path, define a special X-Y coordinate system whose origin
is the starting point of the sequence. Each linear segment is specified by the X-Y coordinate of the final point
expressed in units of resolution, and each circular arc is defined by the arc radius, the starting angle, and the
angular width of the arc. The zero angle corresponds to the positive direction of the X-axis and the CCW direction
of rotation is positive. Angles are expressed in degrees, and the resolution is 1/256th of a degree. For example, the
path shown in Figure 6.8 is specified by the instructions:
VP 0,10000
CR 10000, 180,
VP 20000, 20000
The first line describes the straight line vector segment between points A and B. The next segment is a circular arc,
which starts at an angle of 180° and traverses -90°. Finally, the third line describes the linear segment between
points C and D. Note that the total length of the motion consists of the segments:
A-B Linear
B-C Circular
C-D Linear
Total
In general, the length of each linear segment is

2
L Xk Yk
k 
Where Xk and Yk are the changes in X and Y positions along the linear segment. The length of the circular arc is
  2 360
L R
k k k
The total travel distance is given by
Chapter 6 Programming Motion ▫ 53
2
-90
Y
20000
B
10000
A
Figure 6.8: X-Y Motion Path
10000 units
R   
2
= 15708
360
10000
35708 counts
2

C D
X
10000 20000
DMC-21x5 User Manual 1.0a1