Coordinated Motion - Mathematical Analysis - Galil Motion Control DMC-1600 Series User Manual

Coordinated Motion - 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 X
and Y axes, Vx and Vy.
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 Fig. A.2 is specified by the instructions:
20000
10000
Figure A.2 - X-Y Motion Path
DMC-1600
= +
2 2
Vs Vx Vy
VP 0,10000
CR 10000, 180, -90
VP 20000, 20000
Y
B
A
C
10000
D
X
20000
Appendices • 195