Galil DMC-4040 - Page 235

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 10000 units
B-C Circular
R ∆ θ π 2
360
= 15708
C-D Linear 10000
Total 35708 counts
In general, the length of each linear segment is
L Xk Yk k = +
2 2
Where Xk and Yk are the changes in X and Y positions along the linear segment. The length of the circular arc is
L R k k k = ∆ Θ 2 360 π
The total travel distance is given by
D L k
k
n
=
=
∑
1
The velocity profile may be specified independently in terms of the vector velocity and acceleration.
For example, the velocity profile corresponding to the path of Fig. A.2 may be specified in terms of the vector speed
and acceleration.
VS 100000
VA 2000000
The resulting vector velocity is shown in Fig. A.2.
0.05 0.357
10000
Velocity
time (s)
0.407T
a
T
a
T
s
Figure A..2 - Vector Velocity Profile
The acceleration time, Ta, is given by
T
VS
VA
s a = = =
100000
2000000
0 05.
The slew time, Ts, is given by
DMC-40x0 User Manual Appendices • 226