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
Δ
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
=
ΔΘ
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.3.
0.05
0.357
10000
Velocity
time (s)
0.407
T
a
T
a
T
s
Figure A.3 - Vector Velocity Profile
196
•
Appendices
DMC-1600