180 • Appendices DMC-1500
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
2
360
= 15708
C-D Linear 10000
Total 35708 counts
In general, the length of each linear segment is
Y
k = +
22
Where Xk and Yk are the changes in X and Y positions along the linear segment. The length of the
circular arc is
LRkkk=ΔΘ2 360
The total travel distance is given by
DLk
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. 12.2 may be specified in terms of
the vector speed and acceleration.
VS 100000
VA 2000000
The resulting vector velocity is shown in Fig. 12.3.
Figure 12.3 - Vector Velocity Profile
0.05 0.357
10000
Velocity
time (s)
0.407T
a
T
a
T
s
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