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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
B-C
C-D
In general, the length of each linear segment is
L
Where Xk and Yk are the changes in X and Y positions along the linear segment. The length of the
circular arc is
L
The total travel distance is given by
D
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
VA
The resulting vector velocity is shown in Fig. 12.3.
10000
Figure 12.3 - Vector Velocity Profile
The acceleration time, T a , is given by
DMC-1000
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Linear
10000 units
R Δ
Circular
360
Linear
1000
Total
35708 counts
+
2
2
Xk
Yk
k =
π
=
ΔΘ 2 360
R
k
k
k
n
∑
=
L
k
=
k
1
100000
2000000
Velocity
T
0.05
a
θ π
2
= 15708
T
0.357
s
time (s)
T
0.407
a
Appendices • 171
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