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-14 may be specified in terms of
the vector speed and acceleration.
VS
100000
VA
2000000
The resulting vector velocity is shown in Fig. A-15.
0.05
0.357
10000
Velocity
time (s)
0.407
T
a
T
a
T
s
Figure A-15 - 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
T
D
VS
T
s
s
a
=
−
=
−
=
35708
100000
0 05
0 307
.
.
The total motion time, Tt, is given by
T
D
VS
T
s
t
a
=
+
=
0 407
.
The velocities along the X and Y axes are such that the direction of motion follows the specified path,
yet the vector velocity fits the vector speed and acceleration requirements.
For example, the velocities along the X and Y axes for the path shown in Fig. A-14 are given in Fig.
A-16.
DMC-14x5/6
Appendices
i
181
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