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In Figure 11.44 the blue line represents the calculated joint acceleration for arm 2 of the Delta-
3 robot and the red line describes the reference acceleration in EPAS. If one look at the joint
velocity of joint 2 there is a smaller percentage deviation (Figure 11.42) between the calculated
and the reference value than for joint 1. This is also shown in the acceleration graph for joint 2
where the calculated value match better with the reference value than for joint 1.
Figure 11.45, the blue line shows the calculated acceleration and the red
line shows the reference acceleration from EPAS.
The joint acceleration for the third joint at the Delta-3 robot is shown in Figure 11.45. The blue
line represents the calculated joint acceleration with the Jacobian matrix compared with the red
line which is the reference acceleration from EPAS. As for joint 1 also the percentage velocity
deviation for joint 3 is larger at the time interval where the acceleration deviation is larger.
11.2.4 DISCUSSION
When using the Jacobian matrix in EPAS to calculate the TCP velocity respectively the angular
velocity for the upper arms one can see a small deviation between the measured value and the
calculated value in all three experiments above. The deviation for experiment 1 and 2 is as most
10% and for experiment 2 is the largest deviation around 5%. In general is the arm angle
velocity deviation smaller in experiment 2 than for experiment 1 and 3. One reason for this is
that the angle velocity of the three arms is smaller than for the two other experiments.
If one considers Figure 11.42 (shows the angle velocity deviation in percentage) when looking
at the joint acceleration plots for the three arms one can see that where the joint acceleration
has a big deviation also the velocity has a larger deviation. Figure 11.44 shows when the
calculated velocity has a small deviation also the calculated acceleration will have a very small
deviation.
A factor which affects the calculated values is the kinematic parameters used in the Jacobian
matrix. The kinematic parameters are given from the manufacture of the robot arms and they
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Public Report ELAU GmbH, Marktheidenfeld
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