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Figure 4.5, inverse kinematics transforms the robots TCP position (x,y and z component) into the three upper arm
angle positions θ 1, θ 2, θ 3.
The inverse kinematics gives multiple solutions of the θ vector with the three revolute joint
angles that all satisfies the specific travel plate position. This may cause problems because the
system has to be able to choose one of them. The criteria upon which to base a decision vary,
but a very reasonable choice would be the closest solution (2), which is the solution where the
manipulator moves the links as little as possible.
For the 3-DOF parallel manipulator with the system structure as in Figure 4.1, each arm can
satisfies the same TCP with to different approaches which where called elbow up and elbow
down for the serial robot. Together the three arms of the 3-DOF parallel manipulator result in
eight different combinations of the θ vector for a single goal, see Figure 4.6.
Figure 4.6, The eight solutions of the inverse kinematic for a Delta-3 robot (8).
The inverse kinematic model is obtained by using the three closure equations, constraints, of
the kinematic chains:
2
2
Pc Pb
− l = 0
i i 2
B
Eq. 4.2
i = 1,
2,
3
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Public Report ELAU GmbH, Marktheidenfeld
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