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2-DOF Manipulator. Now, given the joint angles Ө1, Ө 2 we can determine the end effecter coordinates x and y. . Forward kinematics. The coordinates (x, y) of the tool are expressed in this coordinate frame as:. Inverse Kinematics.

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2 dof manipulator

2-DOF Manipulator

Now, given the joint angles Ө1, Ө2 we can determine the end effecter coordinates x and y.

forward kinematics

Forward kinematics

The coordinates (x, y) of the tool are expressed in this coordinate frame as:

inverse kinematics

Inverse Kinematics

In order to command the robot to move to a location we need the inverse; that is, we need the joint variables Ө1, Ө2 in terms of the x and y coordinates of A.

This is the problem of inverse kinematics. In other words, given x and y in the forward kinematic Equations (1.1) and (1.2).

Consider the diagram of Figure 1.26. Using the Law of Cosines we see that the angle Ө2 is given by