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Direct and inverse kinematics of 4 degrees of freedom
Expression for direct and inverse kinematics of 4 degrees of freedom robot Manipulator
A 4-Degree of Freedom Manipulator in (3D) Three Dimensions:
The configuration of a manipulator in three dimensions. The manipulator has 4 degrees - of freedom: joint I (type T joint) allows rotation about the z axis; joint 2 (type R) allows rotation about an axis that is perpendicular to the z axis; joint 3 is a linear joint which is capable of sliding over a certain range; and joint 4 is a type R joint which allows rotation about an axis that is parallel to the joint 2 axis. Thus, we have a TRL: R manipulator.
Let us define the angle of rotation of joint I to be the base rotation 0; the angle of rotation of joint 2 will be called the elevation angle 4.; the length of linear joint 3 will be called the extension L (L-represents a combination of links 2 and 3); and the angle that joint 4 makes with the x — y plane will be called the pitch angle 4.
The position of the end of the wrist, P, defined in the world coordinate system for the robot, is given by
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