Chapter: Mechanical : Robotics : Robot Kinematics And Robot Programming
Direct and inverse kinematics of 4 degrees of freedom
Direct
and inverse kinematics of 4 degrees of freedom
Expression for direct and inverse
kinematics of 4 degrees of freedom robot
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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