Solution:

Direct Kinematics:

For any robotic manipulator, given the joint variable vector, q(t) i.e. q is either a rotary or a prismatic variable, and the geometric link parameter i.e.as and d’s.

ARM matrix i.e. Composite Homogenous Coordinate Transformation Matrix: 4 * 4 matrix.

1st 3 columns give the 3 possible orientations (Yaw, Pitch, Roll) of the tool and the the last column shows the position of the tooltip p, thus solving the DKP.

If we give this matrix as input to the robot,

the robot will go and stop in that particular position and for that specific orientation.

Inverse Kinematics:

Inverse kinematics is simply the reverse problem i.e., given the target position and orientation of the end-effector, we have to find the joint parameters.

Inverse kinematics is the tougher problem when compared to forward kinematics. Since this is tougher, mathematicians have come up with different approaches to solve this problem.

We need to find: Position and rotation in 3D space.

Also called arm solutions or backward solutions.

Normally tasks are formulated in terms of Position and Orientation rather than joint variables.