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An articulated 7 DOF robotic arm would use forward kinematics to determine the location of the gripper.

Forward kinematics is computation of the position and orientation of robot's end effector as a function of its joint angles. It is widely used in robotics, computer games, and animation. The reverse process is known as inverse kinematics.

For a serial chain of n links, and let θi be the angle of link i. Given θ0 ... θn, the frame of link n relative to link 0 is:

{}^{0}T_n = \prod_{i=1}^n {}^{i - 1}T_i(\theta_i)

Where i − 1Tii) is the transformation matrix from the frame of link i to link i − 1. In robotics, these are conventionally described by Denavit-Hartenberg parameters [1].

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