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Industrial robotic manipulators are widely used in applications such as pick & place, welding, and assembly to perform repeated tasks in replace of human labor. Such tasks typically require fully autonomous mechanical arms that are capable of identifying the parts to operate, path planning, and trajectory generation & tracking. A robotic arm consists of a sequence of rigid links connected by movable components (the joints). Proper control of the arm’s motion requires the knowledge of inverse kinematics, which computes/outputs the joint variables, i.e., angles for revolute joints and displacement for prismatic joints, causing the robotic arm’s end effector (e.g., gripper, hand, vacuum suction cup, and etc.) to reach some desired position and orientation in the 3D space.

In this project, a 6-DOF industrial robotic arm, C12XL, is studied to achieve trajectory generation in both the 3D space and the joint space. The entire process of analysis was completed, including 1) drawing the schematic diagram and determining the frames according to the DH convention(Set of variables that shows the relationship between joint axis of a robotic arm); 2) obtaining the forward kinematics, the output of which is a homogeneous transformation matrix measuring the rotation and displacement of the end-effector frame relative to the base frame; and 3) deriving the inverse kinematics analytically, yielding a set of trigonometric equations and rotation matrices to compute the joint variables.

The derived inverse kinematic equations are implemented in MATLAB in the context of trajectory generation. Several simulation examples are presented to confirm the correctness of these equations.


Liu, C., & Ma, L. (2021, November), Inverse Kinematics of the 6DOF C12XL Robotic Arm Paper presented at 2021 Fall ASEE Middle Atlantic Section Meeting, Virtually Hosted by the section. © 2021 American Society for Engineering Education.

This work was conducted under the supervision of Professor Lili Ma at New York City College of Technology during the 2021 STEM Research Academy Summer Internship sponsored by New York City College of Technology, City University of New York (CUNY).

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