Mathematical modelling and forward kinematic analysis of the 6-DOF collaborative robot

Authors

  • T. Ciril Joy Kochu Division of Robotics Engineering, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore-641114, Tamil Nadu, India.
  • S. Aswath Narayanan Division of Robotics Engineering, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore-641114, Tamil Nadu, India.
  • S. Francis Xavier Division of Robotics Engineering, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore-641114, Tamil Nadu, India.
  • B. Vimalsubbu Division of Robotics Engineering, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore-641114, Tamil Nadu, India.
  • P. Rajalakshmy Division of Robotics Engineering, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore-641114, Tamil Nadu, India.
  • Velusamy Kavitha Department of Mathematics and Robotics Engineering, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore-641114, Tamil Nadu, India.
  • Seenith Sivasundaram College of Engineering, Science and Mathematics, Daytona Beach, FL 32114, USA.

Abstract

Collaborative robots (cobots) are integral to modern automation, requiring precise mathematical models for safe and efficient human-robot interaction. This paper presents a complete forward kinematic model of the Yaskawa HC10DTP, a six-degree-of-freedom (6-DOF) collaborative robotic manipulator. Utilizing the Denavit-Hartenberg (DH) convention, we systematically derive the robot's kinematic parameters. The forward kinematic solution is formulated by constructing the homogeneous transformation matrices for each joint, leading to a final transformation matrix that maps the joint space configuration to the Cartesian pose of the end-effector. The analytical model's accuracy is rigorously validated by comparing its predictions against results obtained from the industry-standard simulation software, RoboDK, for multiple distinct joint configurations. The strong correlation between the analytical and simulated results confirms the validity of the derived model, establishing a foundational mathematical framework for subsequent analyses, such as inverse kinematics, trajectory planning, and dynamic control of the Yaskawa HC10DTP.

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Published

11/28/2025

Issue

Vol. 16 No. 4 (2025): Mathematics in Engineering, Science and Aerospace (MESA)

Section

Articles