<![CDATA[This paper presents a virtual-to-real validation framework for the kinematic modeling of a 6-DOF articulated industrial manipulator, Denso VS-6577. The proposed framework integrates analytical forward and inverse kinematics with a virtual simulation environment and physical robot experiments to evaluate trajectory consistency between simulated and real-world robotic environments. Closed-form inverse kinematic solutions based on the Denavit–Hartenberg (DH) convention are derived to enable computationally efficient real-time joint computation and continuous and smooth joint trajectory generation. A graphical simulation environment developed using MATLAB and V-Realm is employed to visualize and analyze robot motion under multiple joint configurations, including elbow-up posture selection and continuity-aware joint configuration management to maintain continuous manipulator motion throughout trajectory execution. To validate the proposed framework, identical circular trajectories are executed in both simulation and physical robot environments using the built-in closed-loop servo control system of the industrial manipulator. Trajectory tracking performance is evaluated by comparing Cartesian position errors along the x, y, and z axes using root-mean-square error (RMSE) analysis. Experimental results show simulation RMSE values of 1.85 mm, 0.49 mm, and 0.054 mm along the x, y, and z axes, respectively, while the physical robot experiments produce RMSE values of 3.125 mm, 1.318 mm, and 0.089 mm. The computational cost of the analytical inverse kinematic solution is less than 5 ms, demonstrating suitability for real-time robotic implementation. The results demonstrate satisfactory agreement between simulation and physical robot trajectories during continuous circular motion, while larger deviations are observed during transitional point-to-point movements. These discrepancies are primarily attributed to actuator dynamics, servo response delay, joint compliance, and mechanical backlash that are not represented in the analytical kinematic model. The proposed framework provides a unified approach for analytical kinematic validation, trajectory evaluation, and virtual-to-real robotic verification. The proposed framework can support future development of digital twin systems, advanced motion planning, and industrial robotic trajectory optimization.]]>
