To address the high failure rate of rollers in coal mine belt conveyors, the inefficiency of manual replacement, and the operational disruptions caused by maintenance shutdowns, this study proposes a robotic arm system capable of replacing rollers without halting conveyor operations. The research focuses on the kinematic performance and path planning strategy of the robotic arm. A kinematic model is established using the Denavit–Hartenberg (DH) parameters, and the workspace distribution is analyzed via the Monte Carlo method. The results show that the horizontal reach exceeds 2020 mm and the vertical reach extends up to 2000 mm, which fully satisfies the spatial requirements for roller replacement across the entire conveyor system. In the path planning phase, an obstacle expansion model is constructed, and an improved Informed RRT* algorithm is implemented to generate collision-free trajectories, ensuring effective obstacle avoidance. To improve trajectory smoothness, path pruning and cubic B-spline interpolation are applied to refine the initial paths. For trajectory planning in joint space, quintic polynomial interpolation is employed, with boundary conditions set to ensure zero velocity and zero acceleration at both the start and end points, thereby guaranteeing smooth and stable motion of the robotic arm. Simulation results indicate that joint angles, angular velocities, and angular accelerations vary smoothly throughout the roller grasping process, without abrupt changes, and converge to zero at the beginning and end of the trajectory. End-effector trajectory tracking error analysis reveals positioning errors within 0.8 mm for side rollers and 3 mm for central rollers, well within acceptable engineering accuracy thresholds. This work provides a theoretical foundation and a practical implementation framework for advancing automation and intelligent operation in roller replacement tasks within coal mine belt conveyor systems.