In this paper, we propose a novel scheme for real-time motion planning of a collaborative robot that assists its fellow human worker in performing assembly tasks by delivering parts and tools to the worker. In the proposed scheme, the delivery position of the parts and tools is determined first, based on a cost function relating to the safety, visibility, and arm comfort terms of the worker by solving the non-convex optimisation problem in real-time using a random sampling-based algorithm in the vicinity of the worker's current position. Then, model predictive control (MPC)-based trajectory planner directly generates a collision-free robot trajectory from the current robot configuration to the delivery configuration under velocity and acceleration constraints of the robot. The proposed motion planning scheme is implemented in the actual collaborative robot system and the effectiveness of the proposed scheme is illustrated experimentally.