The purpose of this paper is to propose a robot-assisted assembly system for the installation of a variety of heavy components in the assembly system. The robot-assisted assembly system is composed of an industrial robot system, a robot path planning system, a visual positioning system and an additional robot motion platform. Stereo vision system is used to improve the accuracy the of robot positioning system. Probabilistic roadmap (PRM) method is used to plan robot path in 3D space with obstacles. The PRM planner divides planning into two phases: the learning phase and the query phase. In the learning phase, collision-free roadmap is built. In the query phase, the nodes of roadmap are connected. We use the A-star algorithm to find a feasible path between the initial node and the goal node. Experiment results show that our method can efficiently make a collision-free path in the workspace with obstacles in the products.