The implementation of manipulator robots has become indispensable in various industries, enabling efficient performance of complex tasks. Swift and efficient movement of these robots is essential to maximize productivity. However, the grip limitations of the tool restrict rapid movement in scenarios where the manipulator's load varies. In this research, we propose a novel method for generating minimum-time trajectories while considering acceleration constraints on the tool. The algorithm incorporates two trajectory generation methods in the joint space: a simple polynomial approach and a composite approach. To validate the proposed method, we apply it to a UR10 robot model equipped with a vacuum gripper, specifically designed for handling boxes with diverse characteristics. By testing the algorithm on different trajectories, we successfully identify satisfactory solutions. The outcomes of this study significantly contribute to the advancement of manipulator robots by addressing the challenges posed by variable payload conditions. Our method enables efficient and rapid movement in real-world applications, enhancing overall productivity and expanding the scope of manipulator robot utilization.