We propose a new method for the analysis and design of a robotic system that minimizes the energy consumption of a six-axis robot arm by controlling the velocity and acceleration of each arm of the robot to achieve the specified trajectory of the robot determined from a lean manufacturing method. A dynamic model of the PUMA 560 robot has been simulated on MATLAB, while the Robotics Toolbox and particle swarm optimization (PSO) are utilized to search for optimal paths and the optimal velocity and acceleration of the robot arms. The optimal velocity and acceleration are described as those giving minimum overall energy consumption constrained by a specified cycle time of the entire robotic system. Typically, the picking and placing of materials are carried out by humans, causing a variation in production rate, whereas our system using a robot arm ensures a stable production rate. Moreover, the optimal results obtained from PSO are adopted to train an artificial neural network (ANN) to extend the design system from discrete optimal values to a continuous and near-optimal value. In other words, the ANN is used to obtain an approximate optimal value between those obtained from PSO to make the system applicable to a real-world system. As shown by the simulation results, this method reduces the energy consumption of 12.3% from the initial energy and reduces the time for optimization by 99.8% compared with that for the PSO technique.