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Recent technological progress is opening up practical applications for quadruped robots. In this context, comprehensive performance demands, including speed, payload, robustness, terrain adaptability, endurance, and techno-economics, are increasing. However, design conflicts inevitably exist among these performance indicators, highlighting design challenges, especially for a heavy-duty, electrically actuated quadruped robots, which are strongly constrained by motor torque density and battery energy density. Starting from task-specific holistic system thinking, in this paper, we present a novel task-oriented approach to the design of such kind of robots, incorporating hierarchical optimization and a control-in-the-loop design, while following a structured design path that effectively exploits the strengths of both heuristic and computational designs. Guided by these philosophies, we utilize heuristic design to obtain the approximate initial form of the prototype and propose a key task-oriented actuator joint configuration, utilizing commercially available components. Subsequently, we build a step-wise analytical models considering trajectory optimization and motor heat constraints for optimization of leg length and joint match parameters to achieve a compact performance requirement envelope and minimize redundancy in the construction of task-specific components. Furthermore, we construct a holistic simulation platform with a module control algorithm for typical scenarios to evaluate subsystem results and adjust design parameters iteratively, balancing conflicts and eventually achieving a reliable design specification for detailed subsystem design. Based on these strategies, we develop a heavy-duty electric prototype achieving a maximum speed of 2 m/s in trotting gait with a load weighting over 160 kg and enduring a period of 2 h. The experiment upon the prototype verifies the efficiency of the proposed approach.