A kinetostatic approach applied to the design of a backflip strategy for quadruped robots is proposed in this paper. Inspired by legged animals and taking the advantage of the leg workspace, this strategy provides an optimal design idea for the low-cost quadruped robots to achieve self-recovery after overturning. Through kinetostatic and energy analysis, a four-stepped backflip strategy based on the selected rotation axis with minimum energy is proposed, with a process of selection, lifting, rotating, and protection. The kinematic factors that affect the backflip are investigated, along with the relationship between the design parameters of the leg and trunk being analyzed. At the end of this paper, the strategy is validated by a simulation and experiments with a prototype called DRbot, demonstrating that the strategy endows the robot a strong self-recovery ability in various terrains.