Both the linear leg spring model and the two-segment leg model with constant spring stiffness have been broadly used as template\nmodels to investigate bouncing gaits for legged robots with compliant legs. In addition to these two models, the other stiffness leg\nspring models developed using inspiration from biological characteristic have the potential to improve high-speed running capacity\nof spring-legged robots. In this paper, we investigate the effects of ââ?¬Å?Jââ?¬Â-curve spring stiffness inspired by biological materials on running\nspeeds of segmented legs during high-speed locomotion.Mathematical formulation of the relationship between the virtual leg\nforce and the virtual leg compression is established.When the SLIP model and the two-segment leg model with constant spring stiffness\nand with ââ?¬Å?Jââ?¬Â-curve spring stiffness have the same dimensionless reference stiffness, the two-segment leg model with ââ?¬Å?Jââ?¬Â-curve\nspring stiffness reveals that (1) both the largest tolerated range of running speeds and the tolerated maximum running speed are\nfound and (2) at fast running speed from25 to 40/92msâË?â??1 both the tolerated range of landing angle and the stability region are the\nlargest. It is suggested that the two-segment leg model with ââ?¬Å?Jââ?¬Â-curve spring stiffness is more advantageous for high-speed running\ncompared with the SLIP model and with constant spring stiffness.
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