Influence of “J”-Curve Spring Stiffness on Running Speeds of Segmented Legs during High-Speed Locomotion

Abstract

Both the linear leg spring model and the two-segment leg model with constant spring stiffness have been broadly used as template models to investigate bouncing gaits for legged robots with compliant legs. In addition to these two models, the other stiffness leg spring models developed using inspiration from biological characteristic have the potential to improve high-speed running capacity of spring-legged robots. In this paper, we investigate the effects of “J”-curve spring stiffness inspired by biological materials on running speeds of segmented legs during high-speed locomotion. Mathematical formulation of the relationship between the virtual leg force and the virtual leg compression is established. When the SLIP model and the two-segment leg model with constant spring stiffness and with “J”-curve spring stiffness have the same dimensionless reference stiffness, the two-segment leg model with “J”-curve spring stiffness reveals that (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mn fontstyle="italic">1</mml:mn></mml:mrow></mml:math>) both the largest tolerated range of running speeds and the tolerated maximum running speed are found and (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mn fontstyle="italic">2</mml:mn></mml:mrow></mml:math>) at fast running speed from 25 to 40/92 m s −1 both the tolerated range of landing angle and the stability region are the largest. It is suggested that the two-segment leg model with “J”-curve spring stiffness is more advantageous for high-speed running compared with the SLIP model and with constant spring stiffness.