Nonlinear Mechanical Modeling and Experimental Validation of CFRP Energy Storage Elements for Jumping Robots

Jumping robots, which offer high energy density and tunable properties, exhibit superior obstacle-crossing capability for exploration missions. However, most existing studies rely on simplified linear spring assumptions for modeling, which fail to accurately capture the nonlinear mechanical behavior of large-deformation composite leaf springs. To address this issue, this paper presents an equivalent mechanical model of a carbon fiber-reinforced polymer (CFRP)-based jumping mechanism derived from geometrically nonlinear theory. First, for a rectangular CFRP leaf spring compressed at both ends, a circular arc assumption is introduced to describe large-deflection deformation. Using the variational principle, an analytical relationship between compression displacement and elastic force is derived in the form of elliptic integrals. Second, an experimental platform consisting of a servo motor, reduction gears, a winding roller, and sensors is developed to enable high-precision compression loading via closed-loop position proportional-integral-derivative (PID) control. Mechanical tests are conducted on CFRP leaf springs of various specifications. Finally, an empirical correction coefficient is introduced to calibrate the parameters of the theoretical model. Experimental results show that the calibrated model achieves a coefficient of determination R2 above 0.99 and a root mean square error below 5% of the peak force, validating its predictive accuracy within a compression range of less than L0/2. The proposed mechanical model provides a reliable theoretical basis for the optimal design and performance prediction of elastic elements in jumping robots.