Fig. 3: Comparison between characteristic curves obtained from theoretical modeling and FEM simulation.

a Force–deflection curves for the anti-spring mechanisms, obtained from theoretical modeling and FEM simulation. b Relative error curves between force–deflection curves obtained from theoretical modeling and FEM simulation. c Stiffness variation of the anti-spring mechanisms at the operating point, obtained from theoretical modeling and FEM simulation. The curves consider the anti-spring mechanisms with a width of 2 μm, a depth of 25 μm, a span of 500 μm, and different G varying from 0.355 to 1.455. d Axial stress–deflection curve and total stress-deflection curve for the anti-spring mechanism with a width of 2 μm, a depth of 25 μm, a span of 500 μm, and a G of 1.155, obtained from FEM simulation