Fig. 7: Two-dimensional theoretical model of lizard locomotion.
From: Coordinating limbs and spine: (Pareto-)optimal locomotion in theory, in vivo, and in robots
The postures of a rigid-spine (a) and curved-spine (b) two-dimensional model lizard are shown at the beginning (black) and end (blue) of a single stride. Dashed black lines indicate the neutral position, where legs are orthogonal to the thoraco-lumbar spine (TLS), and the dotted line on the right indicates the unbent trunk axis, i.e., the axis connecting shoulder and hip, which corresponds to the spine axis on the left. Leg length ℓleg was chosen to be half the TLS length in both configurations. Leg ROM ϕleg equals π/4 in (a) and π/8 in (b) configuration. Spine base ROM ϕbase (see Section B in Supplementary S1) in (b) was chosen as π/3, and total ROM can be calculated by ϕtot = ϕleg + ϕbase (here: 82.5°). According to the law of cosines and basic trigonometric addition formulas, the travel distance ΔS can be calculated by \(\Delta {S}_{r}=4\cdot \sin ({\phi }_{leg}/2)\cdot {\ell }_{leg}\) and \(\Delta {S}_{c}=4\cdot \sin ({\phi }_{tot}/2)\cdot {\ell }_{leg}\) in the rigid and curved configuration, respectively. Hippre/post and shoulderpre/post marks the position of the hip respectively the shoulder at start and end of the stride. The intermediate resolution of a single step of both models is shown in (c) and (d) with front left and hind right foot on the ground (coloured dots, connected by dotted lines for reference). Angles were chosen to ensure the same walking distance, i.e., ϕleg = 105° for the rigid walker and ϕleg = 60°, ϕbase = 45° for the curved spine walker.
