Fig 1.
Three-link theoretical model of a lizard, Callisaurus draconoides, in the horizontal plane.
The moment of inertia for the segment of the body is assumed as a homogenous cylinder. Since the mass percentages of the forelegs and the hind limbs are low relative to the total body mass, the leg motion’s effect is assumed to be negligible.
Table 1.
Morphometrics of Callisaurus draconoides used for the three-link theoretical model.
Fig 2.
Moments and forces periodically acting on the lizard in a period in the horizontal plane.
When a lizard runs, its legs exert a force on the ground with every stride, a fore-aft ground reaction force GRFx (fx), lateral force GRFy (fy), and GRM are produced at its feet. Also, the body torques (Tbw, Tbt) are generated by the bodies’ joint movement. A lizard controls these forces, moments, and torques to run forward by repeating the gait.
Fig 3.
(a) Overall architecture of the dynamics analysis for benefits of the undulatory body movement, (b) simulation for one cycle of the gait of the lizard model with angular body movement (waist, tail, and leg controller are a proportional-derivative (PD) controller) and (c) forces and moments in the lizard model.
Fig 4.
Profiles of (a) GRFx and (b) GRFy approximated as a sine function similar to the previous studies [20,21].
Fig 5.
Movements of the lizard models calculated by the dynamics analysis when the joint torques are minimized.
(* indicates the point at which the foot contacts the ground). (a) l1 = 66 mm, l2 = 42 mm, l3 = 84 mm, m1 = 4.0 g, m2 = 4.0 g, m3 = 2.0 g, (b) l1 = 60 mm, l2 = 40 mm, l3 = 92 mm, m1 = 4.0 g, m2 = 4.0 g, m3 = 2.0 g, (c) l1 = 72 mm, l2 = 42 mm, l3 = 78 mm, m1 = 4.0 g, m2 = 4.0 g, m3 = 2.0 g, (d) l1 = 66 mm, l2 = 42 mm, l3 = 84 mm, m1 = 4.2 g, m2 = 4.0 g, m3 = 1.8 g, (e) l1 = 66 mm, l2 = 42 mm, l3 = 84 mm, m1 = 3.8 g, m2 = 4.0 g, m3 = 2.2 g.
Fig 6.
(a) Captured image of the running lizard for the joint angles of waist and tail from [22] and (b) comparison of the phase differences of the waist and tail joint angles between the real lizard and the dynamic model.
Fig 7.
Kinematic biomechanical model of the lizard to confirm the relationship between the undulatory body movement and bipedal running locomotion: (a) bodies, (b) joints, and (c) lengths.
The number of links used in the model is fifteen, and the number of joints is 33.
Table 2.
Size and mass of a lizard biomechanical model.
Table 3.
Joint motion of the lizard biomechanical model.
Fig 8.
Changes in the angle of the ankle joint while the hind legs touch the ground.
(a) before the foot touches the ground, (b) while the foot touches the ground, and (c) after the foot falls off the ground.
Fig 9.
The dynamic system of the lizard biomechanical model: (a) Non-contact, (b) contact with the ground.
The position of the tiptoe is fixed while the foot touches on the ground.
Fig 10.
Squares of the torques of all joints obtained by varying the body movement.
The magnitude of the waist joint motion changes in the vertical direction, and the magnitude of the tail joint motion changes in the horizontal direction.
Table 4.
Design parameters for optimization.
Fig 11.
Snapshot of a moving video clip of a simulated lizard when the square of the joint torque is minimized.
The lizard biomechanical model has bipedal running locomotion at a speed of 4 m/s.
Fig 12.
Comparison of the tiptoe’s trajectory between the dynamic biomechanical model and the real lizard.
(a) The trajectory of the tiptoe of the lizard biomechanical model in the top view has a length of 58.5 mm in the horizontal direction, and 25.8 mm in the vertical direction. (b) The trajectory of the tiptoe of the real lizard in the top view has a length of 199 mm in the horizontal direction, and 49 mm in the vertical direction. (c) The trajectory of the tiptoe of the lizard biomechanical model in the side view has a length of 58.5 mm in the horizontal direction, and 8.7 mm in the vertical direction. (b) The trajectory of the tiptoe of the real lizard in the side view has a length of 199 mm in the horizontal direction, and 56 mm in the vertical direction.
Fig 13.
The locomotion characteristics of the lizard biomechanical model changed by increasing the undulatory body movement.
(a) Concept of the increase of the lizard’s undulatory body movement. The waist and tail joint angles are set to the same angle. (b) The stride length and (c) duration are increased by increasing the lizard’s undulatory body movement. (c) The duty factor does not be changed by the undulatory body movement of the lizard biomechanical model.
Table 5.
Comparison of locomotion specification between the biomechanical model and the real lizard.
Table.
Nomenclature.
Fig 14.
(a) Kinematic parameters for the lizard theoretical model, (b) the generalized angle of the links and the relative angle between the links and (c) forces and moments acting on each link of the lizard theoretical model in the horizontal plane.