An upright life, the postural stability of birds: a tensegrity system.

Birds are so stable that they can rest and even sleep standing up. We propose that stable static balance is achieved by tensegrity. The rigid bones can be held together by tension in the tendons, allowing the system to stabilize under the action of gravity. We used the proportions of the bird's osteomuscular system to create a mathematical model. First, the extensor muscles and tendons of the leg are replaced by a single cable that follows the leg and is guided by joint pulleys. Analysis of the model shows that it can achieve balance. However, it does not match the biomechanical characteristics of the bird's body and is not stable. We then replaced the single cable with four cables, roughly corresponding to the extensor groups, and added a ligament loop at the knee. The model is then able to reach a stable equilibrium and the biomechanical characteristics are satisfied. Some of the anatomical features used in our model correspond to innovations unique to the avian lineage. We propose that tensegrity, which allows light and stable mechanical systems, is fundamental to the evolution of the avian body plan. It can also be used as an alternative model for bipedal robots.

Estimating motion between avian vertebrae by contact modeling of joint surfaces.

Estimating the motion between two bones is crucial for understanding their biomechanical function. The vertebral column is particularly challenging because the vertebrae articulate at more than one surface. This paper proposes a method to estimate 3D motion between two avian vertebrae, by bones surface reconstruction and contact modeling. The neck of birds was selected as a case study because it is a functionally highly versatile structure combining dexterity and strength. As such, it has great potential to serve as a source for bioinspired design, for robotic manipulators for instance. First, 3D models of the vertebrae are obtained by computed tomography (CT). Next, joint surfaces of contact are approximated with polynomial surfaces, and a system of equations derived from contact modeling between surfaces is established. A constrained optimization problem is defined in order to find the best position of the vertebrae for a set of given orientations in space. As a result, the possible intervertebral range of motion is estimated.

Modeling intervertebral articulation: The rotule à doigt mechanical joint (RAD) in birds and mammals.

The vertebrate skeleton is composed of articulated bones. Most of the articulations are classically described using mechanical joints, except the intervertebral joint. The aim of this study was to identify a joint model with the same mechanical features as the cervical joints. On the neck vertebrae, six articular surfaces participate in the joint: the cranial part of the centrum and the facets of the two prezygapophyses of a vertebra articulate on the caudal part of the centrum and the two articular facets of the postzygapophyses of the previous vertebra. We used the intervertebral joints of the birds neck to identify the mechanical joint representing intervertebral linkage. This link was described in the literature as a joint allowing two or three rotations and no translation. These features correspond to the rotule à doigt (RAD) joint, a ball and socket joint with a pin. We compared the RAD joint to the postaxial intervertebral joints of the avian neck and found it a suitable model to determine the geometrical features involved in the joint mobility. The difference in the angles of virtual axes linking the geometrical center of the centrum to the zygapophysis surfaces determines the mean dorsoventral flexion of the joint. It also helps to limit longitudinal rotation. The orientation of the zygapophysis surfaces determines the range of motion in both dorsoventral and lateral flexion. The overall system prevents dislocation. The model was validated on 13 joints of a vulture neck and 11 joints of a swallow neck and on one joint (C6-C7) in each of three mammal species: the wolf (Canis lupus), mole (Talpa europaea), and human (Homo sapiens). The RAD mechanical joint was found in all vertebral articulations. This validation of the model on different species shows that the RAD intervertebral joint model makes it possible to extract the parameters that guide and limit the mobility of the cervical spine from the complex shape of the vertebrae and to compare them in interspecific studies.