Undulatory locomotion

Undulatory locomotion is the type of motion characterized by wave-like movement patterns that act to propel an animal forward. Examples of this type of gait include crawling in snakes, or swimming in the lamprey. Although this is typically the type of gait utilized by limbless animals, some creatures with limbs, such as the salamander, forgo use of their legs in certain environments and exhibit undulatory locomotion. In robotics this movement strategy is studied in order to create novel robotic devices capable of traversing a variety of environments.

In limbless locomotion, forward locomotion is generated by propagating flexural waves along the length of the animal's body. Forces generated between the animal and surrounding environment lead to a generation of alternating sideways forces that act to move the animal forward. These forces generate thrust and drag.

Simulation predicts that thrust and drag are dominated by viscous forces at low Reynolds numbers and inertial forces at higher Reynolds numbers. When the animal swims in a fluid, two main forces are thought to play a role:

At low Reynolds number (Re~10⁰), skin friction accounts for nearly all of the thrust and drag. For those animals which undulate at intermediate Reynolds number (Re~10¹), such as the Ascidia larvae, both skin friction and form force account for the production of drag and thrust. At high Reynolds number (Re~10²), both skin friction and form force act to generate drag, but only form force produces thrust.

In animals that move without use of limbs, the most common feature of the locomotion is a rostral to caudal wave that travels down their body. However, this pattern can change based on the particular undulating animal, the environment, and the metric in which the animal is optimizing (i.e. speed, energy, etc.). The most common mode of motion is simple undulations in which lateral bending is propagated from head to tail.

Snakes can exhibit five different modes of terrestrial locomotion: (1) lateral undulation, (2) sidewinding, (3) concertina, (4) rectilinear, and (5) slide-pushing. Lateral undulation closely resembles the simple undulatory motion observed in many other animals such as in lizards, eels and fish, in which waves of lateral bending propagate down the snake's body.

The American eel typically moves in an aquatic environment, though it can also move on land for short periods of time. It is able to successfully move about in both environments by producing traveling waves of lateral undulations. However, differences between terrestrial and aquatic locomotor strategy suggest that the axial musculature is being activated differently, (see muscle activation patterns below). In terrestrial locomotion, all points along the body move on approximately the same path and, therefore, the lateral displacements along the length of the eel's body is approximately the same. However, in aquatic locomotion, different points along the body follow different paths with increasing lateral amplitude more posteriorly. In general, the amplitude of the lateral undulation and angle of intervertebral flexion is much greater during terrestrial locomotion than that of aquatic.

A typical characteristic of many animals that utilize undulatory locomotion is that they have segmented muscles, or blocks of myomeres, running from their head to tails which are separated by connective tissue called myosepta. In addition, some segmented muscle groups, such as the lateral hypaxial musculature in the salamander are oriented at an angle to the longitudinal direction. For these obliquely oriented fibers the strain in the longitudinal direction is greater than the strain in the muscle fiber direction leading to an architectural gear ratio greater than 1. A higher initial angle of orientation and more dorsoventral bulging produces a faster muscle contraction but results in a lower amount of force production. It is hypothesized that animals employ a variable gearing mechanism that allows self-regulation of force and velocity to meet the mechanical demands of the contraction. When a pennate muscle is subjected to a low force, resistance to width changes in the muscle cause it to rotate which consequently produces a higher architectural gear ratio (AGR) (high velocity). However, when subject to a high force, the perpendicular fiber force component overcomes the resistance to width changes and the muscle compresses producing a lower AGR (capable of maintaining a higher force output).