Study of animal locomotion

Legged locomotion is a dominant form of terrestrial locomotion, the movement on land. The motion of limbs is quantified by intralimb and interlimb kinematic parameters.[1][2] Intralimb kinematic parameters capture movement aspects of an individual limb, whereas, interlimb kinematic parameters characterize the coordination across limbs. Interlimb kinematic parameters are also referred to as gait parameters. The following are key intralimb and interlimb kinematic parameters of walking:[3][1][2][4][5]

Intralimb kinematic parameters:

Anterior Extreme Position (AEP): position of the leg when it first contacts the ground (i.e. start of stance phase).

Posterior Extreme Position (PEP): position of the leg when it first lifts off of the ground (i.e. start of swing phase).

Stride duration: elapsed time between two onsets of stance.

Stride frequency: inverse of stride duration. The number of strides within a second.

Stance duration: time elapsed between stance onset (i.e. AEP) and swing onset (i.e. PEP).

Swing duration: time elapsed between swing onset (i.e. PEP) and the subsequent stance onset (i.e. AEP).

Stride length: the distance a leg travels between stance onset (i.e. AEP) and swing onset (i.e. PEP).

Stride amplitude: the distance a leg travels between swing onset (i.e. PEP) and the subsequent stance onset (i.e. AEP), while also accounting for the movement of the body.

Interlimb kinematic parameters:

Step length: the distance from the stance onset of a reference leg to its contralateral counterpart.

Phase: the lag of a leg relative to the stride period of a reference leg.

Number of legs in stance: The number of legs in stance at a single point in time.

Tripod coordination strength (TCS): specific to hexapod interlimb coordination, this parameter determines how much the interlimb coordination resembles the canonical tripod gait. TCS is calculated as the ratio of the total time legs belonging to a tripod (i.e. left front, middle right, and hind left legs, or vice versa) are in swing together, by the time elapsed between the first leg of the tripod that enters swing and the last leg of the same tripod that exits swing.

Classifying stance and swing transitions of the front right (red) and left (blue) legs of a fly. The onset of stance (black dot) occurs at the peaks of the leg position signal, whereas, the onset of swing (light blue dot) occurs at the troughs.

Characterizing swing and stance transitions [2][3][4][5]:

The calculation of the above intra- and interlimb kinematics relies on the classification of when the legs of an animal touches and leaves the ground. Stance onset is defined as when a leg first contacts the ground, whereas, swing onset occurs at the time when the leg leaves the ground. Typically, the transition between swing and stance, and vice versa, of a leg is determined by first recording the leg's motion with high-speed videography (see the description of high-speed videography below for more details). From the video recordings of the leg, a marker on the leg (usually placed at the distal tip of the leg) is then tracked manually or in an automated fashion to obtain the position signal of the leg's movement. The position signal associated with each leg is then normalized to that associated with a marker on the body; transforming the leg position signal into body-centered coordinates. This normalization is necessary to isolate the movement of the leg relative to that of the body. For tracking the leg movement of unconstrained/untethered animals, it is important to perform a coordinate transform so that the movement of the animal is aligned along one axis (e.g. a common heading angle). This is also a necessary step because it isolates the oscillatory anterior-posterior movement of the leg along a single axis, rather than being obscured across multiple axes. Once the tracked and normalized leg position is obtained, one way to determine the onsets of stance and swing are to find the peaks and troughs of the leg position signal. The peaks of the leg position signal are the stance onsets, which are also the anterior extreme positions of the leg for each step. On the other hand, the troughs of the leg position signal are the swing onsets as well as the posterior extreme positions of the leg for each step. Therefore, the transitions between stance and swing, and vice versa, are determined by finding the peaks and the troughs of the normalized leg position signal. Alternatively, these transitions can be found by using leg velocity, the derivative of the leg position signal. When using this approach, a threshold is chosen to categorize leg movement into stance and swing given the instantaneous velocity of the leg. This stance and swing classification approach is useful for instances when the interaction between the leg and substrate is unclear (i.e. difficult to tell when the leg truly contacts the substrate). Regardless of the approach, accurately classifying swing and stance is crucial for the above calculations of intra- and interlimb kinematic parameters.

Joint angle analyses:

Walking can also be quantified through the analysis of joint angles.[6][7][8] During legged locomotion, an animal flexes and extends its joints in an oscillatory manner, creating a joint angle pattern that repeats across steps. The following are some useful joint angle analyses for characterizing walking:

Joint angle trace: a trace of the angles that a joint exhibits during walking.

Joint angle distribution: the distribution of angles of a joint.

Joint angle extremes: the maximum (extension) and minimum (flexion) angle of a joint during walking.

Joint angle variability across steps: the variability between joint angle traces of several steps.

Relationship between several joint angles: the relative angles of two joints, either from the same leg or between legs. For example, the angle of a human's left femur-tibia (knee) joint when the right femur-tibia joint is at its most flexed or extended angle.

Aerial locomotion is a form of movement used by many organisms and is typically powered by at least one pair of wings. Some organisms, however, have other morphological features that allow them to glide. There are many different flight modes, such as takeoff, hovering, soaring, and landing.[9] Quantifying wing movements during these flight modes will provide insight about the body and wing maneuvers that are required to execute these behaviors.[9] Wing orientation is quantified throughout the flight cycle by three angles that are defined in a coordinate system relative to the base of the wing.[10][11] The magnitude of these three angles are often compared for upstrokes and downstrokes.[10][11][12][13] In addition, kinematic parameters are used to characterize the flight cycle, which consists of an upstroke and a downstroke.[10][12][13][11] Aerodynamics are often considered when quantifying aerial locomotion, as aerodynamic forces (e.g. lift or drag) are able to influence flight performance.[14] Key parameters from these three categories are defined as follows:

Angles to quantify wing orientation:

Wing orientation is described in the coordinate system centered at the wing hinge.[10] The x-y plane coincides with the stroke plane, the plane parallel to the plane that contains both wing tips and is centered at the wing base.[10] Assuming the wing can modeled by the vector passing through the wing base and wing tip, the following angles describe the orientation of the wing:[10]

Stroke position: angle describing the anterior-to-posterior motion of the wings relative to the stroke plane. This angle is computed as the projection of the wing vector onto the stroke plane.

Stroke deviation: angle describing the vertical amplitude of the wings relative to the stroke plane. This angle is defined as the angle between the wing vector and its projection onto the stroke plane.

Angle of attack: angular orientation of the wings (i.e. tilt) relative to the stroke plane. This angle is computed as the angle between the wing cross section vector and the stroke plane.

Kinematic parameters:

Upstroke amplitude: angular distance through which the wings travel during an upstroke.

Downstroke amplitude: angular distance through which the wings travel during a downstroke.

Stroke duration: time elapsed between the onset of two consecutive upstrokes.

Wingbeat frequency: inverse of stroke duration. The number of wingbeats per second.

Flight distance per wingbeat: the distance covered during each wingbeat.

Upstroke duration: time elapsed between the onset of an upstroke and the onset of a downstroke.

Downstroke duration: time elapsed between the onset of a downstroke and the onset of an upstroke.

Phase: if an organism has both front and hind wings, the lag of a wing pair relative to the other (reference) wing pair.

Aerodynamic parameters:

Reynolds number: ratio of inertial forces to viscous forces. This metric helps describe how wing performance changes with body size.[14]