Fig 1.
(a) Octopus arm marker attachment method. Five retroreflective markers were adhered to the arm. The proximal segment consisted of the first three markers. The distal segment consisted of the last three markers. The two methods for measuring curvature are also shown. (b) The distal segment of the arm depicts the radius of curvature (ko), calculated by the lengths of the sides (a,b, and c) between three points on the circle. (c) The distal segment of the arm depicts the vector curvature (kb), defined by the angle made by two consecutive vectors.
Fig 2.
(a) Markers used to create two distinct local coordinate systems and describe the overall posture of the octopus arm. (b) The upper-case coordinate system () was created on the proximal segment and the lower-case coordinate system (
) was created on the distal segment. (c) Additionally, fixed body and floating axes were created using the two segments. Octopus arm posture was shown such that measurements would result in differences in planar orientation. (d) Differences were reported using three rotations: ∝ representing flexion/extension, β representing abduction/adduction, and γ representing internal/external rotation.
Fig 3.
(a) Octopus arm in nearly straight posture: white line indicates approximate ‘backbone’ of markers. (b) Octopus arm in simple bending posture, where the arm seemingly lays on one plane: white circle depicts again how ko is calculated. (c) Octopus arm in complex bending posture, where the arm is not on one plane: white vectors depict again how kb is calculated.
Table 1.
Outcome measures for proximal and distal arm segments in the three postures as demonstrated through one of the test trials (n = 1): Nearly straight, simple bending, and complex bending which are shown in Fig 3.
The approach using ko is strongly influenced by segment length in comparison to kb approach.
Fig 4.
(a) Octopus arm in straight posture for reference. (b) Octopus in simple bending posture: local coordinate systems are shown in yellow and green for the proximal and distal segments, respectively. Vectors show 3D rotations. Since simple bending appears to have both segments on similar planes, it is expected that the largest contribution to orientation difference will be in the flexion/extension direction.
Table 2.
Average (standard deviation) proximal curvature, distal curvature, and planar orientation values for all disembodied arms (n = 9) while being moved underwater.
The simple bending posture (Fig 4B) consistently had larger proximal curvatures, distal curvatures, and planar orientation differences between proximal and distal segments. Although perfectly planar postures would be expected for observationally straight and simple bending, non-zero values for abduction and internal rotation were measured, indicating that the arm was not in as simple a posture as expected.
Fig 5.
Live octopus exhibiting (a) simple bending posture, where markers appear to lay on the same plane and (b) a complex bending posture, where markers are not in the same plane, due to bending in different directions along with complex rotations. In both images, the white curves highlight the arm of focus and the green circles indicate the marker locations.
Table 3.
Curvature and planar orientation results for a (n = 1) live, swimming octopus, also seen in Fig 5.
Similar abduction and internal rotation data were obtained during the live octopus and the disembodied arm trials. The complex bending scenario had a large, negative internal rotation value, which suggests that the orientation of the distal segment was nearly flipped (145°) in comparison to the proximal segment.