Research ArticleBIOPHYSICS

Leg force interference in polypedal locomotion

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Science Advances  05 Sep 2018:
Vol. 4, no. 9, eaat3721
DOI: 10.1126/sciadv.aat3721
  • Fig. 1 Gait patterns of four-, six-, and eight-legged locomotor systems (A to D) and corresponding overall ground forces over a stride (E) for single leg duty factors of 0.45 (that is, contact duration < swing duration).

    Bars represent contact phases; left (L) and right (R) legs are counted fore to aft. (A) Gait pattern of a trotting hexapod; ipsilateral phases are 0.5. (B to D) Ipsilateral phase shifts (0.26, 0.34, and 0.38) and corresponding gait patterns produce minimal vertical force amplitudes for given numbers of legs (four, six, and eight). These gait patterns correspond to the overall vertical ground forces shown in (E). The gray solid line refers to (A), the black solid line refers to (B), the dash-dotted line refers to (C), and the dotted line refers to (D).

  • Fig. 2 Dependency of total vertical leg force amplitudes on the phase shift of ipsilateral adjacent legs and duty factor for locomotor apparatuses with two to four leg pairs.

    (A) Two pairs of walking legs: Duty factors range from 0.2 (dark gray) to 0.8 (light gray) with the duty factor of 0.5 highlighted in red. With low duty factors and intermediate phase shifts, the peak frequency of the force oscillations deviates from two times the stride frequency; these intervals are shaded in gray. (B) Three pairs of legs. (C) Four pairs of legs.

  • Fig. 3 Specific amplitudes of the overall vertical ground reaction forces for locomotor apparatuses with 2 to 10 pairs of legs (see legend).

    Data are shown for a duty factor of 0.5 in the phase range from the amplitude minimum closest to alternating leg coordination to the amplitude maximum at alternating sets of legs (compare Fig. 2). The slope of the amplitudes increases significantly with an increasing number of leg pairs. The trajectories’ points of intersection with the horizontal dashed line indicate those θ at which only one-half of the maximum force amplitude is retained (see Fig. 4). The vertical dashed line represents a deviation of 0.06 from the strictly alternating gait pattern as found in fast-running desert ants (see main text for further explanations). The red circles indicate the force amplitude values for locomotor systems with two, three, and four pairs of legs at such a deviation from strict alternation.

  • Fig. 4 Position of the first amplitude minimum (triangles) and half peak values (circles) with respect to θ for locomotor apparatuses with 2 to 10 pairs of walking legs.

    Particularly for low leg numbers, the position of the force amplitude minimum decreases with increasing duty factors (decreasing brightness; compare Fig. 2A and labeling at the first column of triangles), while duty factors have virtually no impact on the phase shift at which force amplitudes are halved (see also Fig. 2).

  • Fig. 5 Minimum number of legs on the ground as function of duty factor and phase shift of ipsilateral adjacent legs.

    (A) Two pairs of legs. (B) Three pairs of legs. (C) Four pairs of legs. With sets of legs close to alternating activity and duty factors below 0.5, the minimum number of legs on the ground is always 0, while phase shifts deviating from alternation (0.5) and synchrony (0 and 1) result in increased minimum numbers of legs in contact with the ground.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/9/eaat3721/DC1

    Fig. S1. Speed-dependent transformation of a locomotor system from an underdamped to an overdamped vertical oscillator.

    Fig. S2. Example force spectrums for locomotor apparatuses with three pairs of walking legs at a duty factor of 0.3.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Speed-dependent transformation of a locomotor system from an underdamped to an overdamped vertical oscillator.
    • Fig. S2. Example force spectrums for locomotor apparatuses with three pairs of walking legs at a duty factor of 0.3.

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