Four adult corn snakes caught in the wild, Pantherophis guttatus (Linnaeus 1766), were obtained from a commercial supplier [mean±s.d. snout–vent length (SVL) 102.4±9.3 cm, range 92.6–114.3 cm; mass 463±62.6 g, range 340–550 g). This species was chosen because they are locomotor generalists and thus likely to elicit the desired behavior. All experiments were approved by University of Akron IACUC. Locomotion trials were conducted after warming the snakes to 29–32°C, the field active temperature of a congeneric (Brattstrom, 1965).

We constructed a 248 cm long trackway consisting of a frame of 80/20 longitudinal supports with 11 horizontal oak dowels (91 cm long, 2.5 cm diameter) placed perpendicular to the longitudinal supports and spaced at 20 cm intervals, much like the rungs of a ladder laid horizontally (Fig. 1E). Walls were placed 45 cm apart on either side of the dowels (walls extended 36.5 cm above the dowels and 22.0 cm below) and the trackway was raised 88 cm above the ground to dissuade the snakes from leaving the trackway. Oak dowels were sanded and treated with a polyurethane sealant. Snakes were induced to move along the length of the trackway and thus perpendicular to the dowels (Fig. 1F,G). Trials were performed in sets of three per 24 h and individuals were allowed a minimum of 5 min rest between trials to prevent fatigue. A dark enclosure was placed at the end of the trackway to encourage movement in the desired direction and to allow for a location of rest between trials. Light tapping, rubbing with fingers or touching with a snake hook was used on the tail to encourage movement, though we did not attempt to induce maximal speed from the animals. Snakes were not tested for 24 h after feeding occurred. To provide an experimental control and clear contrast between the forces produced in active versus passive systems, and to show that our data are not an artefact of our measurement system, we dragged a braided nylon rope (229 g, 144 cm long, 1.7 cm diameter) across the dowel array, as this should produce only braking force and braking impulse. The coefficient of friction was measured using a standard tilting plane method, in which snakes were conscious and alert. The snakes were oriented with most body segments parallel to the slope with anterior downwards (the presence of body segments at other angles would slightly over-estimate the coefficient of friction as a result of scale anisotropy) on a plane of oak prepared identically to the dowels and tilted until they began to slide (Astley and Jayne, 2007; Gray and Lissmann, 1950; Sharpe et al., 2015); the average coefficient of friction was 0.17±0.02 (range 0.14–0.19) for the snakes (n=4) and 0.28±0.03 (range 0.23–0.32) for the rope based on 3 trials per individual/object. While there were some trials in which only braking force was recorded, to streamline analysis, only trials with propulsive force were analyzed (see Results and Discussion).

Two six-axis force/torque sensors (Nano 43, ATI Industrial Automation, Apex, NC, USA) were connected on either end of a single dowel mid-way along the trackway (dowel 6 of 11). Outputs of the force sensors were collected using 12 channels (six per sensor) on a NIDAQ N1-USB-6218 (16 bits, National Instruments, Austin, TX, USA) and recorded using the software IGOR Pro (WaveMetrics, Tigard, OR, USA) at 1 kHz. This force-sensing dowel was calibrated using hanging masses and pulleys at different angles and locations along the dowel to apply known anterior/posterior, lateral and vertical forces, which were used to create a calibration matrix using the MATLAB function linsolve (MathWorks, Natick, MA, USA). Force data were splined to smooth the data in IGOR Pro, and analyzed using a custom-written script in MATLAB. Data were normalized to body weight to facilitate comparisons between individuals (Fig. S1). During rope trials, forces induced by inertial motion of the end of the rope dropping from an adjacent dowel would confound analysis; thus, we only included the smooth rise and steady state of the forces during these trials (Fig. S2). The impulse (the time integral of force, in BW s) is the total change in momentum of the system, and was used to determine whether the overall interaction between the snake and the force-sensing dowel had a net propulsive or net braking effect, similar to studies of limbed animals (Budsberg et al., 1987; Hodson et al., 2001).

Kinematics were recorded at 120 images s−1 using six motion capture cameras (Flex 13, NaturalPoint, Inc., Corvallis, OR, USA) placed 1 m above the dowels at varying angles (Fig. 1E). Small markers of infra-red 7610 reflective tape (3M, St Paul, MN, USA) were placed at regular intervals (∼10 cm) along the dorsal side of each snake. Camera synchronization, recording, calibration, point tracking and position calculation were all accomplished using Motive Optitrack software v.2.0.2 (NaturalPoint, Inc.), which then exported 3D marker coordinates. A HERO6 Black GoPro (GoPro Inc., San Mateo, CA, USA) camera was also used to record video from above for visual confirmation, but not analysis. To determine how straight the snake was when moving across the force-sensing dowel (and thereby rule out lateral undulation), we analyzed motion capture data (dorsal view, fore–aft and lateral components) using a custom-written script in MATLAB to perform a linear regression on the points within 20 cm of the force dowel throughout the trial. The captured region spanned three dowels (middle dowel with the force sensors) while the entire snake’s body contacted between five and six dowels at any one time. Snakes occasionally used lateral bends prior to and after this region; however, trials were discarded if any lateral bends occurred on the force-sensing dowel or adjacent dowels. We quantified the maximum residual and the 95% confidence interval of the residuals as metrics of body straightness, and the angle of the body relative to the trackway (θ ϕ=0 deg is parallel and ϕ=90 deg is perpendicular). To quantify the vertical undulations along the captured region, we analyzed the motion capture data (lateral view, vertical and fore–aft components) by splining along the captured region, normalized the splines by height at the force-sensing dowel, and ran both an ANOVA and Tukey’s (5% probability) post hoc statistical tests using custom-written scripts in MATLAB. Overall velocity was calculated from Motive Optitrack data in the horizontal plane, fore–aft and lateral components.

The snake exerts a net normal and frictional force on the dowel, with the normal force being perpendicular to the substrate and the frictional force being tangent and equal to the magnitude of the normal force multiplied by the coefficient of friction (µ) (Fig. 1B–D). The vector sum of the normal force and frictional force is the net substrate reaction force, the angle of which determines whether there is net propulsive or braking force (Fig. 1B–D). The force sensors in our study provide us the antero-posterior (FAP) and the vertical (FV) components of this reaction force (Fig. 1A–D). Based on these relationships (see Appendix for derivations of equations), one can calculate the magnitude of the normal force (FN):

formula

(1)

where θ is the angle of the resultant force (FR):

formula

(2)

From these equations (and those easily derived from them), the magnitude and orientation of any of the vectors can be derived (Fig. 1B–D); however, we report the antero-posterior (FAP) and the vertical (FV) forces (particularly FAP), as these components directly test our hypothesis.

To test whether single vertical asperities of the appropriate orientation could be used to generate propulsion in a terrestrial setting (despite drag on many body segments), we constructed a trackway tunnel made of 1.27 cm thick expanded PVC boards, a common construction material consisting of a foamed PVC interior with a smooth surface finish. This trackway was 5 cm wide and 180 cm long with a sloped wedge three-quarters of the way along the trackway (Fig. 1H,I). All horizontal surfaces were covered with masking tape, which had an average coefficient of friction with the snakes of µtape=0.21±0.06. One lateral wall was clear acrylic, and video was recorded using a Nikon D3300 DSLR camera (Nikon, Tokyo, Japan). In one set of trials, the wedge had a slope of 30 deg, steeper than the predicted minimum necessary for propulsive force [tan−1tape)=11.3 deg] and thus suitable for generating propulsive forces (Fig. 1C; Fig. S4), while in the second series of tests the wedge had an incline of 8 degrees, which is predicted to generate a net propulsive force (Fig. 1D; Fig. S4). Each snake moved three times through the tunnel, separated by rest periods of at least 15 minutes.

To test whether a pure vertical ripple is sufficient to traverse our experimental setup and to rule out unobserved mechanisms, a 13-link snake robot consisting of 12 servo motors (Hitec HS-85BB, Hitec RCD USA, Inc., Poway, CA, USA ) mounted in custom 3D-printed brackets was constructed (total length 73.5 cm, mass 398.6 g, coefficient of friction 0.47 ± 0.03, range 0.45-0.53). The snake robot was controlled via a USB servo controller (Lynxmotion, SSC-32U, Robotshop, Mirabel, QC, Canada) using a specially written Python script (Python Software Foundation, Wilmington, DE, USA; see Supplementary Materials and Methods 1) . using a serpenoid wave (Hirose, 1993) with the equation:

formula

(3)

Where M.I is the angle of the motor I, a is the maximum possible angle, t it’s time pI is the phase shift between successive motors and xI is an offset to ensure that all connections are parallel when all motors are at an angle (M.) from zero. The values ​​used for these experiments were a= 600 µs (for pulse width modulation control) and P.= 1.5 radians, which creates two waves on the body and a correspondingly long, flat wave to span two or more cones to support itself (Movie 3). The robot had no sensors and posture was controlled.

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