SUMMARY

Despite the abundance of octapodal species and their evolutionary importance in originating terrestrial locomotion, the locomotion mechanics of spiders has received little attention so far. In this investigation we use inverse dynamics to study the locomotor performance of Grammostola mollicoma (18 g). Through 3-D kinematic measurements, the trajectory of the eight limbs and cephalothorax or abdomen allowed us to estimate the motion of the body centre of mass (COM) at different speeds. Classic mechanics of locomotion and multivariate analysis of several variables such as stride length and frequency, duty factor, mechanical external work and energy recovery, helped to identify two main gaits, a slow (speed <11 cm s–1) one and a fast one characterised by distinctive 3-D trajectories of COM. The total mechanical work (external + internal) calculated in the present study and metabolic data from the literature allowed us to estimate the locomotion efficiency of this species, which was less than 4%. Gait pattern due to alternating limb support, which generates asymmetrical COM trajectories and a small but consistent energy transfer between potential and kinetic energies of COM, is discussed both in terms of coordination indices and by referring to the octopod as formed by two quadrupeds in series. Analogies and differences of the newly obtained parameters with the allometric data and predictions are also illustrated.

INTRODUCTION

Partially because of the anthropocentric attitude and the tendency towards a manageable simplification, it is intuitive to consider the locomotion of multi-legged species as the result of the combination of gaits of organisms with fewer legs. For example, quadrupedal trot can be regarded as the combination of a front and a rear biped running a half-cycle out of phase, and similar analogies can be made for many other gaits (e.g. gallop is the combination of two bipedal skipping strides). This seems a useful approach when we need to understand the mechanics of complex gaits by starting to analyse simpler ones (Minetti, 1998b). To push this strategy to the limit, monopods have been theoretically analysed (Blickhan and Full, 1993) and successfully designed (Raibert, 1986) in the early stages of locomotion research. Another potential benefit of this approach is in motor control investigations, which could seek simpler central pattern generators (CPGs) and hypothesise a modular control of more complex locomotion forms.

But evolution moved the other way round: the first multi-legged terrestrial animals presumably had eight limbs, lately radiating both towards more complex locomotor organisms (myriapods) (Wilson and Anderson, 2004) and species of larger size and with a lower number of limbs. Six-legged insects appeared later on the terrestrial surface, then vertebrates, down to quadrupeds, bipeds and even to substantially ‘monopodal’ species such as jumping kangaroos (Carroll, 1987).

Eight-legged locomotion was one of the first travelling modes on land, and an extinct group of terrestrial arachnids related to modern-day spiders, the trigonotarbids, are among the most ancient arthropod groups (Upper Silurian, approximately 444–428 million years ago) (Jeram et al., 1990). Spiders display the most versatile locomotor repertoire: they move at slow and fast speeds, forwards, backwards and sideways, and they climb and even jump, both on firm terrain and from the water surface. Even humans, despite the inherent bipedal instability, can walk (Minetti and Ardigò, 2001) and run (Cavagna et al., 2010) backwards, but the performance and the related cost of transport are quite penalised. Spiders can walk forwards and backwards at the same speed, just by reversing their diagonal footfall scheme. They turn on the spot like an armoured tank, with opposite direction of the two treads of limbs. When a spider loses one (or even two) of its legs, it is still capable of comfortably moving around, differently from bipeds and quadrupeds, through a duty factor compensation and a reprogramming of the CPG (Foelix, 1996). Also, the high number of limbs ensures an increased locomotor versatility on uneven and rough terrains, particularly in the likely unawareness of each endpoint location on the ground (despite the up to four pairs of eyes). There is no surprise, then, to learn that the US Defence Advance Research Project Agency had tactical interests in developing up to eight-legged robots capable of semi-automatically facing various terrain roughnesses (Klaassen et al., 2002). Despite all of these reasons, scientific research on eight-legged locomotion is rather sparse and only a few papers (Herreid and Full, 1980; Schmitz, 2005a; Schmitz, 2005b; Sensenig and Schultz, 2006; Ward and Humphreys, 1981a; Wilson, 1967) have addressed spider gaits in detail.

We had the opportunity to capture and analyse the locomotion biomechanics of large spiders in captivity. We aimed to apply to this animal the same methodology used in the past to obtain variables of gait dynamics on bipeds [e.g. humans (Minetti et al., 1993)] and quadrupeds [horses (Minetti et al., 1999)]. The main goals of the present study were to: (1) identify the principal gaits; (2) calculate the mechanical external and internal work at the different speeds and/or gaits; (3) assess any tendency to exchange potential and kinetic energy of the body centre of mass, as in pendulum-like gaits; and 4) evaluate how spiders' mechanical performance and variables allometrically compare with other species. Going back to the simplification approach mentioned above, another question was: can the octopedal gaits be considered as different combinations of the locomotion of two quadrupeds.

MATERIALS AND METHODS

Animals

All measurements were made in adult female specimens of Grammostola mollicoma (Ausserer 1875) (Araneae, Theraphosidae) (N=3, mass=18.5±3.7 g, mean ± s.d.). The species were identified using criteria from the literature (Costa and Pérez-Miles, 2002; Mello-Leitao, 1923). Spiders were collected in the Sierra de Minas region (Department of Lavalleja, Uruguay), and were held in captivity with constant and optimum environmental conditions throughout the experimental period.

Experimental procedure

The position of the body centre of mass (COM) in the static posture, where the main body marker should have been placed, was independently determined in killed specimens (same species, similar sizes). COM coordinates were determined by suspending the legless spider body (cephalothorax) on a nylon fibre glued to the thorax and moving the point of attachment until the spider assumed a horizontal position.

An additional eight markers were placed at the tips of the locomotive legs (Fig. 1). The experimental conditions used in this study were similar to those recently used to analyse locomotion in large mammals (Hutchinson et al., 2006; Wickler et al., 2002; Wickler et al., 2003), with the spiders filmed during free displacements.

Five fixed video cameras (JVC GR-DVL 9800, Yokohama, Japan) were simultaneously used. The recordings were made within a space of 60×30×15 cm, calibrated by using 20 markers evenly distributed in three dimensions (3-D). The frequency used for video recordings (50 frames s–1) has been previously determined as suitable for this type of analysis (Ward and Humphreys, 1981b). The camera synchronisation was performed with a sound signal and all images were digitised. Each of these frames was later used to reconstruct the position of each marker. Orthogonal axes were defined by following the recommendations of the Biomechanics International Society (Wu and Cavanagh, 1995): the direction of the X-axis agreed with the main displacement direction, the direction of the Y-axis agreed with the height with respect to the ground, and the direction of the Z-axis was determined by the right-hand rule (Meneghesso, 2002; Wu and Cavanagh, 1995). The measurement error in the system was assessed according to Barros et al. (Barros et al., 2006).

Fig. 1.

Position of the nine reflective markers.

Fig. 1.

Position of the nine reflective markers.

Data analysis

Only locomotor acts performed in a straight line were chosen. The frame-by-frame analysis was conducted using an image analysis program (Dvideow 6.3, Campinas University) (Barros et al., 1999; Figueroa, 1998; Figueroa et al., 2003). A series of programs written in LabView (ver. 8.6/MacOS, National Instruments, Austin, TX, USA) was built to manage and process the kinematics and/or kinetics data of the legs and of the true COM (tCOM). Virtual markers corresponding to the coxa joint, i.e. the point of insertion of each leg on the thorax of the spider, were calculated according to mean angles of leg origin from the body on the coronal plane as obtained from the analysis of ‘static’ film frames and photographs, and by assuming that the sagittal plane of the body moves parallel to the progression axis.

Further, we had to consider the movement of the legs in term of segments and joints. Each spider leg is formed by seven segments: the coxa and the trochanter, which are very short and represent a kind of ‘shoulder/hip’ joint; a long femur and a knee-like patella; and a long and thin tibia and a metatarsus, followed by a distal tarsus (Foelix, 1996). In order to manage such a complex structure and after inspection of locomotion footage of the spider, we decided to reduce the animal leg to just two segments connected by a ‘knee’ joint between the coxa and the leg tip. Thus, we first clustered the seven segments into a femur, a tibia and a metatarsus (15.5, 15.2 and 12.0 mm, respectively). Then, we decided to build four models, considering the 3-D shape of the leg either as a cone or a frustum of a cone (with diameters ranging from 6.4 mm at the coxa to 4.0 mm at the metatarsus) and the position of the knee either midpoint between the leg extremes (equal-segment model) or at the end of the femur segment, corresponding to the femur–patella joint (patella-joint model). The positions of the virtual ‘knee’ marker were computed for each model and added to the data set (see supplementary material Movie 1).

The 3-D positions of the COM of each leg segment (LCOM) and of the main body (BCOM) and the respective masses were used to compute the 3-D position of the tCOM.

The stride coordination was evaluated by means of the spatiotemporal sequence of support of the locomotive legs (gait diagram). The parameters were: (1) duty factor (d), defined as the ratio between the duration of a foot contact interval and the stride duration; (2) fore lag (FL), defined as the time lag between the two fore feet footfalls (right first), which measures temporal coordination within the fore pair; (3) hind lag (HL), defined as the time lag between the hind feet footfalls (right first), which measures temporal coordination within the hind pair; and (4) pair lag (PL), defined as the time lag between hind and fore feet footfalls (fore feet first), which measures temporal coordination within the two pairs.

The time lag can be expressed as a percentage of the cycle duration. The gait can be defined for the values of FL, HL and PL according to the antero-posterior sequence method described by Abourachid (Abourachid, 2003). According to Minetti (Minetti, 1998b) who considered the horse as two consecutive bipeds in series, we looked at the spider as composed by two successive quadrupeds in series, the first being L1–R1–L2–R2 and the second L3–R3–L4–R4 (where L and R indicate left and right, respectively, and the numbers start from the first pair of feet in anterior–posterior sequence), and we calculated the gait parameters for each quadruped. Further, a new parameter, QL, representing the phase shift between the two quadrupeds and defined as the time lag between two homologous feet of the quadrupeds (e.g. R1 and R3), was calculated.

Because of the periodical characteristics of a gait, where a sequence of footfalls is repeated in time, the gait pattern is summarised by phase shifts of footfalls that can be plotted as points on a trigonometric circumference. Their mean according to circular statistics takes into account their position on the circumference – e.g. two phase shifts, 1 deg and 359 deg, result in a value of 0 deg rather than 180 deg (the arithmetic linear mean).

Let θ be the position on a trigonometric circumference for n observations; we can then define , , and the circular mean (Batschelet, 1981), where (ordinate) and (abscissa) are the rectangular components of the circular mean. The mean resultant length, , is a measure of the dispersion of the data. However, because r decreases from 1 to 0 while the dispersion increases, an index of variability equivalent to the standard deviation in linear statistics is calculated as mean angular deviation: (Batschelet, 1981). The circular mean and mean angular deviation, in radians, have been transformed as fraction of the stride cycle.

Biomechanical analysis

The 3-D trajectories of the body COM in local coordinates, as during locomotion on a treadmill, were calculated by applying a mathematical method based on the Fourier analysis of the three coordinates of tCOM over time (Minetti, 2009; Minetti et al., 2011). The analysis is truncated to the sixth harmonic, because further harmonics addition did not enhance the descriptive power of the result (Perseval's theorem). The final outcome, for each analysed stride, is a system of three parametric equations with a total of 18 amplitude coefficients, 18 phase coefficients and a vertical translation constant, which describes a 3-D closed loop (Lissajous contour). The dynamics of tCOM movement is linked to the mechanical external work and is proven to reflect the metabolic energy needed in many locomotor conditions (Minetti et al., 1993).

Values for the segment mass (as a fraction of body mass) were obtained from average measurements, while the radii of gyration were calculated by assuming a cone frustum or conical shape of segments, according to the mentioned models. Positive internal and external work (Wint and Wext, respectively) were computed using the method of Cavagna and Kaneko (Cavagna and Kaneko, 1977), who used König's theorem to account for the changes in the kinetic energy of segments whose movements do not affect the position of the overall COM (e.g. symmetrical limb displacement). This theorem states that the total kinetic energy of a multi-link system can be divided into two parts: (1) the increases in kinetic energy of the segments arising from their change of speed with respect to the overall COM, and (2) the increases in kinetic energy of the overall COM with respect to the environment. The first term constitutes the positive Wint, whereas the second is included in the positive Wext, defined as the work necessary to raise and accelerate the COM of the body with respect to the environment.

The positive work (Wext) was obtained by summing the increments of the total energy (Etot) with respect to time: Etot=Epot+Ekin,x+Ekin,y, where Epot is the potential energy of the COM of the body, and Ekin,x and Ekin,y are the horizontal and vertical components, respectively, of the kinetic energy of the body's COM. The total mechanical work (Wtot) was computed as the sum of Wext and Wint. Mechanical work was expressed as the (mechanical) cost of transport, i.e. per kilogram of body mass and per unit distance (i.e. J kg–1 m–1). The peak mechanical power, due to sudden acceleration from rest, was estimated from the maximum acceleration recorded during the first strides of the faster filmed sequences. The ‘energy recovery’, an index of the ability of a system to save mechanical energy through the interchange between Epot and Ekin (equal to 100% in an ideal pendulum), was obtained according to Cavagna et al. (Cavagna et al., 1976).

All the data processing and statistics were performed on an Apple iMac computer, using LabView (ver. 8.6, National Instruments), Microsoft Excel (ver. 2008) and SPSS (ver. 17.0, IBM, Somers, NY, USA).

RESULTS

We analyzed a total of 54 strides, distributed in 13 different sequences of three to five strides each. The overall results are shown in Table 1.

Table 1.

Results of the stride analysis

Results of the stride analysis
Results of the stride analysis

Speed, gaits and tCOM trajectory

During the experiments we observed ‘slow’ and ‘fast’ displacements. In order to assess the consistency of these two categories, we considered the following variables: speed, relative stride length, stride frequency, mechanical external work and energy recovery. A preliminary cluster analysis permitted us to identify two main groups with a cut-off speed that ranged from 8.7 to 14 cm s–1, according to the clustering method. In order to choose a reliable boundary speed and define the slow and fast groups, a set of five multivariate analyses of variance (MANOVA) were performed. All the models were highly significant (P<0.001), but the Wilks' F-value and the partial eta-squared, an effect size estimator, reached a maximum for a cut-off speed of 11 cm s–1 (Fig. 2), which corresponds to a Froude number of 0.08.

Fig. 2.

Compound results of five MANOVA analyses (see Speed, gaits and tCOM trajectory in the Results for details). The boundary speed between slow and sprint displacements has been set to 11 cm s–1. In this case we obtained the largest separation of the two groups: both highest Wilks' F-value and highest estimator of effect size.

Fig. 2.

Compound results of five MANOVA analyses (see Speed, gaits and tCOM trajectory in the Results for details). The boundary speed between slow and sprint displacements has been set to 11 cm s–1. In this case we obtained the largest separation of the two groups: both highest Wilks' F-value and highest estimator of effect size.

For slow displacements, gait diagrams (Fig. 3A,B) show a four-legged alternation (R1, R3, L2, L4 to L1, L3, R2, R4). This pattern is summarised by two walking quadrupeds, with almost no phase delay between them. During fast movements, a similar alternation of tetrapods occurs, although with a more variable pattern (Fig. 3C).

The visual analysis of diagrams shows that two anterior pairs of legs (first quadruped) and two posteriors pairs (second quadruped) have the same pattern for slow displacements, whereas during faster gait the pattern is different for both groups of legs, the phase shift between legs of the third and fourth pairs of legs being more irregular. However, the values of the parameters FL, HL and PL (Table 2), correspond to a quadruped walk for slow displacements and a variant walk sequence for fast displacements, as shown by the greater variability of values for the second quadruped. The second quadruped anticipated the first one with average shifts of 16% (slow) and 8% (fast).

Table 2.

Duty factor (d) and stride parameters [fore lag (FL), hind lag (HL), pair lag (PL) and quadruped lag (QL)], calculated considering the spider as two successive quadrupeds

Duty factor (d) and stride parameters [fore lag (FL), hind lag (HL), pair lag (PL) and quadruped lag (QL)], calculated considering the spider as two successive quadrupeds
Duty factor (d) and stride parameters [fore lag (FL), hind lag (HL), pair lag (PL) and quadruped lag (QL)], calculated considering the spider as two successive quadrupeds

Speed (s, m s–1) and duty factor (d) varied inversely according to the equation d=–0.531s+0.666 (R2=0.71, P<0.001), with d always greater than 50%. In both gaits the stride frequency (f) increases proportionally to the speed (Fig. 4). Separate linear regression slopes for slow and fast displacements did not significantly differ (P=0.88), and the fitting for the pooled data produced the following equation: f=14.4s+0.14 (R2=0.92, P<0.001). The linear regression of stride length (l) versus speed increased significantly only at slow speeds: l=28.37s+4.43 (R2=0.61, P<0.001). For fast locomotion, the stride length was almost constant (R2=0.21, P=0.08) at a mean value of 6.14±0.71 cm.

The geometry described by the legs on the ground (support area) is plotted together with energies and gait diagrams in Fig. 3A,B,C. The time course of the support area seems quite irregular during the stride, although a quite distinctive pattern is shown particularly during the slow movement. The mean support area at all speeds was 56.3±4.1 cm2.

Three examples of Lissajous contours of the COM, at different speeds, are shown in Fig. 5 (movies showing the dynamics of tCOM trajectory are available in the supplementary material Movies 1 and 2). The spider's tCOM had small lateral oscillations while proceeding at slow speed (Fig. 5A) (approximately 0.5 cm, when compared with roughly 8 cm of support area diameter), with a more diagonal pattern at higher speeds (Fig. 5B,C).

Mechanical work

Despite the fivefold increase in speed, the external work per unit distance was almost constant with a tendency to increase as the spider proceeds faster (Fig. 6).

The sum of forward and lateral kinetic energy (Ekin=Ekin,x+Ekin,z) changes was lower than the sum of vertical kinetic and potential energy (Epot=Epot+Ekin,y) changes at slow speeds (Ekin=0.022±0.016 mJ; Epot=0.150±0.052 mJ). At higher speeds, changes in Epot maintained almost the same values, while Ekin changes reached and overlapped Epot (Ekin=0.255±0.203 mJ; Epot=0.183±0.123 mJ). The energy recovery, an index of the exchange between Ekin and Epot that occur when their time courses are out of phase, did not significantly change as the speed increased (t-test, P=0.57; see also Table 1 and Fig. 3).

The sum of the leg's masses was approximately 13% of the total mass of the spider. The mechanical internal work (Wint), estimated for each leg model (see Materials and methods), ranged from 0.021 to 0.328 J kg–1 m–1 (mean ± s.d.=0.113±0.083 J kg–1 m–1). Internal work values were significantly lower in the conical shape models than in the frustum shape models (paired t-test, P<0.001), and in the asymmetrical patella-joint than in the equal-segments models (paired t-test, P=0.004). However, we observed a similar pattern of variation of Wint as a function of speed (Fig. 7), independently from the adopted limb model.

According to Fedak et al. (Fedak et al., 1982), who considered intraspecific and interspecific differences in species that ranged from 44 g to almost 100 kg in mass, Wint should scale as:
formula
(1)
where s is the mean progression speed (m s–1).
Fig. 3.

Main characteristics of typical Grammostola mollicoma strides at different speeds. Top: gait diagram of the footfall pattern. Horizontal bars represent the time the foot is on the ground. Each line represents one foot (R and L indicate the legs of the right and left sides, respectively; numbers 1 to 4 indicate the sequence of legs from the head backwards). Middle: support area (cm2), right ordinate. Bottom: mechanical energies (mJ). The blue line represents total energy (Etot), the red line vertical energy (Epot + Ekin,y) and the green line kinetic horizontal energy (Ekin,x + Ekin,z). See Mechanical work in the Results for further explanation. (A) Sequence of five slow strides (5.5, 4.7, 4.2, 3.9 and 3.8 cm s–1). Potential energy, changes in which are tenfold the kinetic energy span, accounts for almost all the changes in total energy. Duty factor=65–69%. (B) Sequence of three strides at medium speed (10.4, 8.7 and 7.5 cm s–1). Changes in kinetic and potential energy are approximately in phase. Duty factor=58–59%. (C) Sequence of two mean fast strides (13.4 to 23.6 cm s–1). Time has been standardised in degrees (1 stride=360 deg). Kinetic energy values are comparable to those of potential energy; a slight phase shift between potential and kinetic energy diagrams accounts for an average 12% of recovery. Duty factor=55–57%.

Fig. 3.

Main characteristics of typical Grammostola mollicoma strides at different speeds. Top: gait diagram of the footfall pattern. Horizontal bars represent the time the foot is on the ground. Each line represents one foot (R and L indicate the legs of the right and left sides, respectively; numbers 1 to 4 indicate the sequence of legs from the head backwards). Middle: support area (cm2), right ordinate. Bottom: mechanical energies (mJ). The blue line represents total energy (Etot), the red line vertical energy (Epot + Ekin,y) and the green line kinetic horizontal energy (Ekin,x + Ekin,z). See Mechanical work in the Results for further explanation. (A) Sequence of five slow strides (5.5, 4.7, 4.2, 3.9 and 3.8 cm s–1). Potential energy, changes in which are tenfold the kinetic energy span, accounts for almost all the changes in total energy. Duty factor=65–69%. (B) Sequence of three strides at medium speed (10.4, 8.7 and 7.5 cm s–1). Changes in kinetic and potential energy are approximately in phase. Duty factor=58–59%. (C) Sequence of two mean fast strides (13.4 to 23.6 cm s–1). Time has been standardised in degrees (1 stride=360 deg). Kinetic energy values are comparable to those of potential energy; a slight phase shift between potential and kinetic energy diagrams accounts for an average 12% of recovery. Duty factor=55–57%.

In our 18.5 g spiders we observed an almost linear relationship between Wint and speed (Wintαs1.05), with measured values lower than predicted by Eqn 1 at slow speeds, and comparable values at higher speeds. However, both the slopes (P<0.001) and the intercepts (P=0.002) of the regression lines significantly differed.

The mechanical internal work rate has been modeled for bipeds by Minetti and Saibene (Minetti and Saibene, 1992), and then extended to quadrupeds (Minetti, 1998a). The model links the internal work to: (1) the stride frequency (f, Hz); (2) the mean progression speed (s, as in Eqn 1); (3) a term related to duty factor (d); and (4) a compound dimensionless term accounting for limb geometry and fractional mass (q), which should be almost constant throughout all the speeds and gaits if the geometry of the oscillated limb remains the same. The value of q for the investigated species can be estimated (Minetti, 1998a) by the equation:
formula
(2)
The actual and the mean values of q calculated for G. mollicoma from our experimental data are compared with the mean values for humans and horses in Fig. 8.
Fig. 4.

Stride length (open circles) and stride frequency (filled circles) versus speed in G. mollicoma.

Fig. 4.

Stride length (open circles) and stride frequency (filled circles) versus speed in G. mollicoma.

Maximum power

In our experimental design the spiders were filmed during free displacements starting from rest. In fast performances they showed a rapid acceleration and reached a high speed during the first stride of each sequence. We could therefore estimate the maximum positive power exerted by the spider during acceleration from rest, which was approximately 8.3 W kg–1 (Table 3).

Table 3.

Maximum power (Pmax) values at fast gait

Maximum power (Pmax) values at fast gait
Maximum power (Pmax) values at fast gait

DISCUSSION

Gait pattern

The stride-based analysis shows contact sequences that were described in previous works (Bowerman, 1981; Wilson, 1967), which observed that the anterior legs pairs have a strong tendency to be used alternately, but the posterior pairs do not. Our data concur with this view, but only in fast sequences (FL and HL, Table 2).

The four-legged alternation associated with those unilateral sequences in slow displacements can be interpreted as an alternating tetrapod stepping pattern, similar to the symmetrical trot gait of four-legged vertebrates but with interfaces longer than the time of quadrupedal support. This is currently accepted as a general model of spider locomotion (Barth and Biedermann-Thorson, 2001; Ward and Humphreys, 1981a), except for a group of functional exapod harvestmen (Opiliones), their antenniform second pair of legs being used as tactile organs, which display an alternating tripod gait (Sensenig and Schultz, 2006).

Alternating tripod gait is a widespread interleg coordination pattern for insects walking at moderate to high speed, and is generally lacking during slow walking (Full and Tu, 1990; Hughes, 1952; Kukillaya and Holmes, 2007; Zollikofer, 1994). Our results showed that an inverse situation could happen for this species of vagrant spider, as the general model of tetrapod alternation is not observed in fast displacements.

We can consider the octopod as formed by two subsequent quadrupeds, where the first two pairs of feet (1 and 2) are the fore and the hind feet of the first quadruped, and the third and fourth pairs are the fore and hind feet of the second quadruped. The two quadrupeds are almost in phase, being the first and third pairs synchronised in their movements as well as the second and fourth (QL, Table 2).

The gait parameters of the first quadruped are more consistent with a kind of diagonal walk (i.e. a trot with no flight phase). The diagonal feet are not moving in phase, as the hind foot of a pair slightly anticipates the contralateral forefoot (PL, Table 2). This could be due to the unusual high trajectory of the first pair of feet, probably used also as helper ‘probes’ to detect obstacles. Their suspended ‘swing’ phase is longer than any other phase and the second pair of footfalls appear to be anticipated.

The second quadruped shows a similar symmetrical stepping pattern with a duty factor of approximately 60% (PL, Table 2), with a tendency towards symmetry at high speeds, probably due to the rhythmic ‘pushing’ role of the fourth pair of legs.

During fast displacements spiders did not maintain a constant speed. An explosive acceleration usually characterise the first stride, with the speed constantly decreasing thereafter. The stepping pattern observed during these sprints was very variable and irregular. The third pair of feet (the forefeet of the second quadruped) was prone to move in phase during the acceleration of the first stride, probably to boost the propulsion (FL second quadruped, fast, Table 2).

Studies of gait pattern in insects have suggested that regularities in the support area are strongly influenced by CPGs under the influence of sensor input (Cruse and Muller, 1986; Delcomyn, 1985). Because sensory feedback seems to be essential for leg coordination during slow walking (Cruse and Muller, 1986; Delcomyn, 1985), the control operated by the action of the CPGs become increasingly important with speed (Delcomyn, 1991). In a study made with different ant species it was proposed that the rigidity of their three-legged gait pattern, regardless of changes in speed, could reveal that CPGs were prevailing over sensory input (Zollikofer, 1994).

Fig. 5.

Trajectory of the centre of mass of G. mollicoma in local coordinates. The axis with an arrow indicates progression direction. The side length of the represented cubes is 5 mm. Each loop corresponds to one stride. Small dots represent the observed positions of the tCOM, lines represent the calculated Lissajous contour, and larger dots represent the actual position of the tCOM during the animated simulations (see supplementary material Movie 2). (A) Slow: 2.9–4.2 cm s–1 (right side view), three strides. (B) Slow: 5.0–6.0 cm s–1 (dorsal view), three strides. (C) Fast: 19.7–23.0 cm s–1 (dorso-lateral view), two strides.

Fig. 5.

Trajectory of the centre of mass of G. mollicoma in local coordinates. The axis with an arrow indicates progression direction. The side length of the represented cubes is 5 mm. Each loop corresponds to one stride. Small dots represent the observed positions of the tCOM, lines represent the calculated Lissajous contour, and larger dots represent the actual position of the tCOM during the animated simulations (see supplementary material Movie 2). (A) Slow: 2.9–4.2 cm s–1 (right side view), three strides. (B) Slow: 5.0–6.0 cm s–1 (dorsal view), three strides. (C) Fast: 19.7–23.0 cm s–1 (dorso-lateral view), two strides.

Fig. 6.

Mechanical work in G. mollicoma at different speeds. External work (Wext, squares) with regression lines and internal work (Wint, circles). The Wint line refers to the predicted values from Fedak et al. (Fedak et al., 1982).

Fig. 6.

Mechanical work in G. mollicoma at different speeds. External work (Wext, squares) with regression lines and internal work (Wint, circles). The Wint line refers to the predicted values from Fedak et al. (Fedak et al., 1982).

Following this argument, the results of spatiotemporal coordination in the legs of G. mollicoma during both regimes of displacement could indicate that in this species there is no rigid neural control by CPGs. However, it may also indicate that locomotion patterns in spiders could be more complex and should be interpreted by means of other variables. In this respect, the present data clearly show a pattern in the time course of the support area and in stability during slow locomotion, but not during faster gaits. This suggests a rigid neural control by CPGs during slow displacements to keep stability, but not at higher speed.

Speed and gaits

A gait transition can be determined by mechanical and energetic factors (Griffin et al., 2004), and can be recognised by an abrupt change in the speed dependency of at least one mechanical or metabolic variable (Alexander, 1989). In G. mollicoma, several variables showed significantly different speed-dependency behaviour between slow and fast gaits: stride frequency (P<0.001), duty factor (P=0.003), internal work (P<0.001) and external work (P=0.011). The stride frequency increased linearly with speed in both gaits, which is typical for walk and run/trot (Heglund et al., 1974). The maximum stride frequency (4.55 Hz) and the maximum speed (0.275 m s–1) recorded during our experiments are well below the predicted trot–gallop transition values for animals of the same mass (Heglund et al., 1974), which should occur at 0.586 m s–1. This comes with no surprise as slow and fast spider gaits are both similar to walking (d>0.5; Table 2).

Octopod locomotion in spiders appears to be completely different from the functional octopod sideways locomotion of crabs (Full, 1987; Weinstein, 1995), where the right and left legs act as leading or trailing ones, depending on the movement direction. Crabs show a walking gait with an inverted pendulum energy-conserving mechanism similar to the quadrupedal and bipedal walking (Cavagna et al., 1976; Margaria, 1976), a slow run and a fast run with an aerial phase similar to a gallop (Blickhan and Full, 1987; Blickhan et al., 1993).

Fig. 7.

Internal work (Wint) values in G. mollicoma at different speeds according to four leg models: (1) open circle – frustum of cone shape, two equal segments; (2) open square – frustum of cone shape, shorter proximal segment (patella joint); (3) open triangle – cone shape, two equal segments; and (4) X – cone shape, shorter proximal segment (patella joint).

Fig. 7.

Internal work (Wint) values in G. mollicoma at different speeds according to four leg models: (1) open circle – frustum of cone shape, two equal segments; (2) open square – frustum of cone shape, shorter proximal segment (patella joint); (3) open triangle – cone shape, two equal segments; and (4) X – cone shape, shorter proximal segment (patella joint).

The inverted pendulum model (Margaria, 1976) applies to animals moving forward while vaulting over stiffened legs. Changes in potential and forward kinetic energy through time occur out of phase, with a consequently high value of energy recovery (Cavagna et al., 1976). Such behaviour has been observed in walking bipeds (Cavagna and Margaria, 1966), quadrupeds (Heglund et al., 1982; Minetti et al., 1999) and the mentioned crabs (Blickhan and Full, 1987; Blickhan et al., 1993), but it has never been observed in other arthropods (Sensenig and Schultz, 2006).

During running gaits the potential and forward kinetic energy change in phase during the stride; therefore, neither exchange nor recovery occurs. The bouncing ball model (Margaria, 1976) is consistent with vertebrate run/trot (Farley et al., 1993), insect locomotion (Full and Tu, 1990) and functional exapodal spider locomotion (Sensenig and Schultz, 2006). Running insects can reach considerably high speeds. The American cockroach Periplaneta americana can run up to 1.5 m s–1 switching from exapodal to quadrupedal and bipedal running (Full and Tu, 1991).

A third paradigm has been proposed to model the skipping gaits (Minetti, 1998b). An analysis of human skipping and galloping in quadrupeds revealed that a combination of potential and forward kinetic pendulum-like exchange and elastic energy storage is responsible for the efficiency of this gait model (Saibene and Minetti, 2003).

The symmetrical gaits by definition are those in which the lag time of the two feet of the pairs (FL and HL) is the same (50% of the cycle duration) (Abourachid, 2003; Hildebrand, 1966; Hildebrand, 1977). Analysing our subject, G. mollicoma, as a combination of two quadrupeds (Minetti, 2000), we observed that the gait parameters roughly represented symmetrical walking at low speed, while during fast locomotion we found a remarkable variability of such parameters and more asymmetric trajectories of the tCOM over a stride, although the duty factor remained above 0.5 and a flight phase was absent (Table 2, Fig. 5). The increase of asymmetry during faster gaits is consistent with the observation that asymmetrical gaits probably evolved, in amphibians and several times in reptiles, to benefit escape (Hildebrand, 1977).

Duty factors greater than 0.5 classically define the kinematics of walking gaits (Alexander, 1989). However, running gaits characterised by d>0.5 and stride frequency, which proportionally increases with the progression speed, have been also described for running frogs (Ahn et al., 2004), for terrestrial locomotion in bats (Riskin et al., 2006), and even in human race walking, where the flight phase is forbidden but the potential and kinetic energy curves of tCOM are in phase as during running.

In conclusion, the locomotion of these spiders, analysed using stride-based analysis, shows significant differences from other arthropods, such as insects. Changes in stability during each support situation show an important difference with other animals, and are in agreement with a backward–forward activation sequence.

Mechanical work and efficiency

We did not find significant differences between the Wext estimated by using a single marker approximating BCOM and that based on the true COM position (nine measured + 16 virtual markers) for the complete strides (paired t-test, P=0.098).

Fig. 8.

Calculated variations of the dimensionless term q (Eqn 2). Dots represent the q-values as obtained from the experimental data. Lines represent the mean values of q in G. mollicoma, humans and horses. Data on humans and horses are from Minetti (Minetti, 1998a). The vertical dotted line represents the cut-off speed between slow and fast displacements.

Fig. 8.

Calculated variations of the dimensionless term q (Eqn 2). Dots represent the q-values as obtained from the experimental data. Lines represent the mean values of q in G. mollicoma, humans and horses. Data on humans and horses are from Minetti (Minetti, 1998a). The vertical dotted line represents the cut-off speed between slow and fast displacements.

Fig. 9.

Cost of transport versus body mass in animals. The upper line shows the allometric regression of the net metabolic cost, the middle line the almost constant mechanical cost (Wext, ignoring fluctuations of internal kinetic energy, and energy saving by elastic mechanisms) and the lower line the internal work (Wint) according to predicted values (Fedak et al., 1982). Asterisks, ants; filled diamonds, spiders; open squares, cockroaches; ×, crabs; open circles, reptiles; filled triangles, amphibians; open diamonds, birds; open triangles, mammals; filled squares, Wext; filled circles, Wint in G. mollicoma (present study, yellow circle represents the mean value), humans and horses. Data are from various sources [Full (Full, 1989) and Full and Tu (Full and Tu, 1991) and references therein] (Lighton and Gillespie, 1989; Steudel, 1990; Secor et al., 1992; Lighton et al., 1993; Minetti et al., 1999; Baudinette et al., 2000; Saibene and Minetti, 2003; Lipp et al., 2005; Schmitz, 2005a; Zani and Kram, 2008).

Fig. 9.

Cost of transport versus body mass in animals. The upper line shows the allometric regression of the net metabolic cost, the middle line the almost constant mechanical cost (Wext, ignoring fluctuations of internal kinetic energy, and energy saving by elastic mechanisms) and the lower line the internal work (Wint) according to predicted values (Fedak et al., 1982). Asterisks, ants; filled diamonds, spiders; open squares, cockroaches; ×, crabs; open circles, reptiles; filled triangles, amphibians; open diamonds, birds; open triangles, mammals; filled squares, Wext; filled circles, Wint in G. mollicoma (present study, yellow circle represents the mean value), humans and horses. Data are from various sources [Full (Full, 1989) and Full and Tu (Full and Tu, 1991) and references therein] (Lighton and Gillespie, 1989; Steudel, 1990; Secor et al., 1992; Lighton et al., 1993; Minetti et al., 1999; Baudinette et al., 2000; Saibene and Minetti, 2003; Lipp et al., 2005; Schmitz, 2005a; Zani and Kram, 2008).

Spiders as a group have lower resting metabolic rates than other poikilothermic animals (Anderson, 1970; Greenstone and Bennett, 1980). However, there are only few available data about the metabolic cost of transport in tarantula spiders of the family Theraphosidae (Herreid and Full, 1980). As pointed out by Herreid (Herreid, 1981) in his review, the minimum cost of transport (Cmin) in spiders is subject to underestimation, due to the long recovery time after every performance, which is a characteristic of these animals (Herreid, 1981). The adjusted Cmin for a 12.7 g Theraphosidae spider was 20.0 J kg–1 m–1. The mean mass-specific mechanical energy used to move the COM a given distance (Fig. 6) was 0.52 J kg–1 m–1, approximately one-half the almost constant value detected in other arthropods, mammals and birds (see Fig. 9 for references).

The mechanical work expressed per kilogram of mass and per metre is almost constant in all the animals, independently of the body mass. A potential reason for the deviation from such a rule detected in spiders could be their particular femoropatellar (knee) extensor mechanism. In fact, spiders, like many arachnids, lack extensor muscles at the femoropatellar joints, and extend them using hydraulic pressure generated by the contraction of endosternal suspensor muscles (Shultz, 1991).

This work is the first attempt to calculate the internal mechanical work in spiders. Octopods have a multiple of eight segments moving with respect to the COM. We would therefore expect a high fraction of the total work accounted for as internal work. In fact, even if the arthropod legs are considerably lighter compared with vertebrate limbs (i.e. the fractional mass of the legs with respect to the body mass is lower in spiders than in vertebrates in spite of the higher number of segments), the calculated value of q (Minetti, 1998a), reflecting the inertial arrangement in leg dynamics, is higher in spiders than in humans and horses, particularly at slow speeds (Fig. 8).

According to that model (Minetti, 1998a; Minetti and Saibene, 1992), the internal work increases proportionally to the progression speed and the stride frequency. Our results are consistent with this prediction but suggest a difference between invertebrates and vertebrates, or between octopods and quadrupeds. The equation proposed by Fedak et al. (Fedak et al., 1982) was based on vertebrates between 0.044 and 98 kg. The spiders considered in the present work are out of this range, and the calculated internal work shows a linear proportionality to speed.

The q term depends on inertial characteristics of moving segments. Arthropod and tetrapod limbs are, from an evolutionary point of view, analogous and in many ways convergent structures, but their geometric and physical parameters can be very different. These peculiarities could account for a different relationship between the internal work and the progression speed, and for a different mean q parameter in arthropods. More data on octopods and invertebrates mechanical internal work could shed light on this issue.

The different behaviour of q (higher during slow than in fast displacements; Fig. 8), could also be explained by different limb geometry and moving patterns. The slow and high ‘exploratory’ trajectory of the first pair of feet, which is expressed during walking in the range of slow speed, has already been stressed. During fast movements this behaviour is lost in order to increase the stride frequency and speed. Another potential explanation for higher q values at slow speed could be a wider base of support, which our data tend to exclude.

The estimated efficiency of locomotion in G. mollicoma, obtained by summing Wint and Wext and dividing the result (Wtot) by the estimated Cmin, ranged between 2.6 and 3.8%, a value comparable to the estimated efficiency in animals of the same mass.

Conclusions

Spider locomotion, here studied in the G. mollicoma, exhibits two main gaits, neither of which incorporate a flight phase, characterised by a consistent limb pattern and a small but remarkable energy recovery index. Both the mechanical internal and external work, never investigated previously, were found to be lower than the allometric predictions. By considering the total work done, the estimated efficiency of locomotion was no greater than 4%.

Further studies estimating the mechanical work through direct dynamics of a greater number of specimens and at higher speeds, if available, could refine the present observations, although the very low mass of these spiders makes the ground reaction force measurement problematic. Also, new metabolic studies on steady-state locomotion in spiders are necessary to detect the presence of optimal speeds within the two identified gaits.

REFERENCES

Abourachid
A.
(
2003
).
A new way of analysing symmetrical and asymmetrical gaits in quadrupeds
.
C. R. Biol.
326
,
625
-
630
.
Ahn
A.
,
Furrow
E.
,
Biewener
A.
(
2004
).
Walking and running in the red-legged running frog, Kassina maculata
.
J. Exp. Biol.
207
,
399
-
410
.
Alexander
R. M.
(
1989
).
Optimization and gaits in the locomotion of vertebrates
.
Physiol. Rev.
69
,
1199
-
1227
.
Anderson
J. F.
(
1970
).
Metabolic rates of spiders
.
Comp. Biochem. Physiol.
33
,
51
-
72
.
Barros
R. M. L.
,
Brezinkofer
R.
,
Leite
N. J.
,
Figueroa
P. J.
(
1999
).
Desenvolvimento e avaliaçao de um sistema para análise tridimensional de movimentos humanos
.
Rev. Bras. Eng. Biomed.
15
,
79
-
86
.
Barros
R. M. L.
,
Russomano
T. G.
,
Brenzikofer
R.
,
Figueroa
P. J.
(
2006
).
A method to synchronise video cameras using the audio band
.
J. Biomech.
39
,
776
-
780
.
Barth
F. G.
,
Biedermann-Thorson
M. A.
(
2001
).
A Spider’s World: Senses and Behaviour
.
Berlin
,
Heidelberg: Springer
.
Batschelet
E.
(
1981
).
Circular Statistics in Biology
.
London
:
Academic Press
.
Baudinette
R. V.
,
Miller
A. M.
,
Sarre
M. P.
(
2000
).
Aquatic and terrestrial locomotory energetics in a toad and a turtle: a search for generalisations among ectotherms
.
Physiol. Biochem. Zool.
73
,
672
-
682
.
Blickhan
R.
,
Full
R. J.
(
1987
).
Locomotion energetics of the ghost crab. II. Mechanics of the centre of mass during walking and running
.
J. Exp. Biol.
130
,
155
-
174
.
Blickhan
R.
,
Full
R.
(
1993
).
Similarity in multilegged locomotion: bouncing like a monopode
.
J. Comp. Physiol. A Sens. Neural Behav. Physiol.
173
,
509
-
517
.
Blickhan
R.
,
Full
R. J.
,
Ting
L.
(
1993
).
Exoskeletal strain: evidence for a trot–gallop transition in rapidly running ghost crabs
.
J. Exp. Biol.
179
,
301
-
321
.
Bowerman
R.
(
1981
).
Arachnid locomotion
. In
Locomotion and Energetics in Arthropods
(ed.
Herreid
C. F.
,
Fourtner
C. R.
), pp.
73
-
102
.
New York
:
Plenum Press
.
Carroll
R. L.
(
1987
).
Vertebrate Paleontology and Evolution
.
New York
:
W. H. Freeman
.
Cavagna
G. A.
,
Kaneko
M.
(
1977
).
Mechanical work and efficiency in level walking and running
.
J. Physiol.
268
,
467
-
481
.
Cavagna
G. A.
,
Margaria
R.
(
1966
).
Mechanics of walking
.
J. Appl. Physiol.
21
,
271
-
278
.
Cavagna
G. A.
,
Thys
H.
,
Zamboni
A.
(
1976
).
The sources of external work in level walking and running
.
J. Physiol.
262
,
639
-
657
.
Cavagna
G.
,
Legramandi
M.
,
La Torre
A.
(
2010
).
Running backwards: soft landing-hard takeoff, a less efficient rebound
.
Proc. Biol. Sci.
278
,
339
-
346
.
Costa
F. G.
,
Pérez-Miles
F.
(
2002
).
Reproductive biology of Uruguayan theraphosids (Araneae, Mygalomorphae)
.
J. Arachnol.
30
,
571
-
587
.
Cruse
H.
,
Muller
U.
(
1986
).
Two coupling mechanisms which determine the coordination of ipsilateral legs in the walking crayfish
.
J. Exp. Biol.
121
,
349
-
369
.
Delcomyn
F.
(
1985
).
Insect locomotion: past, present and future
. In
Insect Locomotion
(ed.
Gewecke
M.
,
Wendler
G.
), pp.
1
-
18
.
Berlin
:
Paul Parey
.
Delcomyn
F.
(
1991
).
Perturbation of the motor system in freely walking cockroaches. II. The timing of motor activity in leg muscles after amputation of a middle leg
.
J. Exp. Biol.
156
,
503
-
517
.
Farley
C. T.
,
Glasheen
J.
,
McMahon
T. A.
(
1993
).
Running springs: speed and animal size
.
J. Exp. Biol.
185
,
71
-
86
.
Fedak
M. A.
,
Heglund
N. C.
,
Taylor
C. R.
(
1982
).
Energetics and mechanics of terrestrial locomotion. II. Kinetic energy changes of the limbs and body as a function of speed and body size in birds and mammals
.
J. Exp. Biol.
97
,
23
-
40
.
Figueroa
P. J.
(
1998
).
Persequiçao de marcadores para análise de movimentos humanos
.
MSc thesis, Facultad de Educación Física
,
Universidad Estadual de Campinas
,
Campinas, Brazil
.
Figueroa
P. J.
,
Leite
N. J.
,
Barros
R. M. L.
(
2003
).
A flexible software for tracking of markers used in human motion analysis
.
Comput. Methods Programs Biomed.
72
,
155
-
165
.
Foelix
R. F.
(
1996
).
Biology of Spiders
.
New York, Oxford
:
Oxford University Press
.
Full
R. J.
(
1987
).
Locomotion energetics of the ghost crab. I. Metabolic cost and endurance
.
J. Exp. Biol.
130
,
137
-
153
.
Full
R. J.
(
1989
).
Mechanics and energetics of terrestrial locomotion: from bipeds to polypeds
. In
Energy Transformation in Cells and Animals
(ed.
Wieser
W.
,
Gnaiger
E.
), pp.
175
-
182
.
Stuttgart
:
Thieme
.
Full
R. J.
,
Tu
M. S.
(
1990
).
Mechanics of six-legged runners
.
J. Exp. Biol.
148
,
129
-
146
.
Full
R. J.
,
Tu
M. S.
(
1991
).
Mechanics of a rapid running insect: two-, four- and six-legged locomotion
.
J. Exp. Biol.
156
,
215
-
231
.
Greenstone
M. H.
,
Bennett
A. F.
(
1980
).
Foraging strategy and metabolic rate in spiders
.
Ecology
61
,
1255
-
1259
.
Griffin
T. M.
,
Kram
R.
,
Wickler
S. J.
,
Hoyt
D. F.
(
2004
).
Biomechanical and energetic determinants of the walk-trot transition in horses
.
J. Exp. Biol.
207
,
4215
-
4223
.
Heglund
N. C.
,
Taylor
C. R.
,
McMahon
T. A.
(
1974
).
Scaling stride frequency and gait to animal size: mice to horses
.
Science
186
,
1112
-
1113
.
Heglund
N. C.
,
Cavagna
G. A.
,
Taylor
C. R.
(
1982
).
Energetics and mechanics of terrestrial locomotion. III. Energy changes of the centre of mass as a function of speed and body size in birds and mammals
.
J. Exp. Biol.
97
,
41
-
56
.
Herreid
C. F. I.
(
1981
).
Energetics of pedestrian anthropods
. In
Locomotion and Energetics in Arthropods
(ed.
Herreid
C. F.
,
Fourtner
C. R.
), pp.
491
-
526
.
New York
:
Plenum Press
.
Herreid
C. F. I.
,
Full
R. J.
(
1980
).
Energetics of running tarantulas
.
Physiologist
23
,
40
.
Hildebrand
M.
(
1966
).
Analysis of the symmetrical gaits of tetrapods
.
Folia Biotheor.
6
,
9
-
22
.
Hildebrand
M.
(
1977
).
Analysis of asymmetrical gaits
.
J. Mammal.
58
,
131
-
156
.
Hughes
G. M.
(
1952
).
The coordination of insect movements. I. The walking movements of insects
.
J. Exp. Biol.
29
,
267
-
284
.
Hutchinson
J.
,
Schwerda
D.
,
Famini
D.
,
Dale
R.
,
Fischer
M.
,
Kram
R.
(
2006
).
The locomotor kinematics of Asian and African elephants: changes with speed and size
.
J. Exp. Biol.
209
,
3812
-
3827
.
Jeram
A.
,
Selden
P.
,
Edwards
D.
(
1990
).
Land animals in the silurian: arachnids and myriapods from shropshire, England
.
Science
250
,
658
-
661
.
Klaassen
B.
,
Linnemann
R.
,
Spenneberg
D.
,
Kirchner
F.
(
2002
).
Biomimetic walking robot SCORPION: control and modeling
.
Robot. Auton. Syst.
41
,
69
-
76
.
Kukillaya
R. P.
,
Holmes
P.
(
2007
).
A hexapedal jointed-leg model for insect locomotion in the horizontal plane
.
Biol. Cybern.
97
,
379
-
395
.
Lighton
J. R. B.
,
Gillespie
R. G.
(
1989
).
The energetics of mimicry: the cost of pedestrian transport in a formicine ant and its mimic, a clubionid spider
.
Physiol. Entomol.
14
,
173
-
177
.
Lighton
J. R. B.
,
Garrigan
D. A.
,
Duncan
F. D.
,
Johnson
R. A.
(
1993
).
Spiracular control of respiratory water loss in female alates of the harvester ant Pogonomyrmex rugosus
.
J. Exp. Biol.
179
,
233
-
244
.
Lipp
A.
,
Wolf
H.
,
Lehmann
F.-O.
(
2005
).
Walking on inclines: energetics of locomotion in the ant Camponotus
.
J. Exp. Biol.
208
,
707
-
719
.
Margaria
R.
(
1976
).
Biomechanics and Energetics of Muscular Exercise
.
Oxford
:
Clarendon Press
.
Mello-Leitao
C. F. D.
(
1923
).
Theraphosideas do Brasil
.
Rev. Mus. Paulista
13
,
1
-
438
.
Meneghesso
L.
(
2002
).
Análise da Marcha: protocolo experimental a partir de variáveis cinemáticas e Antropométricas
.
MSc thesis, Facultad de Educación Física
,
Universidad Estadual de Campinas
,
Campinas, Brazil
.
Minetti
A. E.
(
1998a
).
A model equation for the prediction of mechanical internal work of terrestrial locomotion
.
J. Biomech.
31
,
463
-
468
.
Minetti
A. E.
(
1998b
).
The biomechanics of skipping gaits: a third locomotion paradigm?
Proc. Biol. Sci.
265
,
1227
-
1235
.
Minetti
A. E.
(
2000
).
The three modes of terrestrial locomotion
. In
Biomechanics and Biology of Movement Motion: Human Kinetics
(ed.
Nigg
B. M.
,
MacIntosh
B. R.
,
Joochim
M.
), pp.
67
-
78
.
Champaign, IL
:
Human Kinetics
.
Minetti
A. E.
(
2009
).
The mathematical description (Lissajous contour) of the 3D trajectory of the body centre of mass: a locomotor ‘signature’ for the physiology, biomechanics and pathology of human and animal gaits
.
Gait Posture
30
,
S153
.
Minetti
A. E.
,
Ardigò
L.
(
2001
).
The transmission efficiency of backward walking at different gradients
.
Pflugers Arch.
442
,
542
-
546
.
Minetti
A. E.
,
Saibene
F.
(
1992
).
Mechanical work rate minimization and freely chosen stride frequency of human walking: a mathematical model
.
J. Exp. Biol.
170
,
19
-
34
.
Minetti
A. E.
,
Ardigò
L. P.
,
Saibene
F.
(
1993
).
Mechanical determinants of gradient walking energetics in man
.
J. Physiol.
472
,
725
-
735
.
Minetti
A. E.
,
Ardigò
L. P.
,
Reinach
E.
,
Saibene
F.
(
1999
).
The relationship between mechanical work and energy expenditure of locomotion in horses
.
J. Exp. Biol.
202
,
2329
-
2338
.
Minetti
A. E.
,
Cisotti
C.
,
Mian
O. S.
(
2011
).
The mathematical description of the body centre of mass 3D path in human and animal locomotion
.
J. Biomech.
44
,
1471
-
1477
.
Raibert
M. H.
(
1986
).
Legged Robots that Balance
.
Cambridge, MA
:
MIT Press
.
Riskin
D.
,
Parsons
S.
,
Schutt
W. J.
,
Carter
G.
,
Hermanson
J.
(
2006
).
Terrestrial locomotion of the New Zealand short-tailed bat Mystacina tuberculata and the common vampire bat Desmodus rotundus
.
J. Exp. Biol.
209
,
1725
-
1736
.
Saibene
F.
,
Minetti
A. E.
(
2003
).
Biomechanical and physiological aspects of legged locomotion in humans
.
Eur. J. Appl. Physiol.
88
,
297
-
316
.
Schmitz
A.
(
2005a
).
Metabolic rates in harvestmen (Arachnida, Opiliones): the influence of running activity
.
Physiol. Entomol.
30
,
75
-
81
.
Schmitz
A.
(
2005b
).
Spiders on a treadmill: influence of running activity on metabolic rates in Pardosa lugubris (Araneae, Lycosidae) and Marpissa muscosa (Araneae, Salticidae)
.
J. Exp. Biol.
208
,
1401
-
1411
.
Secor
S. M.
,
Jayne
B. C.
,
Bennett
A. F.
(
1992
).
Locomotor performance and energetic cost of sidewinding by the snake Crotalus cerastes
.
J. Exp. Biol.
163
,
1
-
14
.
Sensenig
A. T.
,
Schultz
J. W.
(
2006
).
Mechanical energy oscillations during locomotion in the harvestman Leiobunum vittatum (Opiliones)
.
J. Arachnol.
34
,
627
-
633
.
Shultz
J. W.
(
1991
).
Evolution of locomotion in Arachnida: the hydraulic pressure pump of the Giant Whipscorpion, Mastigoproctus giganteus (Uropygi)
.
J. Morphol.
210
,
13
-
31
.
Steudel
K.
(
1990
).
The work and energetic cost of locomotion. II. Partitioning the cost of internal and external work within a species
.
J. Exp. Biol.
154
,
287
-
303
.
Ward
T. M.
,
Humphreys
F. W.
(
1981a
).
Locomotion in Burrowing and Vagrant Wolf Spiders (Licosidae)
.
J. Exp. Biol.
92
,
305
-
321
.
Ward
T. M.
,
Humphreys
F. W.
(
1981b
).
The effect of filming speed on the interpretation of arthropod locomotion
.
J. Exp. Biol.
92
,
323
-
331
.
Weinstein
R. B.
(
1995
).
Locomotor behavior of nocturnal ghost crabs on the beach: focal animal sampling and instantaneous velocity from three-dimensional motion analysis
.
J. Exp. Biol.
198
,
989
-
999
.
Wickler
S. J.
,
Hoyt
D. F.
,
Cogger
E. A.
,
McGuire
R.
(
2002
).
The cost of transport in an extended trot
.
Equine Vet. J. Suppl.
34
,
126
-
130
.
Wickler
S. J.
,
Hoyt
D. F.
,
Cogger
E. A.
,
Myers
G.
(
2003
).
The energetics of the trot-gallop transition
.
J. Exp. Biol.
206
,
1557
-
1564
.
Wilson
D. M.
(
1967
).
Stepping patterns in tarantula spiders
.
J. Exp. Biol.
47
,
133
-
151
.
Wilson
H.
,
Anderson
L.
(
2004
).
Morphology and taxonomy of Paleozoic millipedes (Diplopoda: Chilognatha: Archipolypoda) from Scotland
.
J. Paleontol.
78
,
169
-
184
.
Wu
G.
,
Cavanagh
P.
(
1995
).
ISB recommendations for standardization in the reporting of kinematic data
.
J. Biomech.
10
,
1257
-
1260
.
Zani
P. A.
,
Kram
R.
(
2008
).
Low metabolic cost of locomotion in ornate box turtles, Terrapene ornata
.
J. Exp. Biol.
211
,
3671
-
3676
.
Zollikofer
C.
(
1994
).
Stepping patterns in ants.1. Influence of speed and curvature
.
J. Exp. Biol.
192
,
95
-
106
.