ABSTRACT

During quadrupedal walking in most animals, the forelimbs play a net braking role, whereas the hindlimbs are net propulsive. However, the mechanism by which this differentiation occurs remains unclear. Here, we test two models to explain this pattern using primates and felines: (1) the horizontal strut effect (in which limbs are modeled as independent struts), and (2) the linked strut model (in which limbs are modeled as linked struts with a center of mass in between). Video recordings were used to determine point of contact, timing of mid-stance, and limb protraction/retraction duration. Single-limb forces were used to calculate contact time, impulses and the proportion of the stride at which the braking-to-propulsive transition (BP) occurred for each limb. We found no association between the occurrence of the BP and mid-stance, little influence of protraction and retraction duration on the braking–propulsive function of a limb, and a causative relationship between vertical force distribution between limbs and the patterns of horizontal forces. These findings reject the horizontal strut effect, and provide some support for the linked strut model, although predictions were not perfectly matched. We suggest that the position of the center of mass relative to limb contact points is a very important, but not the only, factor driving functional differentiation of the braking and propulsive roles of the limbs in quadrupeds. It was also found that primates have greater differences in horizontal impulse between their limbs compared with felines, a pattern that may reflect a fundamental arboreal adaptation in primates.

INTRODUCTION

During steady-state quadrupedal locomotion there is a functional differentiation of the braking and propulsive roles of the limbs. For most quadrupeds studied to date, the forelimbs are net braking (i.e. the horizontal force impulse is net negative), whereas the hindlimbs are net propulsive (i.e. the horizontal force impulse is net positive) (Demes et al., 1994; Gray, 1944, 1968; Lee et al., 2004). Although this finding of differential braking and propulsive roles of the forelimbs and hindlimbs has been reported in numerous studies and is generally accepted as universal (Demes et al., 1994; Franz et al., 2005; Granatosky et al., 2016a; Gray, 1944, 1968; Ishida et al., 1990), few researchers have addressed its underlying mechanisms (although see Lee et al., 2004) and the larger questions of adaptation that it raises. Furthermore, previous studies (Kimura et al., 1979; Demes et al., 1994) have suggested that primates show this differentiation to a greater degree than other mammals and that this reflects an important adaptive characteristic of primates. However, without understanding what drives these differences between non-primate mammals and primates, it is challenging to make robust adaptive arguments.

In Gray's (1944, 1968) seminal works on the mechanics of the tetrapod skeleton, he posited that the differential braking and propulsive function of the limbs could be understood simply by considering the need for the horizontal forces to be equal and by modeling the limbs as a system of struts and levers. A limb acting as an independent strut will, by definition, exert forces that act along the axis of the limb [i.e. a line from the point of contact (POC) of the hand or foot to the center of rotation of the shoulder or hip joint] (Gray, 1944, 1968; Reynolds, 1985) (Fig. 1A). In a simple strut, the magnitude of the horizontal force will be equal to the vertical force multiplied by the tangent of the angle between the limb and vertical. If the limb acts solely as an independent strut, any limb in a protracted position applies a braking force and any limb in a retracted position applies a propulsive force. This was described by Reynolds (1985) as the horizontal strut effect (HSE) and formed the basis for much of his subsequent arguments for vertical force distribution in animals. In this model, the braking-to-propulsive transition (BP; the point at which the horizontal force switches from an applied braking force to an applied propulsive force) should occur at the same time as mid-stance, when the POC is directly below the proximal limb joint (shoulder or hip). In the HSE, therefore, the determinant of whether a limb is net braking or net propulsive is based on the relative duration of protraction and retraction relative to the hip or shoulder of that limb during the support phase (Larson and Demes, 2011; Larson and Stern, 2009; Young, 2012).

Fig. 1.

Proposed models for functional differentiation of the braking and propulsive roles of the forelimbs and hindlimbs in quadrupeds. Blue represents the forelimb (FL) and red represents the hindlimb (HL). Specific footfall events are shown at touchdown (TD), early stance phase (ES), mid-stance (MS), late stance phase (LS) and lift-off (LO). (A) The horizontal strut effect (HSE) occurs when no muscles are active. The limb acts as a strut as the body moves over the forelimb or hindlimb point of contact (POC), and the direction of the applied force vector is determined by the orientation of the limb. If the strut limb is not vertically oriented underneath the shoulder or hip joint, it will exert a horizontal force on the substrate. Solid arrows represent the force applied to the substrate by the limb, and their orientation indicates the direction of that force. The dashed arrows represent the vertical and horizontal components of the applied force. (B) The linked strut model (LSM) assumes that force acts through the POC and the center of mass (COM) (i.e. a line from the forelimb or hindlimb POC to the COM). The direction of the applied force vector is determined by the orientation of the line connecting the POC and COM. If the POC is not directly underneath the COM, the limb will exert a horizontal force on the substrate. The circle with an inlaid hourglass represents the COM. Solid arrows represent the force applied to the substrate by the limb, and their orientation indicates the direction of that force. The black dashed arrows represent the vertical and horizontal components of the applied force.

Fig. 1.

Proposed models for functional differentiation of the braking and propulsive roles of the forelimbs and hindlimbs in quadrupeds. Blue represents the forelimb (FL) and red represents the hindlimb (HL). Specific footfall events are shown at touchdown (TD), early stance phase (ES), mid-stance (MS), late stance phase (LS) and lift-off (LO). (A) The horizontal strut effect (HSE) occurs when no muscles are active. The limb acts as a strut as the body moves over the forelimb or hindlimb point of contact (POC), and the direction of the applied force vector is determined by the orientation of the limb. If the strut limb is not vertically oriented underneath the shoulder or hip joint, it will exert a horizontal force on the substrate. Solid arrows represent the force applied to the substrate by the limb, and their orientation indicates the direction of that force. The dashed arrows represent the vertical and horizontal components of the applied force. (B) The linked strut model (LSM) assumes that force acts through the POC and the center of mass (COM) (i.e. a line from the forelimb or hindlimb POC to the COM). The direction of the applied force vector is determined by the orientation of the line connecting the POC and COM. If the POC is not directly underneath the COM, the limb will exert a horizontal force on the substrate. The circle with an inlaid hourglass represents the COM. Solid arrows represent the force applied to the substrate by the limb, and their orientation indicates the direction of that force. The black dashed arrows represent the vertical and horizontal components of the applied force.

Although the HSE model may be overly simplified, it is currently widely cited and has been used in a large number of studies that address the mechanism of this differentiation (Larson and Demes, 2011; Larson and Stern, 2009; Raichlen et al., 2009; Roberts and Belliveau, 2005; Young, 2012). Unfortunately, the HSE has not been empirically tested and there are strong theoretical grounds to question its explanatory power. But, in the absence of explicit data, it is not easy to reject this model either. Data collected by Schmitt (1994, 1995) on forelimb loading in five species of Old World monkey and one species of New World monkey reveal that the BP in these primates never occurs at mid-stance, as would have been predicted if the simple HSE model were a primary explanation for the braking and propulsive roles of the limb. Instead, in these species the BP occurred, on average, at about 22% of the stance phase after mid-stance. If this finding is consistent across other quadrupeds, then it is reasonable to argue that the BP is independent of mid-stance and the HSE does not explain the net braking role of the forelimb and net propulsive role of the hindlimb. In that case, it seems likely that an additional or alternative mechanism is driving functional differentiation of the braking and propulsive roles of the limbs in quadrupeds. It is easy to see the HSE as a good starting point that requires more information to explain the broader patterns, a point also made by Raichlen et al. (2009).

The HSE considers the limbs as independent struts. But it may be more effective and realistic to model a quadruped as a set of linked struts with a center of mass (COM) lying somewhere in the middle (Bertram, 2016; Usherwood et al., 2007). In a linked strut model (LSM), animals apply forces that act along a line from the POC to the COM (Bertram, 2016; Fig. 1B). Thus, the magnitude of the horizontal force will be equal to the vertical force multiplied by the tangent of the angle between a line from the POC to the COM and the vertical. In this model, the BP will not occur at mid-stance, but instead at the time that the POC passes under the COM. If one assumes the animal's COM is roughly midway between the shoulder and hip, although this certainly varies slightly (Farrell et al., 2015; Hoy and Zernicke, 1985; Larson and Demes, 2011; Lee et al., 2004; Rollinson and Martin, 1981; Usherwood et al., 2007; Vilensky, 1979), the forelimb POC will be anterior to the COM throughout most of the forelimb support phase, and the hindlimb POC will be posterior to the COM throughout most of the hindlimb support phase. Therefore, the forelimb will have a long braking phase and a short propulsive phase, resulting in a net braking impulse (BI). The hindlimb will have a short braking phase and a long propulsive phase, resulting in a net propulsive impulse (PI).

Body proportions potentially have an enormous effect on the LSM. In this model, an animal with a long trunk and short limbs will have higher levels of limb differentiation than an animal with a short trunk and long limbs. Similarly, in this model, if the COM is more anterior on the trunk, the forelimb will shift to a propulsive role sooner than it would if the COM were in the middle or relatively posterior. Conversely, if the COM is relatively posterior, the hindlimb will have a longer braking period than it would if the COM were in the middle or relatively anterior. As a result, the degree of functional differentiation between limbs is driven by body form and body mechanics in animals, and may reflect important ecological adaptations. For example, during arboreal locomotion, which requires rapid changes of direction on flexible and unpredictable supports, and in which the consequences of falling due to forward pitch is very high during deceleration (Pinkard et al., 2013), it may be advantageous for the forelimb to play an almost exclusively braking role and for the hindlimb to play both a braking and propulsive role, albeit still being net propulsive.

It is important to note that a corollary of the LSM is the potential that changes in limb position relative to the COM will influence vertical force distribution between the limbs (Gray, 1944, 1968; Larson and Demes, 2011; Raichlen et al., 2009; Reynolds, 1985; Young, 2012). In the LSM, the limb that is closest to the COM will support a greater proportion of body weight (Larson and Demes, 2011; Raichlen et al., 2009; Young et al., 2007).

In this study, we explore patterns in the braking and propulsive components of walking steps in a sample of primate and feline quadrupeds, and test hypotheses derived from the HSE model and LSM to determine the mechanisms that drive the differential braking and propulsive roles of the forelimbs and hindlimbs. The comparative sample captures important behavioral and body form variation in mammals. Primates are a primarily arboreal radiation with long limbs relative to trunk length and body mass (Alexander et al., 1979; Jungers, 1985). Primates also show, on average, forelimbs and hindlimbs that often are more protracted or retracted compared with non-primate mammals (Larson et al., 2000), and are known to exhibit higher peak vertical forces on the hindlimb relative to the forelimb, the opposite of the pattern seen in most mammals (Demes et al., 1994; Kimura et al., 1979). Felines, in contrast, are a primarily terrestrial radiation whose limb range of motion is not as protracted or retracted as primates (Larson et al., 2000) and demonstrate higher peak vertical forces on the forelimb relative to the hindlimb (Demes et al., 1994). To focus the investigation, we develop the following hypotheses based on the HSE model and LSM.

Hypothesis 1: quadrupeds regulate horizontal forces via the HSE

Prediction 1: the BP will occur when the POC is directly below the proximal joint (shoulder or hip) of the limb (i.e. at mid-stance).

Prediction 2: the BP will occur independently of the time when the POC passes below the COM.

Prediction 3: the relative ratio of protraction duration to retraction duration will determine if a limb is net braking or net propulsive.

Hypothesis 2: quadrupeds regulate horizontal forces via the LSM

Prediction 1: the BP will be independent of mid-stance.

Prediction 2: the BP will occur when the POC passes below the COM.

Prediction 3: the relative ratio of protraction duration to retraction duration will be independent of whether a limb is net braking or net propulsive.

Prediction 4: vertical force distribution between the limbs can be predicted by the average position of the forelimb and hindlimb POC relative to the COM.

MATERIALS AND METHODS

Kinematic and kinetic data were collected on five species of lemurs, five species of New World monkeys, four species of Old World monkeys, and five species of felines (Table 1). All data collection followed previously established methods (Granatosky et al., 2016a; Schmitt, 1999; Schmitt and Hanna, 2004; Schmitt and Lemelin, 2002), and was attained from animals housed at the Duke Lemur Center (Durham, NC, USA; lemurs), Monkey Jungle (Miami, FL, USA; New World monkeys), Stony Brook University (Stony Brook, NY, USA; Old World monkeys) and the Carolina Tiger Rescue (Pittsboro, NC, USA; felines). All data collection protocols were approved by each institution's respective Institutional Animal Care and Use Committee (IACUC).

Table 1.

Animal subjects used in the study and the number of steps collected per individual

Animal subjects used in the study and the number of steps collected per individual
Animal subjects used in the study and the number of steps collected per individual

Data were collected from animals walking on their most commonly used substrate in the wild, with a simulated arboreal support substituting for branches (diameter 3.10–3.81 cm) (see Table 1). During all trials, animals were video recorded from a lateral view at 60–120 fields s–1. Only walking strides (i.e. duty factor over 50%) in which the animal was traveling in a straight path and not accelerating or decelerating (i.e. steady-state locomotion) were selected for analysis. Steady-state locomotion was determined by calculating the instantaneous velocity between subsequent video frames throughout the entire stride and then using regression analysis to determine whether velocity changed throughout the stride (Bishop et al., 2008; Granatosky, 2015; Granatosky et al., 2016a). Only strides in which no change in speed (i.e. slope not significantly different than zero) was detected were analyzed.

Forelimb and hindlimb forces were collected while animals walked on a wooden runway or raised horizontal pole. A small subsection of the runway or pole was instrumented with Kistler force plates (models 9317B or 9281B; Kistler Instrument Corp., Amherst, NY, USA) following methods described in detail elsewhere (Bishop et al., 2008; Granatosky et al., 2016a,b; Schmitt, 1999; Schmitt and Hanna, 2004; Schmitt and Lemelin, 2002). Force plate output was sampled at 12,000 Hz, imported, summed and processed using BioWare™ v.5.1 software (Kistler Instrument Corp.), and then filtered (Butterworth, 30 Hz) and analyzed in MATLAB (MATLAB version 2016a; MathWorks, Natick, MA, USA). Only steps with single-limb contacts on the plate or those steps in which the forelimb and hindlimb forces could be clearly differentiated were analyzed. All forces were normalized as a percentage of body mass (%BM) for each animal.

Contact time, PI, BI, net horizontal impulse (HI), vertical impulse (VI) and the proportion of the stride at which the BP occurred were calculated for each limb. PI and BI were the positive or negative area under the force–time curve in the horizontal component of the substrate reaction force, respectively. The HI provided a means for differentiating the net braking or propulsive role of the limb during particular locomotor behaviors (Demes et al., 1994). Positive HI values indicated a net propulsive limb, whereas negative HI values indicated a net braking limb (Demes et al., 1994; Franz et al., 2005; Granatosky et al., 2016a; Ishida et al., 1990; Kimura et al., 1979). VI was the area under the force–time curve in the vertical component of the substrate reaction force. In order to make statistical comparisons between subjects of differing body masses, all impulses were measured as a percentage of body mass s–1 (%BM s–1).

Prior to testing the primary predictions of the study, a Shapiro–Wilk and Levene's test was used to test for normality and homoscedasticity within the data set (Sokal and Rohlf, 2012). Subsequent statistical tests were conducted based on these results. We conducted three separate analyses comparing grouped primate data to the felines. HI was compared across limbs in both groups of animals to ensure that, in all animals examined here, the forelimb served a net braking function, whereas the hindlimb was net propulsive. Additionally, we compared contact time and dimensionless speed between primates and felines to determine whether differences observed between taxa were potentially influenced by these variables. The square root of the Froude number (Fr) was used for normalizing speed to a dimensionless parameter (see Alexander, 1992):
formula
(1)

where ν is the average velocity of the stride, g is 9.81 m s−2 and l is forelimb length (m) of the individual. Dimensionless speed was analyzed using a Mann–Whitney U-test, whereas HI and contact time were analyzed with a paired-sample t-test. All analyses were carried out using MATLAB (MATLAB version 2016a; MathWorks, Natick, MA, USA).

To address predictions concerning the relationship between the timing of the BP and mid-stance of each limb, the time at touchdown, mid-stance [the POC is directly below the proximal limb joint (shoulder or hip)] and lift-off were recorded from video sequences for each stride. From these event times, the proportion of support phase at which mid-stance occurred was determined. A Mann–Whitney U-test was conducted to determine the statistical likelihood that BP and mid-stance occur at the same time for each limb and each species separately.

Our ability to address predictions concerning the relationship between the timing of the BP and the POC passing beneath the approximate position of COM was constrained by the availability of previously published data on COM position in our sample of animals. This limited our sample to only five species of primate [Ateles geoffroyi (COM is 57% of trunk length from shoulder) and Cebus capucinus (45.8% of trunk length from shoulder) (Larson and Demes, 2011); Saimiri sciureus (56.8–60.1% of trunk length from shoulder depending on body weight) (Young, 2012); Erythrocebus patas (50% of trunk length from shoulder) (Young et al., 2007); Macaca mulatta (50.4% of trunk length from shoulder) (Vilensky and Larson, 1989)] and one feline [Felis catus (43.7% of trunk length from shoulder) (Farrell et al., 2015; Hoy and Zernicke, 1985; Vilensky and Larson, 1989)]. For these species, we digitized the known position of the COM along the trunk and, for each single-limb contact, collected the timing of touchdown, the point at which the POC passed beneath the COM, and lift-off. We then calculated the proportion of support phase at which the POC passed beneath the COM for each single-limb contact. It should be noted that these COM positions were collected from animals not used in this study and that the COM does not remain static during locomotion [but see Farrell et al. (2015) and Young et al. (2007), which suggest that anterior/posterior movement appears to be minimal]. Taken together, it is possible that potential errors in the timing of events may have occurred. We conducted a Mann–Whitney U-test to determine the statistical likelihood of the BP and the point at which the POC passed beneath the COM occurring at the same time, for each limb and each species separately.

To address predictions concerning the relationship between the protraction duration to retraction duration ratio and whether a limb was net braking or net propulsive, we conducted a regression analysis and an associated ANOVA between the protraction duration to retraction duration ratio and HI. We compared this relationship for each of the major phylogenetic groups (i.e. lemurs, New World Monkeys, Old World Monkeys and felines) separately.

Finally, our ability to address predictions concerning the relationship between vertical force distribution between the limbs and the average position of the forelimb and hindlimb POC relative to the COM was again constrained by the availability of previously published data on COM position in our sample of animals. Additional limitations in the availability of samples came from the need to collect both forelimb and hindlimb forces within a single stride. Because primates tend to walk with a diagonal sequence gait (i.e. each hindlimb footfall is followed by a contralateral forelimb footfall), the likelihood of obtaining single-limb forces from both the forelimb and the hindlimb during a single stride is low compared with felines, which walk with a lateral sequence gait (i.e. each hindlimb footfall is followed by an ipsilateral forelimb footfall). This limited our sample to only four species of primates (A. geoffroyi, C. capucinus, S. sciureus and M. mulatta) and one feline (F. catus). To address prediction 4, we followed the methods used by Raichlen et al. (2009) and Larson and Demes (2011) in which the observed vertical force distribution [i.e. the VI ratio (Robs)] was compared with the predicted distribution of vertical force (Rpred) based on the average position of the forelimb and hindlimb POC relative to the COM (Fig. S1). We calculated Robs as:
formula
(2)
where VIFL is the VI in the forelimb and VItotal is the sum of the VI in the forelimb and hindlimb within the same stride. Values equal to 0.5 represent equal weight distribution between the limbs; values lower than 0.5 indicate greater weight distribution borne by the hindlimbs; and values greater than 0.5 indicate greater weight distribution borne by the forelimbs. To calculate Rpred, we used the following equation:
formula
(3)

where X1 is the average horizontal distance from the hindlimb POC to the COM during hindlimb support and X2 is the average horizontal distance from the forelimb POC to the COM during forelimb support, as calculated from the video recordings. As with prediction 2, the fact that estimated COM position was based on individual animals not included in this study could cause errors in calculations. For each species, we conducted a Mann–Whitney U-test to determine the statistical likelihood of Robs and Rpred being the same.

RESULTS

In total, 768 single-limb forces were analyzed (Fig. 2). Summary statistics for dimensionless speed, contact time, PI, BI, HI and VI for each species and limb are presented in Table 2.

Fig. 2.

Representative force traces of the forelimb and hindlimb during steady-state locomotion. All force data were corrected to indicate the applied force by the animal and was standardized for the direction of travel and differing body mass. This resulted in comparable force curves that all displayed vertical and propulsive force as positive values and braking force as negative values. In order to make comparisons between subjects of differing body masses, all force traces originally measured in Newtons were converted into a proportion of the animal's body mass (%BM).

Fig. 2.

Representative force traces of the forelimb and hindlimb during steady-state locomotion. All force data were corrected to indicate the applied force by the animal and was standardized for the direction of travel and differing body mass. This resulted in comparable force curves that all displayed vertical and propulsive force as positive values and braking force as negative values. In order to make comparisons between subjects of differing body masses, all force traces originally measured in Newtons were converted into a proportion of the animal's body mass (%BM).

Table 2.

Summary statistics (mean±s.d.) for dimensionless speed, contact time, and impulse in five feline species and 14 species of primate

Summary statistics (mean±s.d.) for dimensionless speed, contact time, and impulse in five feline species and 14 species of primate
Summary statistics (mean±s.d.) for dimensionless speed, contact time, and impulse in five feline species and 14 species of primate

In all species analyzed, the forelimb tended to apply a net braking force to the substrate, whereas the hindlimb tended to apply a net propulsive force. The magnitude of the HI was significantly (P<0.001) greater in both limbs in primates (forelimb mean HI=−2.14±1.50%BM s–1, n=311; hindlimb mean HI=2.17±1.70%BM s–1, n=255) compared with felines (forelimb mean HI=−0.89±0.86%BM s–1, n=107; hindlimb mean HI=1.53±0.80%BM s–1, n=95).

Contact time was significantly (P<0.001) lower in primates compared with felines (forelimb mean contact time=0.46±0.20 s, n=311; hindlimb mean contact time=0.55±0.25 s, n=255; versus forelimb mean contact time=0.70±0.20 s, n=107; hindlimb mean contact time=0.69±0.19 s, n=95, respectively). There were no significant (P=0.089) differences observed in dimensionless speed between primates (mean dimensionless speed=0.24±0.18, n=497) and felines (mean dimensionless speed=0.31±0.24, n=124).

The hypothesis that the BP always occurred at mid-stance was rejected in this study (Table 3). In the forelimb, the BP occurred significantly later than did mid-stance in all species. In the hindlimb, the BP occurred significantly earlier than did mid-stance in most species. The only instance where the timing of the BP and mid-stance was not statistically different was in the hindlimb of Aotus nancymae.

Table 3.

The timing (mean±s.d.) and P-value of the braking-to-propulsive transition (BP) and mid-stance within the support phase for each species

The timing (mean±s.d.) and P-value of the braking-to-propulsive transition (BP) and mid-stance within the support phase for each species
The timing (mean±s.d.) and P-value of the braking-to-propulsive transition (BP) and mid-stance within the support phase for each species

Statistical analyses of the association between the occurrence of the BP and the point at which the forelimb/hindlimb POC passed under the estimated COM revealed different results for different species. For E.patas (the most terrestrial primate in our sample) and F.catus there was a significant difference in both the forelimbs and hindlimbs between the timing of these two events. In A.geoffroyi and S.sciureus there was a significant difference in the timing of these two events in the forelimb, but not in the hindlimb. The opposite pattern was observed in M.mulatta, in which these events occurred at different times in the hindlimb, but not in the forelimb. In C.capucinus there was no statistically significant difference in the occurrence of these events in either the forelimb or the hindlimb (Table 3).

The regression analysis for the protraction duration to retraction duration ratio and HI revealed no association between the two variables in almost all instances (Fig. 3). For the primates observed, there was no significant association between the relative amount of time spent in protraction and retraction and whether the limb was net braking or propulsive. In the felines, there was no significant association observed in the hindlimb, but there was significant (P=0.02) negative association (y=−0.85x−0.237, R2=0.05) between the relative duration of protraction and retraction and the net HI in the forelimb. In this instance, a greater amount of time spent in a protracted position compared with a retracted position tended to result in relatively lower net HIs.

Fig. 3.

The relationship between net horizontal impulse and limb protraction duration to retraction duration ratio during steady-state locomotion. (A) Lemurs (N=150 steps in the forelimb; N=110 steps in the hindlimb); (B) New World monkeys (N=126 steps in the forelimb; N=107 steps in the hindlimb); (C) Old World monkeys (N=35 steps in the forelimb; N=38 steps in the hindlimb); and (D) felines (N=107 steps in the forelimb; N=95 steps in the hindlimb). All horizontal impulse (HI) measures are presented as a percentage of body mass s–1 (%BM s–1). Negative impulse values represent a limb that is net braking, whereas positive impulse values represent a limb that is net propulsive. Limb protraction duration to retraction duration ratios greater than one indicate a limb that spends the majority of time in a protracted position, whereas a limb protraction duration to retraction duration ratio of less than one indicates a limb that spends the majority of time in a retracted position. In the primates, there was no significant association between the relative amount of protraction duration and retraction duration and whether the limb (forelimb or hindlimb) was net braking or propulsive. In the felines, there was no significant association observed in the hindlimb, but there was a significant (P=0.02) negative association (y=−0.85×−0.237; R2=0.05) between the relative amount of time spent with the limb in protraction or retraction and the net horizontal impulse in the forelimb.

Fig. 3.

The relationship between net horizontal impulse and limb protraction duration to retraction duration ratio during steady-state locomotion. (A) Lemurs (N=150 steps in the forelimb; N=110 steps in the hindlimb); (B) New World monkeys (N=126 steps in the forelimb; N=107 steps in the hindlimb); (C) Old World monkeys (N=35 steps in the forelimb; N=38 steps in the hindlimb); and (D) felines (N=107 steps in the forelimb; N=95 steps in the hindlimb). All horizontal impulse (HI) measures are presented as a percentage of body mass s–1 (%BM s–1). Negative impulse values represent a limb that is net braking, whereas positive impulse values represent a limb that is net propulsive. Limb protraction duration to retraction duration ratios greater than one indicate a limb that spends the majority of time in a protracted position, whereas a limb protraction duration to retraction duration ratio of less than one indicates a limb that spends the majority of time in a retracted position. In the primates, there was no significant association between the relative amount of protraction duration and retraction duration and whether the limb (forelimb or hindlimb) was net braking or propulsive. In the felines, there was no significant association observed in the hindlimb, but there was a significant (P=0.02) negative association (y=−0.85×−0.237; R2=0.05) between the relative amount of time spent with the limb in protraction or retraction and the net horizontal impulse in the forelimb.

For all species, Rpred was significantly greater than Robs [A. geoffroyi (P=0.003), C. capucinus (P=0.006), S. sciureus (P≤0.001), M. mulatta (P=0.003) and F. catus (P=0.021)] (Table 4, Fig. 4). This means that, for all species, Rpred overestimated the percentage of weight supported by the forelimbs.

Fig. 4.

Mean and s.d. values of the observed vertical impulse ratio (Robs) and predicted vertical impulse ratio (Rpred). The Robs was calculated as a fraction of forelimb mass support, and Rpred was based on the average horizontal distances of the forelimb/hindlimb POC from the COM. In all species, Rpred overestimates the actual values of forelimb mass support for all subjects.

Fig. 4.

Mean and s.d. values of the observed vertical impulse ratio (Robs) and predicted vertical impulse ratio (Rpred). The Robs was calculated as a fraction of forelimb mass support, and Rpred was based on the average horizontal distances of the forelimb/hindlimb POC from the COM. In all species, Rpred overestimates the actual values of forelimb mass support for all subjects.

Table 4.

Mean and s.d. of the observed VI ratio (Robs) and predicted VI ratio (Rpred)

Mean and s.d. of the observed VI ratio (Robs) and predicted VI ratio (Rpred)
Mean and s.d. of the observed VI ratio (Robs) and predicted VI ratio (Rpred)

DISCUSSION

The primate and feline data collected in this study confirm previous findings (Demes et al., 1994; Franz et al., 2005; Granatosky et al., 2016a; Kimura et al., 1979; Lee, 2011; Lee et al., 2004; Reynolds, 1985) that, during steady-state quadrupedal locomotion, there is a functional differentiation in the braking and propulsive roles of the limbs. In all species analyzed, the forelimb tends to be net braking, whereas the hindlimb is typically net propulsive.

This study finds little data supporting the HSE model, which suggests that the functional differentiation of forelimbs and hindlimbs can be explained by treating the limbs as if they were independent struts. The HSE predicted that the point at which the limb switches from exerting a braking-to-propulsive force should occur when the POC passes beneath the proximal limb joint (i.e. mid-stance) and the limb switches from protraction to retraction. However, none of our data supported that prediction consistently. In one species, we found evidence for the co-occurrence of these events in the hindlimb. In all other species, the timing of these events was statistically independent, in contradiction to the prediction of the model.

Instead of the functional differentiation of the limbs being explained by modeling the limbs as simple struts, the data presented here suggest that the limbs function as linked struts (Gray, 1944, 1968; Lee, 2011; Lee et al., 2004; Reynolds, 1985; Usherwood et al., 2007) and that this pattern explains, in part, the differentiation of braking and propulsive roles of the limbs observed in quadrupeds. In the forelimb of all animals, the BP always occurred after mid-stance and, in the hindlimb of all animals, the BP always occurred before mid-stance. This means that there is a portion of forelimb support phase in which the forelimb is in a retracted position yet applies a braking force to the substrate, and a portion of hindlimb support phase in which the hindlimb is in a protracted position yet applies a propulsive force to the substrate. This finding suggests that the position of the limb POC relative to the COM determines whether a particular limb will produce a braking or propulsive force.

The finding that relative protraction and retraction duration have little influence on whether a limb is net propulsive or net braking further emphasizes the need for additional input on the HSE model. Only in the forelimb of the felines was any significant association observed but, even in this circumstance, the explanatory power of this relationship is low. This is interesting, considering that the more exaggerated levels of forelimb protraction observed in primates (Larson et al., 2000; Schmidt, 2008) have been cited as responsible for the greater levels of braking within the primate forelimb (Demes et al., 1994; Schmitt, 1995, 1999). It should be noted that this assumption is based on angular positions of the limbs within a stride and not relative duration (as measured in the present study). Further work should be conducted to explore the relationship between horizontal force patterns and the angular positions of the limbs and the interactions of multiple limbs making contact with the substrate at once.

However, an LSM also does not explain all of the variance observed. In all species analyzed, the LSM consistently overestimates the percentage of weight supported on the forelimbs. This finding is consistent with Larson and Demes (2011) and has been interpreted as evidence for an alternative model, the hindlimb lever effect (HLE). The HLE predicts that an animal can actively redistribute body mass to the forelimbs or hindlimbs by pitching the trunk via extrinsic muscles (Reynolds, 1985). Torque created by limb retractors (forelimb or hindlimb) will shift mass onto the hindlimb, whereas limb protractors (forelimb or hindlimb) will increase the vertical force on the forelimb (Larson and Demes, 2011; Larson and Stern, 2009; Raichlen et al., 2009; Reynolds, 1985; Young, 2012). This mechanism has been proposed to be especially important in primates as a means to redistribute body mass away from the highly mobile but weak joints of the forelimb (Larson and Demes, 2011; Larson and Stern, 2009; Reynolds, 1985; Young, 2012). By contrast, in favor of the LSM, some species demonstrate the BP at the point at which the forelimb or hindlimb POC passed under the COM. Thus, it appears that the LSM is supported for some species and for some limbs, but not for all species in this study. Further work integrating COM position, kinematics, kinetics and the timing of muscle activation patterns from the same animal should be conducted to test the HLE model. It is certainly the case that both the LSM and HLE model could be important in understanding the functional differentiation of the limbs and that the prominence of each model for explaining limb behavior varies by species anatomy and ecology, with the possibility that the HLE plays a particularly strong role in arboreal primates, as argued by Reynolds (1985) and Larson and Stern (2009). This requires more study with more detailed mechanics in a primate and non-primate sample, and could not be explicitly rejected or accepted by the data presented here.

This study reveals that primates have greater differences in HI between their limbs compared with differences found in felines. In primates, the forelimb might be best described as ‘increased braking’ and the hindlimb as ‘increased propulsive’ relative to other quadrupeds. A comparison of previously published data for HI in other non-primate mammals (Demes et al., 1994; Kimura et al., 1979; Lee et al., 2004; Shine et al., 2015) shows similarly low HI differences between the limbs compared with primates. In our study, this difference is not a result of longer contact times or higher dimensionless speed (factors known to increase impulse) in primates, but may instead represent differences in body proportions and locomotor ecology. It is argued that primates, including those in this study, have a more posteriorly positioned COM than other animals (Rollinson and Martin, 1981), but data from Vilensky and Larson (1989) suggest that the actual difference calculated from cadavers of primates and non-primates is not markedly apparent. Previous studies show that F.catus have a COM placed at 43.7% of trunk length from the shoulder (Farrell et al., 2015; Hoy and Zernicke, 1985; Vilensky and Larson, 1989), but C.capucinus have a COM position at 45.8% (Larson and Demes, 2011) and that of the other primate species ranges from 50 to 60.1% (Larson and Demes, 2011; Vilensky and Larson, 1989; Young et al., 2007; Young, 2012). It has also been argued by Reynolds (1985) that primates have a dynamically posterior COM (also see Schmitt and Hanna, 2004;Larson and Stern, 2009). Based on the assumptions of the LSM, greater forelimb braking in primates may be explained by COM positions that are further away from the POC of the forelimbs. It is also worth noting that C. capucinus, whose COM position is close to that of F. catus, showed different patterns of BP timing compared with other primates. Furthermore, E.patas, whose COM position is posterior compared to that of F. catus, showed similar BP timing to F. catus, perhaps as a function of long limbs relative to trunk length. Data from our study add to the body of evidence indicating that functional differentiation between the forelimbs and hindlimbs of primates, both in vertical force and in braking/propulsive force, is greater than that of non-primate mammals, but further investigation is sorely needed to substantiate this claim.

Data from this study of primates and felines provide evidence for considering the limbs as a cooperating set of struts linked together with a COM lying somewhere in between the shoulder and hip joints. It may also be the case that muscles of the back, shoulder and hip may play a role in limb functional differentiation, but further tests are required. It should be noted that models tested in this study are simplistic in nature and are meant to only provide a starting point for others to investigate. In this current analysis, all representations of the limbs were considered as stiff rods, and only one limb was considered at a time. The use of single-limb forces were necessary in our analysis, but this technique has limitations for interpreting whole-body interactions. Each limb only exerts part of the force acting on the body; consequently, the action of other limbs will influence the forces measured at each contact. Our analyses were conducted over a narrow speed range with similar contact times between limbs, but even slight variation in temporal variables between single-limb contacts may influence comparisons. Furthermore, COM was considered static throughout the stride. Quadrupedal locomotion is a complex interaction of multiple limbs making contact with the support at any point in time, with multiple joints moving relative to each other within each limb, activation of muscles both concentrically and eccentrically, and a COM that changes position. In future works these factors should be considered in order to achieve better predictive power of what drives the patterns of horizontal forces in quadrupeds. The expansive data set in this manuscript provides a foundation for further exploration of the forces acting upon the limbs of quadrupeds.

Acknowledgements

We thank all those that helped with animal care and use. Without their help, we would not be able to complete this study. We thank Pierre Lemelin, Herman Pontzer, Christine Wall, Jandy Hanna and the two anonymous reviewers for their comments and inspiration that improved the overall quality of this work.

Footnotes

Author contributions

Conceptualization: M.C.G., D.S.; Methodology: M.C.G., A.F., A.Z., D.S.; Software: M.C.G., A.F.; Validation: A.F.; Formal analysis: M.C.G., A.F.; Investigation: M.C.G., A.Z., D.S.; Resources: M.C.G., D.S.; Data curation: M.C.G.; Writing - original draft: M.C.G., A.Z., D.S.; Writing - review & editing: M.C.G., A.F., A.Z., D.S.; Supervision: M.C.G., D.S.; Project administration: M.C.G., D.S.; Funding acquisition: M.C.G., D.S.

Funding

This research was funded in part by the Leakey Foundation, Force and Motion Foundation, and the National Science Foundation’s Graduate Research Fellowship Program.

References

Alexander
,
R. M.
(
1992
).
Exploring Biomechanics: Animals in Motion
, 2nd edn.
New York
:
W H Freeman & Co
.
Alexander
,
R. McN.
,
Jayes
,
A. S.
,
Maloiy
,
G. M. O.
and
Wathuta
,
E. M.
(
1979
).
Allometry of the limb bones of mammals from shrews (Sorex) to elephant (Loxodonta)
.
J. Zool.
189
,
305
-
314
.
Bertram
,
J. E.
(ed.) (
2016
).
Concepts in locomotion: levers, struts, pendula and springs
. In
Understanding Mammalian Locomotion: Concepts and Applications
, pp.
79
-
110
.
Hoboken, New Jersey
:
John Wiley & Sons, Inc
.
Bishop
,
K. L.
,
Pai
,
A. K.
and
Schmitt
,
D.
(
2008
).
Whole body mechanics of stealthy walking in cats
.
PLoS ONE
3
,
e3808
-
e3808
.
Demes
,
B.
,
Larson
,
S. G.
,
Stern
,
J. T.
,
Jungers
,
W. L.
,
Biknevicius
,
A. R.
and
Schmitt
,
D.
(
1994
).
The kinetics of primate quadrupedalism: “hindlimb drive” reconsidered
.
J. Hum. Evol.
26
,
353
-
374
.
Farrell
,
B. J.
,
Bulgakova
,
M. A.
,
Sirota
,
M. G.
,
Prilutsky
,
B. I.
and
Beloozerova
,
I. N.
(
2015
).
Accurate stepping on a narrow path: mechanics, EMG, and motor cortex activity in the cat
.
J. Neurophysiol.
114
,
2682
-
2702
.
Franz
,
T. M.
,
Demes
,
B.
and
Carlson
,
K. J.
(
2005
).
Gait mechanics of lemurid primates on terrestrial and arboreal substrates
.
J. Hum. Evol.
48
,
199
-
217
.
Granatosky
,
M. C.
(
2015
).
Kinetic and kinematic patterns of arm-swinging in the red-shanked douc langur (Pygathrix nemaeus)
.
J. Vietnam. Primatol.
2
,
33
-
40
.
Granatosky
,
M. C.
,
Tripp
,
C. H.
and
Schmitt
,
D.
(
2016a
).
Gait kinetics of above and below branch quadrupedal locomotion in lemurid primates
.
J. Exp. Biol.
219
,
53
-
63
.
Granatosky
,
M. C.
,
Tripp
,
C. H.
,
Fabre
,
A.-C.
and
Schmitt
,
D.
(
2016b
).
Patterns of quadrupedal locomotion in a vertical clinging and leaping primate (Propithecus coquereli) with implications for understanding the functional demands of primate quadrupedal locomotion
.
Am. J. Phys. Anthropol.
160
,
644
-
652
.
Gray
,
J.
(
1944
).
Studies in the mechanics of the tetrapod skeleton
.
J. Exp. Biol.
20
,
88
-
116
.
Gray
,
J.
(
1968
).
Animal Locomotion
.
London
:
William Clowes and Sons
.
Hoy
,
M. G.
and
Zernicke
,
R. F.
(
1985
).
Modulation of limb dynamics in the swing phase of locomotion
.
J. Biomech.
18
,
49
-
60
.
Ishida
,
H.
,
Jouffroy
,
F.
and
Nakano
,
Y.
(
1990
).
Comparative dynamics of pronograde and upside down horizontal quadrupedalism in the slow loris (Nycticebus coucang)
. In
Gravity, posture and locomotion in primates
(ed.
F.
Jouffroy
,
M.
Stack
and
C.
Niemitz
), pp.
209
-
220
.
Florence, Italy
:
Il Sedicesimo
.
Jungers
,
W. L.
(
1985
).
Body size and scaling of limb proportions in primates
. In
Size and Scaling in Primate Biology
(ed.
W. J.
Jungers
), pp.
345
-
381
.
New York
:
Springer
.
Kimura
,
T.
,
Okada
,
M.
and
Ishida
,
H.
(
1979
).
Kinesiological characteristics of primate walking: its significance in human walking
. In
Environment, Behaviour, Morphology: Dynamic Interactions in Primates
(ed.
M.
Morbeck
,
H.
Preuschoft
and
N.
Gomberg
), pp.
297
-
311
.
New York
:
Gustav Fischer
.
Larson
,
S. G.
and
Demes
,
B.
(
2011
).
Weight support distribution during quadrupedal walking in Ateles and Cebus
.
Am. J. Phys. Anthropol.
144
,
633
-
642
.
Larson
,
S. G.
and
Stern
,
J. T.
(
2009
).
Hip extensor EMG and forelimb/hind limb weight support asymmetry in primate quadrupeds
.
Am. J. Phys. Anthropol.
138
,
343
-
355
.
Larson
,
S. G.
,
Schmitt
,
D.
,
Lemelin
,
P.
and
Hamrick
,
M.
(
2000
).
Uniqueness of primate forelimb posture during quadrupedal locomotion
.
Am. J. Phys. Anthropol.
112
,
87
-
101
.
Lee
,
D. V.
(
2011
).
Effects of grade and mass distribution on the mechanics of trotting in dogs
.
J. Exp. Biol.
214
,
402
-
411
.
Lee
,
D. V.
,
Stakebake
,
E. F.
,
Walter
,
R. M.
and
Carrier
,
D. R.
(
2004
).
Effects of mass distribution on the mechanics of level trotting in dogs
.
J. Exp. Biol.
207
,
1715
-
1728
.
Pinkard
,
H.
,
Schmitt
,
D.
,
Johnson
,
L. E.
and
Miller
,
C. E.
(
2013
).
The mechanics of acceleration and deceleration in primate quadrupeds:implications for primate locomotor evolution
.
FASEB J.
27
,
755.12
-
755.12
.
Raichlen
,
D. A.
,
Pontzer
,
H.
,
Shapiro
,
L. J.
and
Sockol
,
M. D.
(
2009
).
Understanding hind limb weight support in chimpanzees with implications for the evolution of primate locomotion
.
Am. J. Phys. Anthropol.
138
,
395
-
402
.
Reynolds
,
T.
(
1985
).
Mechanics of increased support weight by the hindlimbs in primates
.
Am. J. Phys. Anthropol.
67
,
335
-
349
.
Roberts
,
T. J.
and
Belliveau
,
R. A.
(
2005
).
Sources of mechanical power for uphill running in humans
.
J. Exp. Biol.
208
,
1963
-
1970
.
Rollinson
,
J.
and
Martin
,
R.
(
1981
).
Comparative aspects of primate locomotion, with special reference to arboreal cercopithecines
.
Symp. Zool. Soc. Lond.
48
,
377
-
427
.
Schmidt
,
M.
(
2008
).
Forelimb proportions and kinematics: how are small primates different from other small mammals?
J. Exp. Biol.
211
,
3775
-
3789
.
Schmitt
,
D.
(
1994
).
Forelimb mechanics as a function of substrate type during quadrupedalism in two anthropoid primates
.
J. Hum. Evol.
26
,
441
-
457
.
Schmitt
,
D.
(
1995
).
A kinematic and kinetic analysis of forelimb use during arboreal and terrestrial quadrupedalism in Old World Monkeys. PhD thesis, Stony Brook University, Stony Brook, NY
.
Schmitt
,
D.
(
1999
).
Compliant walking in primates
.
J. Zool.
248
,
149
-
160
.
Schmitt
,
D.
and
Hanna
,
J. B.
(
2004
).
Substrate alters forelimb to hindlimb peak force ratios in primates
.
J. Hum. Evol.
46
,
239
-
254
.
Schmitt
,
D.
and
Lemelin
,
P.
(
2002
).
Origins of primate locomotion: gait mechanics of the woolly opossum
.
Am. J. Phys. Anthropol.
118
,
231
-
238
.
Shine
,
C. L.
,
Penberthy
,
S.
,
Robbins
,
C. T.
,
Nelson
,
O. L.
and
McGowan
,
C. P.
(
2015
).
Grizzly bear (Ursus arctos horribilis) locomotion: gaits and ground reaction forces
.
J. Exp. Biol.
218
,
3102
-
3109
.
Sokal
,
R. R.
and
Rohlf
,
F. J.
(
2012
).
Biometry: the Principles and Practice of Statistics in Biological Research, p. 937. New York: W. H. Freeman
.
Usherwood
,
J. R.
,
Williams
,
S. B.
and
Wilson
,
A. M.
(
2007
).
Mechanics of dog walking compared with a passive, stiff-limbed, 4-bar linkage model, and their collisional implications
.
J. Exp. Biol.
210
,
533
-
540
.
Vilensky
,
J. A.
(
1979
).
Masses, centers-of-gravity, and moments-of-inertia of the body segments of the rhesus monkey (Macaca mulatta)
.
Am. J. Phys. Anthropol.
50
,
57
-
65
.
Vilensky
,
J. A.
and
Larson
,
S. G.
(
1989
).
Primate locomotion: utilization and control of symmetrical gaits
.
Annu. Rev. Anthropol.
18
,
17
-
35
.
Young
,
J. W.
(
2012
).
Ontogeny of limb force distribution in squirrel monkeys (Saimiri boliviensis): insights into the mechanical bases of primate hind limb dominance
.
J. Hum. Evol.
62
,
473
-
485
.
Young
,
J. W.
,
Patel
,
B. A.
and
Stevens
,
N. J.
(
2007
).
Body mass distribution and gait mechanics in fat-tailed dwarf lemurs (Cheirogaleus medius) and patas monkeys (Erythrocebus patas)
.
J. Hum. Evol.
53
,
26
-
40
.

Competing interests

The authors declare no competing or financial interests.

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