Apples, oranges, and angles: Comparative kinematic analysis of disparate limbs
Highlights
► Limb angles are not directly comparable among disparate species. ► Geometric constraints restrict limbs to different regions of configuration space. ► A non-angular parameterization of intersegmental coordination is needed.
Introduction
Terrestrial locomotion is a complex, coordinated activity involving the dynamic interaction of numerous parts (e.g., Bernstein, 1967). During walking and running, a tetrapod's multi-segmented limbs continuously change configuration as they oscillate with each cycle. Motion can be quite diagnostic, such that a person's stride reveals clues about age (Elble et al., 1991), sex (Troje, 2002), health (Manor and Li, 2009), emotion (Michalak et al., 2009), and even individual identity (Richardson and Johnston, 2005). Yet despite such rich intraspecific variation, human limb movements would never be confused with those of a chimp, cat, or quail, which have their own characteristic motion profiles.
How, why, and when limb kinematic patterns have changed along various lineages are major questions in functional morphology, comparative biomechanics, and paleontology (Biewener, 1989, Irschick and Jayne, 1999, Hutchinson and Gatesy, 2000, Blob, 2001, Gasc, 2001, Larson et al., 2001, Russell and Bels, 2001, Fischer et al., 2002, Schmidt, 2008, Hutchinson and Allen, 2009). The evolution of locomotor movements should be traceable throughout the tree of life using comparative methods (e.g., Harvey and Pagel, 1991). Just as for morphological, genetic, and behavioral traits, combining data from extant species with an explicit phylogenetic hypothesis should reveal evidence of movement patterns likely present in hypothetical common ancestors. Such inferences should help clarify trends along specific lineages and inform reconstruction of fossil taxa.
In order for limb motion to be compared and mapped out through time, movement patterns must be quantified. Most kinematic descriptions rely on external and/or internal angular data to characterize a limb's changing pose throughout the stride cycle. “Elevation” or “segment” angles are external angles that quantify the orientation of a limb segment (femur, tibia, metatarsus, etc.) relative to vertical or horizontal. “Joint” angles (hip, knee, ankle, etc.) are internal angles that measure the relative orientation of adjacent segments. Both types of angles are typically compared at equivalent times within the stride cycle. The mid-stance pose is frequently emphasized because the ground reaction force is often largest at this time (e.g., Biewener, 1989). Excursion angles between touch-down and lift-off are one way to summarize the amount of rotation a segment or joint undergoes during the stance phase.
Angles are routinely compared among species to answer a range of questions. For example, Fischer et al. (2002) measured limb motion in eight species of small mammals to see if all share a basic kinematic pattern. Ashley-Ross (1994) compared data from walking salamanders to hind limb angles of a broad sampling of amniotes to highlight common features. More statistical treatments include a study of sprinting in five lizard species (Irschick and Jayne, 1999), an assessment of joint angles among cercopithecine primates (Polk, 2002), and a kinematic analysis of scaling in nine felids (Day and Jayne, 2007). As these and countless other publications attest, angles are ubiquitous. Herein, we attempt to shed light on previously overlooked limitations of such angular parameterization for evolutionary analyses of terrestrial locomotion.
Section snippets
Transferability—a prerequisite for comparison
Comparative kinematic studies are founded on a concept of similarity. Evaluating whether a parameter such as hip angle, for example, differs among two or more species presumes that their hip angles could be the same. If two species are incapable of angular similarity, testing for significant differences is misguided (or, at best, unguided). Potential similarity is implied even when angles from two species are plotted on the same graph for more qualitative comparison. Yet this implicit premise –
Terrestrial limbs as constrained kinematic chains
We represent the main components of the hind limb (femur, tibia, metatarsus) as three articulated line segments (Fig. 1A) that vary only in relative length. In the plane formed by the forward velocity and gravity vectors, each segment's orientation is measured by its elevation angle (θf, θt, θm) with respect to vertical. The 2-D position of the most proximal or “root” joint (hip) determines the limb's translation. Note that the location of the distal “end effector” (metatarso-phalangeal or MP
Discussion
In this study we carried out simple, 2-D examples of interspecific motion transfer. When hind limb angles from a walking human and running guineafowl were applied to a flamingo limb, undesirable motion artifacts were introduced. Footskate, ground penetration, lifting, and extreme deviations in hip height all indicate failure of transferability. Thus, although it may always be theoretically possible for a flamingo to use the same angles as a human or guineafowl and vice versa, motion transfer
Conclusion
In this paper, we have tried to show that despite being well established and convenient, angles are not directly equivalent among disparate, constrained limbs. Yet from discussions with our colleagues (functional morphologists, biomechanists, animators, roboticists, paleontologists), it is clear that angles hold a central place in motion analysis. Indeed, the conceptual link between rotary motion and angular measurement can sometimes be so strong that the terms become one and the same—rotations
Acknowledgments
We thank Kevin Middleton, Jessica Hodgins, Young-Hui Chang, and members of the Brown Evolutionary Vertebrate Morphology Group for helpful discussion and critical advice, as well as the Ornithology Department at the Museum of Comparative Zoology, Harvard University for access to avian skeletons. Three anonymous reviewers improved the manuscript. Supported by National Science Foundation grants DBI-9974424 and IOS-0925077, the Bushnell Faculty Research Fund, and Autodesk, Inc. (to S.M.G.) as well
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