Limb work and joint work minimization reveal an energetic benefit to the elbows-back, knees-forward limb design in parasagittal quadrupeds

Abstract

Quadrupedal animal locomotion is energetically costly. We explore two forms of mechanical work that may be relevant in imposing these physiological demands. Limb work, due to the forces and velocities between the stance foot and the centre of mass, could theoretically be zero given vertical limb forces and horizontal centre of mass path. To prevent pitching, skewed vertical force profiles would then be required, with forelimb forces high in late stance and hindlimb forces high in early stance. By contrast, joint work—the positive mechanical work performed by the limb joints—would be reduced with forces directed through the hip or shoulder joints. Measured quadruped kinetics show features consistent with compromised reduction of both forms of work, suggesting some degree of, but not perfect, inter-joint energy transfer. The elbows-back, knees-forward design reduces the joint work demand of a low limb-work, skewed, vertical force profile. This geometry allows periods of high force to be supported when the distal segment is near vertical, imposing low moments about the elbow or knee, while the shoulder or hip avoids high joint power despite high moments because the proximal segment barely rotates—translation over this period is due to rotation of the distal segment.

Modeling and Trajectory Optimization for Standing Long Jumping of a Quadruped with A Preloaded Elastic Prismatic Spine

“…Results obtained herein, appear to suggest that knee-forward hind legs are more likely to produce better solutions with less computing time even though both arrangements should be dynamically identical in principle. Shedding more light in this direction is part of future work, building upon recent related findings that suggest the energetic efficiency of the elbows-back, knees-forward arrangement [44].…”

Positions of pivot points in quadrupedal locomotion: limbs and trunk global control in four different dog breeds

“…Early skew vertical force profiles for pelvic limbs and late ones for thoracic limbs are ubiquitous across quadrupeds, e.g., (Andrada et al, 2013; Fischer and Lilje, 2011; Manter, 1938; Merkens et al, 1986; Pontzer et al, 2014; Ren et al, 2010; Zumwalt et al, 2006). In previous works it has been pointed out that those vertical force profiles minimize the pitching moment around the center of mass and reduce limb-work (Jayes and Alexander, 1980; Usherwood and Granatosky, 2020). To reduce pitching moment, late vertical skew forces from the thoracic limb are low during early stance, because they act on a large moment arm around the CoM.…”

“…The opposite is true for the pelvic limbs. Larger vertical GRF are exerted in the early support phase, as the moment arm is short, and they are diminished as the lever arm becomes longer (Usherwood and Granatosky, 2020).…”

Roles of Mono- and Bi-articular Muscles in Human Limbs: Two-joint Link Model and Applications

“…2015 ; Valle et al. 2016 ; Usherwood and Granatosky 2020 ), the antagonistic pairs of mono- and bi-articular muscles in the thigh have rarely been regarded as a contributor to contact task. An antagonistic pair of bi-articular muscles alone were proposed to have a role in contact task ( Fujikawa et al.…”