Energy Comparison Between Trot, Bound, and Gallop Using a Simple Model

Power Systems Research Dept., General Motors R&D Center, Warren, Ml 48090, USA.
Journal of Biomechanical Engineering (Impact Factor: 1.78). 12/1995; 117(4):466-73. DOI: 10.1115/1.2794209
Source: PubMed


In this paper, the dynamics of quadruped trot, gallop, and bound will be examined using a simple model for the quadruped. The body of the quadruped is modeled as a uniform bar and the legs are modeled by massless springs. It will be shown that symmetry can be used to study the locomotion of this system. Using symmetry, a technique will be developed to obtain periodic solutions for each of the gaits of the quadruped model. These periodic solutions will be computed at various speeds. The energy levels will be compared for each of the gaits. The exchange of energy between its different forms will be shown for different gaits. It will be shown that even without body flexibility, there are significant savings in energy due to gait transition from trot to gallop. The energy levels will be used to predict the trot-gallop transition speed. These results will be compared with the experimental results for horses and dogs.

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    • "In this paper we use a physical model, which consists of a rigid body and four massless springs in two dimensions (Fig. 2), as used in Nanua and Waldron (1995). x and y are, respectively, the horizontal and vertical positions of the COM of the body, and θ is the pitch angle. "
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    ABSTRACT: Among quadrupedal gaits, the galloping gait has specific characteristics in terms of locomotor behavior. In particular, it shows a left-right asymmetry in gait parameters such as touchdown angle and the relative phase of limb movements. In addition, asymmetric gait parameters show a characteristic dependence on locomotion speed. There are two types of galloping gaits in quadruped animals: the transverse gallop, often observed in horses; and the rotary gallop, often observed in dogs and cheetahs. These two gaits have different footfall sequences. Although these specific characteristics in quadrupedal galloping gaits have been observed and described in detail, the underlying mechanisms remain unclear. In this paper, we use a simple physical model with a rigid body and four massless springs and incorporate the left-right asymmetry of touchdown angles. Our simulation results show that our model produces stable galloping gaits for certain combinations of model parameters and explains these specific characteristics observed in the quadrupedal galloping gait. The results are then evaluated in comparison with the measured data of quadruped animals and the gait mechanisms are clarified from the viewpoint of dynamics, such as the roles of the left-right touchdown angle difference in the generation of galloping gaits and energy transfer during one gait cycle to produce two different galloping gaits. Copyright © 2015 Elsevier Ltd. All rights reserved.
    Journal of Biomechanics 06/2015; 48(12). DOI:10.1016/j.jbiomech.2015.06.003 · 2.75 Impact Factor
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    • "Therefore, the transverse galloping pattern might be more suitable for a large, heavy, and long distance running quadruped. For theoretical analysis, Nanua and Waldron modeled the quadruped as a rigid beam with four massless springy legs [10]. They found that gallop was more efficient than bound, and the range of vertical fluctuation of the center of mass was lesser in a galloping pattern. "
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    ABSTRACT: Transverse gallop is a common gait used by a large number of quadrupeds. This paper employs the simplified dimensionless quadrupedal model to discuss the underlying mechanism of the transverse galloping pattern. The model is studied at different running speeds and different values of leg stiffness, respectively. If the horizontal running speed reaches up to a critical value at a fixed leg stiffness, or if the leg stiffness reaches up to a critical value at a fixed horizontal speed, a key property would emerge which greatly reduces the overall mechanical forces of the dynamic system in a proper range of initial pitch angular velocities. Besides, for each horizontal speed, there is an optimal stiffness of legs that can reduce both the mechanical loads and the metabolic cost of transport. Furthermore, different body proportions and landing distance lags of a pair of legs are studied in the transverse gallop. We find that quadrupeds with longer length of legs compared with the length of the body are more suitable to employ the transverse galloping pattern, and the landing distance lag of a pair of legs could reduce the cost of transport and the locomotion frequency.
    Applied Bionics and Biomechanics 01/2015; 2015:1-16. DOI:10.1155/2015/631354 · 0.26 Impact Factor
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    • "Mechanical efficiency of locomotion of the existing walking machines is very low in comparison to the living animals and low in comparison to the wheeled locomotion. Referred to the living world the expectation is that in the future the artificial legged locomotion will be one of the most energetically effective sources of transportation [3]. The designer of a walking machine must analyze of the energy consumption which determines the choice of mechanical structure, and the propulsion and powering systems. "
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    ABSTRACT: An improvement of the computer technology caused the progress in building of the developed machines, indispensable in some works which are too dangerous or onerous for humans. The article deals with prototyping problems in constructing autonomous walking machines including design problems, evaluation of required motor power, evaluation of expecting walking velocity as well as the control system design considerations etc., presenting themselves as key factors which must be taken into account while walking robots prototyping.
    Bulletin of the Polish Academy of Sciences, Technical Sciences 09/2010; 58(3). DOI:10.2478/v10175-010-0042-2 · 0.91 Impact Factor
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