Mechanics of six-legged runners

1990 ◽  
Vol 148 (1) ◽  
pp. 129-146 ◽  
Author(s):  
R. J. Full ◽  
M. S. Tu
Keyword(s):  
Mechanical Energy ◽  
Center Of Mass ◽  
Force Production ◽  
Stride Frequency ◽  
Gravitational Potential Energy ◽  
Vertical Force ◽  
Body Form ◽  
Blaberus Discoidalis ◽  
Ghost Crabs ◽  
Reaction Forces

Six-legged pedestrians, cockroaches, use a running gait during locomotion. The gait was defined by measuring ground reaction forces and mechanical energy fluctuations of the center of mass in Blaberus discoidalis (Serville) as they travelled over a miniature force platform. These six-legged animals produce horizontal and vertical ground-reaction patterns of force similar to those found in two-, four- and eight-legged runners. Lateral forces were less than half the vertical force fluctuations. At speeds between 0.08 and 0.66 ms-1, horizontal kinetic and gravitational potential energy changes were in phase. This pattern of energy fluctuation characterizes the bouncing gaits used by other animals that run. Blaberus discoidalis attained a maximum sustainable stride frequency of 13 Hz at 0.35 ms-1, the same speed and frequency predicted for a mammal of the same mass. Despite differences in body form, the mass-specific energy used to move the center of mass a given distance (0.9 J kg-1m-1) was the same for cockroaches, ghost crabs, mammals, and birds. Similarities in force production, stride frequency and mechanical energy production during locomotion suggest that there may be common design constraints in terrestrial locomotion which scale with body mass and are relatively independent of body form, leg number and skeletal type.

Many-legged maneuverability: dynamics of turning in hexapods

1999 ◽  
Vol 202 (12) ◽  
pp. 1603-1623 ◽  
Author(s):  
D.L. Jindrich ◽  
R.J. Full
Keyword(s):  
Horizontal Plane ◽  
Center Of Mass ◽  
Vertical Plane ◽  
Force Production ◽  
The Body ◽  
Mean Velocity ◽  
Blaberus Discoidalis ◽  
Body Design ◽  
Reaction Forces ◽  
Straight Ahead

Remarkable similarities in the vertical plane of forward motion exist among diverse legged runners. The effect of differences in posture may be reflected instead in maneuverability occurring in the horizontal plane. The maneuver we selected was turning during rapid running by the cockroach Blaberus discoidalis, a sprawled-postured arthropod. Executing a turn successfully involves at least two requirements. The animal's mean heading (the direction of the mean velocity vector of the center of mass) must be deflected, and the animal's body must rotate to keep the body axis aligned with the heading. We used two-dimensional kinematics to estimate net forces and rotational torques, and a photoelastic technique to estimate single-leg ground-reaction forces during turning. Stride frequencies and duty factors did not differ among legs during turning. The inside legs ended their steps closer to the body than during straight-ahead running, suggesting that they contributed to turning the body. However, the inside legs did not contribute forces or torques to turning the body, but actively pushed against the turn. Legs farther from the center of rotation on the outside of the turn contributed the majority of force and torque impulse which caused the body to turn. The dynamics of turning could not be predicted from kinematic measurements alone. To interpret the single-leg forces observed during turning, we have developed a general model that relates leg force production and leg position to turning performance. The model predicts that all legs could turn the body. Front legs can contribute most effectively to turning by producing forces nearly perpendicular to the heading, whereas middle and hind legs must produce additional force parallel to the heading. The force production necessary to turn required only minor alterations in the force hexapods generate during dynamically stable, straight-ahead locomotion. A consideration of maneuverability in the horizontal plane revealed that a sprawled-postured, hexapodal body design may provide exceptional performance with simplified control.

Mechanics of a rapid running insect: two-, four- and six-legged locomotion

1991 ◽  
Vol 156 (1) ◽  
pp. 215-231 ◽  
Author(s):  
R. J. Full ◽  
M. S. Tu
Keyword(s):  
Periplaneta Americana ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Reaction Force ◽  
Metabolic Cost ◽  
Legged Locomotion ◽  
American Cockroach ◽  
Stride Frequency ◽  
Gravitational Potential Energy ◽  
Vertical Ground Reaction Force

To examine the effects of variation in body form on the mechanics of terrestrial locomotion, we used a miniature force platform to measure the ground reaction forces of the smallest and, relative to its mass, one of the fastest invertebrates ever studied, the American cockroach Periplaneta americana (mass = 0.83 g). From 0.44-1.0 ms-1, P. americana used an alternating tripod stepping pattern. Fluctuations in gravitational potential energy and horizontal kinetic energy of the center of mass were nearly in phase, characteristic of a running or bouncing gait. Aerial phases were observed as vertical ground reaction force approached zero at speeds above 1 ms-1. At the highest speeds (1.0-1.5 ms-1 or 50 body lengths per second), P. americana switched to quadrupedal and bipedal running. Stride frequency approached the wing beat frequencies used during flight (27 Hz). High speeds were attained by increasing stride length, whereas stride frequency showed little increase with speed. The mechanical power used to accelerate the center of mass increased curvilinearly with speed. The mass-specific mechanical energy used to move the center of mass a given distance was similar to that measured for animals five orders of magnitude larger in mass, but was only one-hundredth of the metabolic cost.

scholarly journals Walking in simulated reduced gravity: mechanical energy fluctuations and exchange

1999 ◽  
Vol 86 (1) ◽  
pp. 383-390 ◽  
Author(s):  
Timothy M. Griffin ◽  
Neil A. Tolani ◽  
Rodger Kram
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Metabolic Cost ◽  
Metabolic Energy ◽  
Gravitational Potential Energy ◽  
Reduced Gravity

Walking humans conserve mechanical and, presumably, metabolic energy with an inverted pendulum-like exchange of gravitational potential energy and horizontal kinetic energy. Walking in simulated reduced gravity involves a relatively high metabolic cost, suggesting that the inverted-pendulum mechanism is disrupted because of a mismatch of potential and kinetic energy. We tested this hypothesis by measuring the fluctuations and exchange of mechanical energy of the center of mass at different combinations of velocity and simulated reduced gravity. Subjects walked with smaller fluctuations in horizontal velocity in lower gravity, such that the ratio of horizontal kinetic to gravitational potential energy fluctuations remained constant over a fourfold change in gravity. The amount of exchange, or percent recovery, at 1.00 m/s was not significantly different at 1.00, 0.75, and 0.50 G (average 64.4%), although it decreased to 48% at 0.25 G. As a result, the amount of work performed on the center of mass does not explain the relatively high metabolic cost of walking in simulated reduced gravity.

scholarly journals Active foot placement control ensures stable gait: Effect of constraints on foot placement and ankle moments

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0242215
Author(s):  
A. M. van Leeuwen ◽  
J. H. van Dieën ◽  
A. Daffertshofer ◽  
S. M. Bruijn
Keyword(s):  
Steady State ◽  
Center Of Pressure ◽  
Center Of Mass ◽  
Reaction Force ◽  
Stride Frequency ◽  
Tight Control ◽  
Foot Placement ◽  
Ankle Moment ◽  
Reaction Forces ◽  
Moment Control

Step-by-step foot placement control, relative to the center of mass (CoM) kinematic state, is generally considered a dominant mechanism for maintenance of gait stability. By adequate (mediolateral) positioning of the center of pressure with respect to the CoM, the ground reaction force generates a moment that prevents falling. In healthy individuals, foot placement is complemented mainly by ankle moment control ensuring stability. To evaluate possible compensatory relationships between step-by-step foot placement and complementary ankle moments, we investigated the degree of (active) foot placement control during steady-state walking, and under either foot placement-, or ankle moment constraints. Thirty healthy participants walked on a treadmill, while full-body kinematics, ground reaction forces and EMG activities were recorded. As a replication of earlier findings, we first showed step-by-step foot placement is associated with preceding CoM state and hip ab-/adductor activity during steady-state walking. Tight control of foot placement appears to be important at normal walking speed because there was a limited change in the degree of foot placement control despite the presence of a foot placement constraint. At slow speed, the degree of foot placement control decreased substantially, suggesting that tight control of foot placement is less essential when walking slowly. Step-by-step foot placement control was not tightened to compensate for constrained ankle moments. Instead compensation was achieved through increases in step width and stride frequency.

scholarly journals The Possibility of Zero Limb-Work Gaits in Sprawled and Parasagittal Quadrupeds: Insights from Linkages of the Industrial Revolution

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
J R Usherwood
Keyword(s):  
Potential Energy ◽  
Industrial Revolution ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Phase Fluctuation ◽  
Vertical Axis ◽  
The Body ◽  
Mechanical Work ◽  
Gravitational Potential Energy ◽  
Pull Out

Synopsis Animal legs are diverse, complex, and perform many roles. One defining requirement of legs is to facilitate terrestrial travel with some degree of economy. This could, theoretically, be achieved without loss of mechanical energy if the body could take a continuous horizontal path supported by vertical forces only—effectively a wheel-like translation, and a condition closely approximated by walking tortoises. If this is a potential strategy for zero mechanical work cost among quadrupeds, how might the structure, posture, and diversity of both sprawled and parasagittal legs be interpreted? In order to approach this question, various linkages described during the industrial revolution are considered. Watt’s linkage provides an analogue for sprawled vertebrates that uses diagonal limb support and shows how vertical-axis joints could enable approximately straight-line horizontal translation while demanding minimal mechanical power. An additional vertical-axis joint per leg results in the wall-mounted pull-out monitor arm and would enable translation with zero mechanical work due to weight support, without tipping or toppling. This is consistent with force profiles observed in tortoises. The Peaucellier linkage demonstrates that parasagittal limbs with lateral-axis joints could also achieve the zero-work strategy. Suitably tuned four-bar linkages indicate this is feasibly approximated for flexed, biologically realistic limbs. Where “walking” gaits typically show out of phase fluctuation in center of mass kinetic and gravitational potential energy, and running, hopping or trotting gaits are characterized by in-phase energy fluctuations, the zero limb-work strategy approximated by tortoises would show zero fluctuations in kinetic or potential energy. This highlights that some gaits, perhaps particularly those of animals with sprawled or crouched limbs, do not fit current kinetic gait definitions; an additional gait paradigm, the “zero limb-work strategy” is proposed.

scholarly journals Active foot placement control ensures stable gait: Effect of constraints on foot placement and ankle moments

2020 ◽  
Author(s):  
A.M. van Leeuwen ◽  
J.H. van Dieën ◽  
A. Daffertshofer ◽  
S.M. Bruijn
Keyword(s):  
Steady State ◽  
Center Of Pressure ◽  
Center Of Mass ◽  
Reaction Force ◽  
Stride Frequency ◽  
Tight Control ◽  
Foot Placement ◽  
Ankle Moment ◽  
Reaction Forces ◽  
Moment Control

AbstractStep-by-step foot placement control, relative to the center of mass (CoM) kinematic state, is generally considered a dominant mechanism for maintenance of gait stability. By adequate (mediolateral) positioning of the center of pressure with respect to the CoM, the ground reaction force generates a moment that prevents falling. In healthy individuals, foot placement is complemented mainly by ankle moment control ensuring stability. To evaluate possible compensatory relationships between step-by-step foot placement and complementary ankle moments, we investigated the degree of (active) foot placement control during steady-state walking, and under either foot placement-, or ankle moment constraints. Thirty healthy participants walked on a treadmill, while full-body kinematics, ground reaction forces and EMG activities were recorded. As a replication of earlier findings, we first showed step-by-step foot placement is associated with preceding CoM state and hip ab-/adductor activity during steady-state walking. Tight control of foot placement appears to be important at normal walking speed because there was a limited change in the degree of foot placement control despite the presence of a foot placement constraint. At slow speed, the degree of foot placement control decreased substantially, suggesting that tight control of foot placement is less essential when walking slowly. Step-by-step foot placement control was not tightened to compensate for constrained ankle moments. Instead compensation was achieved through increases in step width and stride frequency.

Mechanics of locomotion in lizards.

1997 ◽  
Vol 200 (16) ◽  
pp. 2177-2188 ◽  
Author(s):  
C T Farley ◽  
T C Ko
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Gravitational Potential Energy ◽  
Lateral Bending ◽  
Walking Gait ◽  
Bending Force

Lizards bend their trunks laterally with each step of locomotion and, as a result, their locomotion appears to be fundamentally different from mammalian locomotion. The goal of the present study was to determine whether lizards use the same two basic gaits as other legged animals or whether they use a mechanically unique gait due to lateral trunk bending. Force platform and kinematic measurements revealed that two species of lizards, Coleonyx variegatus and Eumeces skiltonianus, used two basic gaits similar to mammalian walking and trotting gaits. In both gaits, the kinetic energy fluctuations due to lateral movements of the center of mass were less than 5% of the total external mechanical energy fluctuations. In the walking gait, both species vaulted over their stance limbs like inverted pendulums. The fluctuations in kinetic energy and gravitational potential energy of the center of mass were approximately 180 degrees out of phase. The lizards conserved as much as 51% of the external mechanical energy required for locomotion by the inverted pendulum mechanism. Both species also used a bouncing gait, similar to mammalian trotting, in which the fluctuations in kinetic energy and gravitational potential energy of the center of mass were nearly exactly in phase. The mass-specific external mechanical work required to travel 1 m (1.5 J kg-1) was similar to that for other legged animals. Thus, in spite of marked lateral bending of the trunk, the mechanics of lizard locomotion is similar to the mechanics of locomotion in other legged animals.

scholarly journals Dynamics of locomotion in the seed harvesting ant Messor barbarus: effect of individual body mass and transported load mass

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e10664
Author(s):  
Hugo Merienne ◽  
Gérard Latil ◽  
Pierre Moretto ◽  
Vincent Fourcassié
Keyword(s):  
Body Mass ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Load Carriage ◽  
Gravitational Potential Energy ◽  
Body Parts ◽  
Messor Barbarus ◽  
Seed Harvesting ◽  
Load Transport ◽  
Load Mass

Ants are well-known for their amazing load carriage performances. Yet, the biomechanics of locomotion during load transport in these insects has so far been poorly investigated. Here, we present a study of the biomechanics of unloaded and loaded locomotion in the polymorphic seed-harvesting ant Messor barbarus (Linnaeus, 1767). This species is characterized by a strong intra-colonial size polymorphism with allometric relationships between the different body parts of the workers. In particular, big ants have much larger heads relative to their size than small ants. Their center of mass is thus shifted forward and even more so when they are carrying a load in their mandibles. We investigated the dynamics of the ant center of mass during unloaded and loaded locomotion. We found that during both unloaded and loaded locomotion, the kinetic energy and gravitational potential energy of the ant center of mass are in phase, which is in agreement with what has been described by other authors as a grounded-running gait. During unloaded locomotion, small and big ants do not display the same posture. However, they expend the same amount of mechanical energy to raise and accelerate their center of mass per unit of distance and per unit of body mass. While carrying a load, compared to the unloaded situation, ants seem to modify their locomotion gradually with increasing load mass. Therefore, loaded and unloaded locomotion do not involve discrete types of gait. Moreover, small ants carrying small loads expend less mechanical energy per unit of distance and per unit of body mass and their locomotion thus seem more mechanically efficient.

Three-dimensional kinematics and limb kinetic energy of running cockroaches.

1997 ◽  
Vol 200 (13) ◽  
pp. 1919-1929 ◽  
Author(s):  
R Kram ◽  
B Wong ◽  
R J Full
Keyword(s):  
Kinetic Energy ◽  
High Speed ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Three Dimensional ◽  
The Body ◽  
Morphological Data ◽  
Fast Running ◽  
Total Mechanical Energy ◽  
Reaction Forces

We tested the hypothesis that fast-running hexapeds must generate high levels of kinetic energy to cycle their limbs rapidly compared with bipeds and quadrupeds. We used high-speed video analysis to determine the three-dimensional movements of the limbs and bodies of cockroaches (Blaberus discoidalis) running on a motorized treadmill at 21 cm s-1 using an alternating tripod gait. We combined these kinematic data with morphological data to calculate the mechanical energy produced to move the limbs relative to the overall center of mass and the mechanical energy generated to rotate the body (head + thorax + abdomen) about the overall center of mass. The kinetic energy involved in moving the limbs was 8 microJ stride-1 (a power output of 21 mW kg-1, which was only approximately 13% of the external mechanical energy generated to lift and accelerate the overall center of mass at this speed. Pitch, yaw and roll rotational movements of the body were modest (less than +/- 7 degrees), and the mechanical energy required for these rotations was surprisingly small (1.7 microJ stride-1 for pitch, 0.5 microJ stride-1 for yaw and 0.4 microJ stride-1 for roll) as was the power (4.2, 1.2 and 1.1 mW kg-1, respectively). Compared at the same absolute forward speed, the mass-specific kinetic energy generated by the trotting hexaped to swing its limbs was approximately half of that predicted from data on much larger two- and four-legged animals. Compared at an equivalent speed (mid-trotting speed), limb kinetic energy was a smaller fraction of total mechanical energy for cockroaches than for large bipedal runners and hoppers and for quadrupedal trotters. Cockroaches operate at relatively high stride frequencies, but distribute ground reaction forces over a greater number of relatively small legs. The relatively small leg mass and inertia of hexapeds may allow relatively high leg cycling frequencies without exceptionally high internal mechanical energy generation.

scholarly journals Locomotion Energetics of the Ghost Crab: II. Mechanics of the Centre of Mass During Walking and Running

1987 ◽  
Vol 130 (1) ◽  
pp. 155-174 ◽  
Author(s):  
REINHARD BLICKHAN ◽  
ROBERT J. FULL
Keyword(s):  
Mechanical Design ◽  
Mechanical Energy ◽  
Stride Frequency ◽  
Centre Of Mass ◽  
Unit Distance ◽  
Ghost Crab ◽  
Locomotor Apparatus ◽  
Terrestrial Locomotion ◽  
Ghost Crabs ◽  
Energy Conserving

Terrestrial locomotion involving appendages has evolved independently in vertebrates and arthropods. Differences in the mechanical design of the locomotor apparatus could impose constraints on the energetics of locomotion. The mechanical energy fluctuations of the centre of mass of an arthropod, the ghost crab Ocypode quadrata (Fabricius), were examined by integrating the ground reaction forces exerted during sideways locomotion. Crabs used a pendulum-type energy exchange mechanism during walking, analogous to an egg rolling end over end, with the same effectiveness as birds and mammals. Moreover, ghost crabs were found to have two running gaits. A switch from a slow to a fast run occurred at the same speed and stride frequency predicted for the trot-gallop transition of a quadrupedal mammal of the same body mass. In addition, the mass-specific mechanical energy developed over a unit distance was independent of speed and was within the limits measured for birds and mammals. Despite the obvious differences in mechanical design between crabs and mammals, energy-conserving mechanisms and the efficiency of locomotion were remarkably similar. These similarities may result from the fact that the muscles that generate forces during terrestrial locomotion have relatively conservative mechanical and energetic properties.

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