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Invertebrate Locomotor Systems

Robert J. Full

10.1002/cphy.cp130212

Source: Supplement 30: Handbook of Physiology, Comparative Physiology

Originally published: 1997

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Mechanisms of Locomotion
1.1 Swimming
1.2 Crawling
1.3 Walking, Running, and Rolling
1.4 Jumping
1.5 Flying
1.6 Comparison of Locomotor Dynamics
2 Production of Locomotion: Musculoskeletal Systems
2.1 Filament, Sarcomere, and Muscle Level
3 Energetics of Locomotion
3.1 Aerobic Metabolism
3.2 Anaerobic Metabolism
3.3 Endurance and Metabolism
3.4 Metabolic Cost of Transport
4 Conclusions
4.1 Trends
5 Future Research
5.1 Comparative Muscle Physiology
5.2 Comparative Bioenergetics and Exercise Physiology
5.3 Comparative Biomechanics
5.4 Collaboration
5.5 Direct‐Experiments Using Innovative Technology
5.6 Cybercreatures and Experiments: Computer Modeling
6 Appendix: List of Symbols
Figure 1. Figure 1.

Schematic diagram showing integration of comparative bioenergetics, exercise physiology, functional morphology, muscle physiology, and comparative biomechanics. A: Energy available from several sources is transduced to segments (appendages or body sections) through muscles, depending on geometry. The chapter is organized in sections from right to left. B: Magnification of musculoskeletal role in transducing energy. Musculoskeletal parameters determine musculoskeletal forces. Musculoskeletal forces and joint geometry determine moment. Moment gives rise to acceleration, velocity, and angle change. Velocity and angle change (change in muscle length) feedback to affect musculoskeletal force production. Moment and joint angular velocity determine amount of energy transferred. Direction of movement and moment determine whether energy enters, leaves, or is transferred from a segment. Segmental energy and morphology of all segments determine power output of whole body and represent locomotor mechanical energy in A.
Figure 2. Figure 2.

Legs of animals in general, and of invertebrates in particular, can provide biological inspiration for the design of new robot legs. A: Legs operating in a more upright posture in a vertical plane parallel to the body (horizontal first joint axis for body–leg attachment), as seen in many birds and mammals, are gravitationally loaded and muscles must bear part of the body's weight 24. Animals using a horizontal first axis, however, can take advantage of gravity in swinging their legs. B–D: Legs operating in a sprawled posture (vertical first joint axis for body–leg attachment, like some lizards, amphibians, and arthropods) can potentially decouple gravitational loading of muscles from moving forward. To move forward, vertical first axis legs must project out to the side, resulting in increased static stability. Robots inspired from the design of cockroaches 62,63, whose legs operate in a horizontal plane, demonstrate a linear step, large step lengths, and proficiency at climbing.

adapted from ref. 62
Figure 3. Figure 3.

Speed as a function of body mass. A: Speeds of fliers, jumpers, runners, jetters, swimmers, and crawlers. Shown are maximum speeds available from the literature. Some speeds are reported as truly maximum. The majority are near maximum aerobic speed (speed at which maximal oxygen consumption is attained). Many are preferred speeds. For jumpers, take‐off speeds shown. The shaded area bounds the speed of crawlers. Data include runners 22,41,69,83,134,136,181,199,201,202,207,208,212,259,261,263,264,265,266,278,290,343,344,345,346,347,383,392,413,458,523, crawlers 97,145,277,292,353, jumpers 11,48,53,179,180,282,352, swimmers 7,65,114,119,184,241,276,278,280,290,293,328,369,386,409,466,468,482,511, jetters 106,127,128,130,132,294,338,395,398,399,473,474,475, and fliers 45,152,155,156,173,273,367. (Ref. 158 published after submission of figures.) B: Regression lines of major taxonomic groups (Table 1). Data to generate regressions include insect runners 41,136,181,207,208,212,259,263,266,343,344,345,346,347,383,392,458; crustacean runners 69,83,199,202,261,264,265,278,290,523; crustacean swimmers 7,119,184,241,276,280,293,328,369,386,409,466,468,482; crustacean underwater runners 114,276,278,280,290; bee, fly, and mosquito fliers 156,173,273; and lepidopteran fliers 152,155. Note the change in speed axis from A.
Figure 4. Figure 4.

Cycle frequency as a function of body mass. A: Cycle frequency of fliers, runners, jetters, and swimmers. Frequencies shown are the maximum available from the literature. Some frequencies are reported as truly maximum. The majority are preferred speeds. Data include runners 22,69,134,207,208,212,261; swimmers 7,65,114,290,409; jetters 29,106,127,140,338,473,495; and fliers such as mosquitoes 84,273,366,507, aphids, white flies 84,524, dragonflies 84,366,367, bees, wasps 84,96,156,171,306,366,507, beetles 84,507, flies 84,273,318,366,507,524, flower flies 84,318,507, butterflies 84,152,507, saturnid moths 39,84,96,507, sphinx moths 94,96,366,507, and crane flies 84,171,366,507. B: Regression lines of major taxanomic groups (Table 2). Note the change in cycle frequency axis from A.
Figure 5. Figure 5.

Whole‐animal mass‐specific mechanical power output as a function of body mass. Shaded areas and connected points represent the range of possible values for fliers, assuming 0 (upper bound) and 100% (lower bound) elastic storage. Speeds selected are the maximum available from the literature. Some speeds are reported as truly maximum. Many are preferred speeds. Data include insects 207,208 and crabs 69 for terrestrial locomotion; crustaceans 385,467, insects (65, 3890), jellyfish 140, and molluscs 127,397,398 for aquatic locomotion; and insects 94,102,153,173,299,504 for aerial locomotion.
Figure 6. Figure 6.

Sarcomere morphometrics. Muscles were divided into fast and slow groups based on a variety of criteria, which included fiber type, enzyme level or activity, and contraction kinetics. In general, if a study designated a muscle as fast or slow, this characterization was used. All insect flight muscles were considered to be fast. All crawlers—larvae, worms, and nematodes—have slow muscles. Walking and swimming organisms have both fiber types. Bars represent ± 1 S.D. Numbers in parentheses are sample size. Lmyo, myosin filament length; Lcsarc, length of a sarcomere. A: Sarcomere length. Data include insects such as locusts 48,51,285,504, cockroaches 163,185,287,296,382,415,454,479, water bugs 5,25,163, water beetles 162, katydids 5,164, lepidopterans 89,422, dragonflies 444, larvae 86,88,243,401,422, nymphs 87, flies 405,434, and hemipterans 125; crustaceans such as lobsters 287,295,296,415, crayfish 1,415,461,528, crabs 188,283,476, and merostomatans such as horseshoe crabs 490; arachnids such as spiders 321,436 and scorpions 26,425; molluscs such as scallops 379 and cuttlefish 286; annelids such as worms 376,462 and polychaetes 365; chaetognaths such as arrow worms 161; and coelenterates such as jellyfish 107,439. B: Myosin filament length. Data include insects such as locusts 118,285, cockroaches 5,163,239,240,287,296,415,479, water bugs 5,25,163, water beetles 162, katydids 5,164, lepidopterians 5,513, dragon‐flies 444, larvae 86,88,243,401, and nymphs 87,90; crustaceans such as lobsters 295,296,297,415, crayfish 415,528, and crabs 188,283,476; arachnids such as spiders 321,436; molluscs such as scallops 379 and cuttlefish 286; annelids such as worms 376,462, and polychaetes 365; nematodes 426; and coelenterates such as jellyfish 107,439. C; Ratio of thin/thick filament number. Data include insects such as locusts 118,285, cockroaches 5,239,240,287,296,415,454,479, water bugs 5,25, katydids 5,164, lepidopterians 89,422,513, dragonflies 444, larvae 86,88,243,401,422, nymphs 87,90, and flies 405; crustaceans such as lobsters 287,296,415 and crabs 188,283; arachnids such as spiders 436 and scorpions 26,425; molluscs such as scallops 379 and cuttlefish 286; annelids 376,462; nematodes 426; and coelenterates such as jellyfish 107. D: Sarcomere diagram shows designated lengths.
Figure 7. Figure 7.

Active length‐tension or strain‐stress curves of invertebrate muscles. Stress is normalized to peak isometric tension. Strain is normalized as a fraction of the length that gives peak isometric stress. Shaded areas represent strains that correspond to stresses above 50% maximal isometric stress. Data include bee flight 242, locust flight 353, crayfish 528, frog 271, leech 378, and fly larvae 243 muscles.
Figure 8. Figure 8.

Mechanical power output of invertebrate muscle and its determinants as a function of cycle frequency. Data are from isolated muscle studies using the work‐loop method (Fig. 9) and come from unpublished data of Stevenson and Casey. A: Mass‐specific mechanical power output and work per cycle. Gilmour and Ellington 223 have demonstrated values as high as 110 W/kg from asynchronous, glycerinated muscle fibers of bumblebees. B: Muscle stress, strain, and strain rate. Data include insects 312,349,380,453, crustaceans 455, and molluscs 362.
Figure 9. Figure 9.

Work‐loop method to determine power output of an isolated muscle. A: Muscle is subjected to cyclic length changes (strain) while force per area (stress) is measured. The stimulation pattern is controlled. B: Area under the stress‐strain curve represents energy produced (output) during shortening or absorbed (input) during lengthening. The difference between the curves represents the net work per cycle. Counterclockwise loops result in energy production, whereas clockwise loops result in energy absorption by the muscle. C: Variation in work‐loop shape. Rectangular shape observed at low frequencies (<30 Hz). Triangular shape observed at intermediate frequencies (30–60 Hz). Ellipsoid shape observed at high frequencies (60–180 Hz).

after ref. 311
Figure 10. Figure 10.

Three‐dimensional musculoskeletal model of themeta‐thoracic leg of the cockroach Blaberus discoidalis. Left: Shaded polygons represent the exoskeleton, which was reconstructed from serial sections. Right: Heavy lines represent the lines of action of Hill‐type muscles. The model is articulated at the coxa/trochanter–femur and femurtibia joints so that muscle lengths, moment arms, forces, and joint moments can be estimated for a range of body positions 195. The computer model was created using SIMM.

MusculoGraphics, Evanston, IL
Figure 11. Figure 11.

Whole‐animal mass‐specific metabolic power input as a function of body mass. Oxygen consumption rates are the highest available for the species. In some cases, they are known to be maximal rates. A: Oxygen consumption as a function of body mass for runners, crawlers, swimmers, jetters, and fliers. Shaded areas represent jetters; top right area includes molluscs such as squid; bottom area includes jellyfish. Insect runners can warm their bodies. The regression line shown is for the Q10 corrected data set not shown (Q10 = 2). Data include runners (22,41,42,43,44,190,199,200,201,202,210,212,258,259,261,262,263,264,265,266,301,343,345,346,347,368,374,427,433,514,522; W. J. Van Aardt, unpublished data), runners with elevated body temperature 37,209, crawlers 97,277,292, swimmers 119,184,276,278,279,293,328,369,371,428,466, jetters 29,130,338,395,399,474,495,511, and fliers 36,39,42,91,92,93,96,100,102,104,108,109,110,173,250,251,273,318,333,384,393,427,447,502,507,521. B: Oxygen consumption rates by taxonomic groups (Table 3). Data include insect runners 41,42,43,44,210,212,259,263,266,301,343,345,346,347,368,427; crustacean runners (190,199,200,202,261,262,264,265,514,522; W. J. Van Aardt, unpublished data); swimmers 119,184,276,278,279,293,328,369,371,428,466,474; moth fliers 39,91,92,93,96,100; and bee, fly, and mosquito fliers 36,42,96,102,104,108,109,110,173,250,251,273,318,333,384,393,427,447,502,507,521.
Figure 12. Figure 12.

Aerobic factorial scopes for invertebrate activity. Oxygen consumption rates are the highest available for the species. In some cases, they are known to be maximal rates. Bars represent ± 1 S.D. Numbers in parentheses are sample size. Data include aquatic groups such as coelenterates 338, gastropods 277,292, crustaceans 119,184,276,278,279,293,328,369,371,428,466, and cephalopods 29,395,399,495,511; terrestrial groups such as gastropods 277,292, myriapods 201, crustaceans (190,199,200,202,261,262,264,265,514,522; W. J. Van Aardt, unpublished data), arachnids 22,258,347,374,433, and insects 41,42,43,44,210,212,259,263,266,301,343,345,346,347,368,427; insects with elevated body temperature 37,209; and aerial groups such as insects 36,39,42,91,92,93,96,100,102,104,108,10,173,250,251,273,318,333,384,393,427,447,502,507,521.
Figure 13. Figure 13.

Mass‐specific metabolic cost of transport as a function of body mass. Values represent minimum cost of locomotion available. Shaded area represents hydrostatic crawlers and burrowers. Data include runners 41,43,44,55,159,191,199,200,201,209,212,259,260,263,264,265,301,343,345,346,347, crawlers 97,143,267,277,292, burrowers 54,291,469, swimmers 119,184,241,276,278,280,293,328,369,468,474,511, jetters 130,338,395,399,495, and fliers 173,273,478,483,503,521.
Figure 14. Figure 14.

Hypothesized relationships of invertebrate locomotion based on literature review. A: Mass‐specific mechanical power output (see Fig. 5), the product of cycle frequency and mass‐specific mechanical work output per cycle. B: Cycle frequency (see Fig. 4). C: Mass‐specific metabolic power input (see Fig. 11), the product of cycle frequency and mass‐specific metabolic cost input per cycle. D: Mass‐specific mechanical work output per cycle, the product of cycle distance and mass‐specific mechanical work output per cycle, the product of cycle distance and mass‐specific resistive force or mass‐specific mechanical energy of transport. E: Cycle distance. F: Mass‐specific metabolic cost input per cycle (see Fig. 12), the product of cycle distance and mass‐specific metabolic cost of transport. G: Mass‐specific resistive force or mass‐specific mechanical energy of transport. H: Speed (see Fig. 3), the product of cycle frequency and cycle distance. I: Mass‐specific metabolic cost of transport (see Fig. 13).
Figure 15. Figure 15.

Mass‐specific metabolic cost input per cycle as a function of body mass. Regression lines represent a range of body masses for a given species. Data include runners 22,190,209,210,212,261, a crawler 97, and fliers 42,251,273,447,502,507 such as moths 96 and bees 96,102,521.
Figure 16. Figure 16.

Trends for variation in power output. Two hypothetical animals of the same mass are compared. The morphology of a hypothetical appendage is shown to illustrate mechanical advantage, muscle strain, and the angle swept by the appendage. Left column represents trends for an animal that generates lower power output than the animal represented at right. Equations show how variables (muscle moment, joint angle, and muscle power output) are used to derive mass‐specific muscle power output (PM*). See text for explanation.
Figure 17. Figure 17.

Cyber‐invertebrates. Dynamic models of legged animals designed by M. Raibert, MIT, and Boston Dynamics in collaboration with R. J. Full at U.C. Berkeley. Simulations consist of equations of motion, ground contact models, a numerical integrator, and a three‐dimensional graphics program. All models obey the laws of Newtonian physics and are not simple kinematic representations. The Hexahopper (center) is an abstracted insect with telescoping legs attached to a hemispherical body. The model exhibits dynamic locomotion without an aerial phase as it bounces along. Three legs act as one spring‐mass system. The Hexabug (right) uses articulated legs attached to a long body. The legs have the length dimensions of cockroach legs. The Playback cockroach (left) uses the actual morphology of cockroach legs along with three‐dimensional kinematics during running. The kinematic motion data can be played through the control system and the resulting dynamics analyzed. The controller uses the motion data to drive servos at each joint to apply moments which attempt to maintain target positions.


Figure 1.

Schematic diagram showing integration of comparative bioenergetics, exercise physiology, functional morphology, muscle physiology, and comparative biomechanics. A: Energy available from several sources is transduced to segments (appendages or body sections) through muscles, depending on geometry. The chapter is organized in sections from right to left. B: Magnification of musculoskeletal role in transducing energy. Musculoskeletal parameters determine musculoskeletal forces. Musculoskeletal forces and joint geometry determine moment. Moment gives rise to acceleration, velocity, and angle change. Velocity and angle change (change in muscle length) feedback to affect musculoskeletal force production. Moment and joint angular velocity determine amount of energy transferred. Direction of movement and moment determine whether energy enters, leaves, or is transferred from a segment. Segmental energy and morphology of all segments determine power output of whole body and represent locomotor mechanical energy in A.



Figure 2.

Legs of animals in general, and of invertebrates in particular, can provide biological inspiration for the design of new robot legs. A: Legs operating in a more upright posture in a vertical plane parallel to the body (horizontal first joint axis for body–leg attachment), as seen in many birds and mammals, are gravitationally loaded and muscles must bear part of the body's weight 24. Animals using a horizontal first axis, however, can take advantage of gravity in swinging their legs. B–D: Legs operating in a sprawled posture (vertical first joint axis for body–leg attachment, like some lizards, amphibians, and arthropods) can potentially decouple gravitational loading of muscles from moving forward. To move forward, vertical first axis legs must project out to the side, resulting in increased static stability. Robots inspired from the design of cockroaches 62,63, whose legs operate in a horizontal plane, demonstrate a linear step, large step lengths, and proficiency at climbing.

adapted from ref. 62


Figure 3.

Speed as a function of body mass. A: Speeds of fliers, jumpers, runners, jetters, swimmers, and crawlers. Shown are maximum speeds available from the literature. Some speeds are reported as truly maximum. The majority are near maximum aerobic speed (speed at which maximal oxygen consumption is attained). Many are preferred speeds. For jumpers, take‐off speeds shown. The shaded area bounds the speed of crawlers. Data include runners 22,41,69,83,134,136,181,199,201,202,207,208,212,259,261,263,264,265,266,278,290,343,344,345,346,347,383,392,413,458,523, crawlers 97,145,277,292,353, jumpers 11,48,53,179,180,282,352, swimmers 7,65,114,119,184,241,276,278,280,290,293,328,369,386,409,466,468,482,511, jetters 106,127,128,130,132,294,338,395,398,399,473,474,475, and fliers 45,152,155,156,173,273,367. (Ref. 158 published after submission of figures.) B: Regression lines of major taxonomic groups (Table 1). Data to generate regressions include insect runners 41,136,181,207,208,212,259,263,266,343,344,345,346,347,383,392,458; crustacean runners 69,83,199,202,261,264,265,278,290,523; crustacean swimmers 7,119,184,241,276,280,293,328,369,386,409,466,468,482; crustacean underwater runners 114,276,278,280,290; bee, fly, and mosquito fliers 156,173,273; and lepidopteran fliers 152,155. Note the change in speed axis from A.



Figure 4.

Cycle frequency as a function of body mass. A: Cycle frequency of fliers, runners, jetters, and swimmers. Frequencies shown are the maximum available from the literature. Some frequencies are reported as truly maximum. The majority are preferred speeds. Data include runners 22,69,134,207,208,212,261; swimmers 7,65,114,290,409; jetters 29,106,127,140,338,473,495; and fliers such as mosquitoes 84,273,366,507, aphids, white flies 84,524, dragonflies 84,366,367, bees, wasps 84,96,156,171,306,366,507, beetles 84,507, flies 84,273,318,366,507,524, flower flies 84,318,507, butterflies 84,152,507, saturnid moths 39,84,96,507, sphinx moths 94,96,366,507, and crane flies 84,171,366,507. B: Regression lines of major taxanomic groups (Table 2). Note the change in cycle frequency axis from A.



Figure 5.

Whole‐animal mass‐specific mechanical power output as a function of body mass. Shaded areas and connected points represent the range of possible values for fliers, assuming 0 (upper bound) and 100% (lower bound) elastic storage. Speeds selected are the maximum available from the literature. Some speeds are reported as truly maximum. Many are preferred speeds. Data include insects 207,208 and crabs 69 for terrestrial locomotion; crustaceans 385,467, insects (65, 3890), jellyfish 140, and molluscs 127,397,398 for aquatic locomotion; and insects 94,102,153,173,299,504 for aerial locomotion.



Figure 6.

Sarcomere morphometrics. Muscles were divided into fast and slow groups based on a variety of criteria, which included fiber type, enzyme level or activity, and contraction kinetics. In general, if a study designated a muscle as fast or slow, this characterization was used. All insect flight muscles were considered to be fast. All crawlers—larvae, worms, and nematodes—have slow muscles. Walking and swimming organisms have both fiber types. Bars represent ± 1 S.D. Numbers in parentheses are sample size. Lmyo, myosin filament length; Lcsarc, length of a sarcomere. A: Sarcomere length. Data include insects such as locusts 48,51,285,504, cockroaches 163,185,287,296,382,415,454,479, water bugs 5,25,163, water beetles 162, katydids 5,164, lepidopterans 89,422, dragonflies 444, larvae 86,88,243,401,422, nymphs 87, flies 405,434, and hemipterans 125; crustaceans such as lobsters 287,295,296,415, crayfish 1,415,461,528, crabs 188,283,476, and merostomatans such as horseshoe crabs 490; arachnids such as spiders 321,436 and scorpions 26,425; molluscs such as scallops 379 and cuttlefish 286; annelids such as worms 376,462 and polychaetes 365; chaetognaths such as arrow worms 161; and coelenterates such as jellyfish 107,439. B: Myosin filament length. Data include insects such as locusts 118,285, cockroaches 5,163,239,240,287,296,415,479, water bugs 5,25,163, water beetles 162, katydids 5,164, lepidopterians 5,513, dragon‐flies 444, larvae 86,88,243,401, and nymphs 87,90; crustaceans such as lobsters 295,296,297,415, crayfish 415,528, and crabs 188,283,476; arachnids such as spiders 321,436; molluscs such as scallops 379 and cuttlefish 286; annelids such as worms 376,462, and polychaetes 365; nematodes 426; and coelenterates such as jellyfish 107,439. C; Ratio of thin/thick filament number. Data include insects such as locusts 118,285, cockroaches 5,239,240,287,296,415,454,479, water bugs 5,25, katydids 5,164, lepidopterians 89,422,513, dragonflies 444, larvae 86,88,243,401,422, nymphs 87,90, and flies 405; crustaceans such as lobsters 287,296,415 and crabs 188,283; arachnids such as spiders 436 and scorpions 26,425; molluscs such as scallops 379 and cuttlefish 286; annelids 376,462; nematodes 426; and coelenterates such as jellyfish 107. D: Sarcomere diagram shows designated lengths.



Figure 7.

Active length‐tension or strain‐stress curves of invertebrate muscles. Stress is normalized to peak isometric tension. Strain is normalized as a fraction of the length that gives peak isometric stress. Shaded areas represent strains that correspond to stresses above 50% maximal isometric stress. Data include bee flight 242, locust flight 353, crayfish 528, frog 271, leech 378, and fly larvae 243 muscles.



Figure 8.

Mechanical power output of invertebrate muscle and its determinants as a function of cycle frequency. Data are from isolated muscle studies using the work‐loop method (Fig. 9) and come from unpublished data of Stevenson and Casey. A: Mass‐specific mechanical power output and work per cycle. Gilmour and Ellington 223 have demonstrated values as high as 110 W/kg from asynchronous, glycerinated muscle fibers of bumblebees. B: Muscle stress, strain, and strain rate. Data include insects 312,349,380,453, crustaceans 455, and molluscs 362.



Figure 9.

Work‐loop method to determine power output of an isolated muscle. A: Muscle is subjected to cyclic length changes (strain) while force per area (stress) is measured. The stimulation pattern is controlled. B: Area under the stress‐strain curve represents energy produced (output) during shortening or absorbed (input) during lengthening. The difference between the curves represents the net work per cycle. Counterclockwise loops result in energy production, whereas clockwise loops result in energy absorption by the muscle. C: Variation in work‐loop shape. Rectangular shape observed at low frequencies (<30 Hz). Triangular shape observed at intermediate frequencies (30–60 Hz). Ellipsoid shape observed at high frequencies (60–180 Hz).

after ref. 311


Figure 10.

Three‐dimensional musculoskeletal model of themeta‐thoracic leg of the cockroach Blaberus discoidalis. Left: Shaded polygons represent the exoskeleton, which was reconstructed from serial sections. Right: Heavy lines represent the lines of action of Hill‐type muscles. The model is articulated at the coxa/trochanter–femur and femurtibia joints so that muscle lengths, moment arms, forces, and joint moments can be estimated for a range of body positions 195. The computer model was created using SIMM.

MusculoGraphics, Evanston, IL


Figure 11.

Whole‐animal mass‐specific metabolic power input as a function of body mass. Oxygen consumption rates are the highest available for the species. In some cases, they are known to be maximal rates. A: Oxygen consumption as a function of body mass for runners, crawlers, swimmers, jetters, and fliers. Shaded areas represent jetters; top right area includes molluscs such as squid; bottom area includes jellyfish. Insect runners can warm their bodies. The regression line shown is for the Q10 corrected data set not shown (Q10 = 2). Data include runners (22,41,42,43,44,190,199,200,201,202,210,212,258,259,261,262,263,264,265,266,301,343,345,346,347,368,374,427,433,514,522; W. J. Van Aardt, unpublished data), runners with elevated body temperature 37,209, crawlers 97,277,292, swimmers 119,184,276,278,279,293,328,369,371,428,466, jetters 29,130,338,395,399,474,495,511, and fliers 36,39,42,91,92,93,96,100,102,104,108,109,110,173,250,251,273,318,333,384,393,427,447,502,507,521. B: Oxygen consumption rates by taxonomic groups (Table 3). Data include insect runners 41,42,43,44,210,212,259,263,266,301,343,345,346,347,368,427; crustacean runners (190,199,200,202,261,262,264,265,514,522; W. J. Van Aardt, unpublished data); swimmers 119,184,276,278,279,293,328,369,371,428,466,474; moth fliers 39,91,92,93,96,100; and bee, fly, and mosquito fliers 36,42,96,102,104,108,109,110,173,250,251,273,318,333,384,393,427,447,502,507,521.



Figure 12.

Aerobic factorial scopes for invertebrate activity. Oxygen consumption rates are the highest available for the species. In some cases, they are known to be maximal rates. Bars represent ± 1 S.D. Numbers in parentheses are sample size. Data include aquatic groups such as coelenterates 338, gastropods 277,292, crustaceans 119,184,276,278,279,293,328,369,371,428,466, and cephalopods 29,395,399,495,511; terrestrial groups such as gastropods 277,292, myriapods 201, crustaceans (190,199,200,202,261,262,264,265,514,522; W. J. Van Aardt, unpublished data), arachnids 22,258,347,374,433, and insects 41,42,43,44,210,212,259,263,266,301,343,345,346,347,368,427; insects with elevated body temperature 37,209; and aerial groups such as insects 36,39,42,91,92,93,96,100,102,104,108,10,173,250,251,273,318,333,384,393,427,447,502,507,521.



Figure 13.

Mass‐specific metabolic cost of transport as a function of body mass. Values represent minimum cost of locomotion available. Shaded area represents hydrostatic crawlers and burrowers. Data include runners 41,43,44,55,159,191,199,200,201,209,212,259,260,263,264,265,301,343,345,346,347, crawlers 97,143,267,277,292, burrowers 54,291,469, swimmers 119,184,241,276,278,280,293,328,369,468,474,511, jetters 130,338,395,399,495, and fliers 173,273,478,483,503,521.



Figure 14.

Hypothesized relationships of invertebrate locomotion based on literature review. A: Mass‐specific mechanical power output (see Fig. 5), the product of cycle frequency and mass‐specific mechanical work output per cycle. B: Cycle frequency (see Fig. 4). C: Mass‐specific metabolic power input (see Fig. 11), the product of cycle frequency and mass‐specific metabolic cost input per cycle. D: Mass‐specific mechanical work output per cycle, the product of cycle distance and mass‐specific mechanical work output per cycle, the product of cycle distance and mass‐specific resistive force or mass‐specific mechanical energy of transport. E: Cycle distance. F: Mass‐specific metabolic cost input per cycle (see Fig. 12), the product of cycle distance and mass‐specific metabolic cost of transport. G: Mass‐specific resistive force or mass‐specific mechanical energy of transport. H: Speed (see Fig. 3), the product of cycle frequency and cycle distance. I: Mass‐specific metabolic cost of transport (see Fig. 13).



Figure 15.

Mass‐specific metabolic cost input per cycle as a function of body mass. Regression lines represent a range of body masses for a given species. Data include runners 22,190,209,210,212,261, a crawler 97, and fliers 42,251,273,447,502,507 such as moths 96 and bees 96,102,521.



Figure 16.

Trends for variation in power output. Two hypothetical animals of the same mass are compared. The morphology of a hypothetical appendage is shown to illustrate mechanical advantage, muscle strain, and the angle swept by the appendage. Left column represents trends for an animal that generates lower power output than the animal represented at right. Equations show how variables (muscle moment, joint angle, and muscle power output) are used to derive mass‐specific muscle power output (PM*). See text for explanation.



Figure 17.

Cyber‐invertebrates. Dynamic models of legged animals designed by M. Raibert, MIT, and Boston Dynamics in collaboration with R. J. Full at U.C. Berkeley. Simulations consist of equations of motion, ground contact models, a numerical integrator, and a three‐dimensional graphics program. All models obey the laws of Newtonian physics and are not simple kinematic representations. The Hexahopper (center) is an abstracted insect with telescoping legs attached to a hemispherical body. The model exhibits dynamic locomotion without an aerial phase as it bounces along. Three legs act as one spring‐mass system. The Hexabug (right) uses articulated legs attached to a long body. The legs have the length dimensions of cockroach legs. The Playback cockroach (left) uses the actual morphology of cockroach legs along with three‐dimensional kinematics during running. The kinematic motion data can be played through the control system and the resulting dynamics analyzed. The controller uses the motion data to drive servos at each joint to apply moments which attempt to maintain target positions.

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Article Title: Invertebrate Locomotor Systems
 

How to Cite

Robert J. Full. Invertebrate Locomotor Systems. Compr Physiol 2011, Supplement 30: Handbook of Physiology, Comparative Physiology: 853-930. First published in print 1997. doi: 10.1002/cphy.cp130212