QUICK SEARCH:   [advanced] Author: Keyword(s):
Home     Help     Feedback     Subscriptions     Archive     Search     Table of Contents

First published online July 20, 2006
Journal of Experimental Biology 209, 2990-3000 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02322

This Article Summary Full Text Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Goldman, D. I. Articles by Full, R. J. Search for Related Content PubMed PubMed Citation Articles by Goldman, D. I. Articles by Full, R. J.

Dynamics of rapid vertical climbing in cockroaches reveals a template

Daniel I. Goldman^*, Tao S. Chen, Daniel M. Dudek and Robert J. Full

Department of Integrative Biology, University of California, Berkeley, CA 94720-3140, USA

View larger version (63K): [in a new window]   Fig. 1. The death-head cockroach Blaberus discoidalis climbs a force plate coated in 700 µm glass beads using claws and adhesive pads. (A) The fore-aft (blue), lateral (green) and normal (red) wall reaction forces are measured using a three-axis force platform. (B) Normal view of the middle right tarsus engaging the beaded surface. (C) Side view of front right tarsus engagement.

View larger version (48K): [in a new window]   Fig. 2. Representative vertical climb of B. discoidalis up a force plate at average velocity 0.18 m s-1. (A) Sequential video frames of the cockroach as it enters (left), is fully on (middle), and leaves (right) the force plate. Red arrows indicate single legs on the force plate. (B) Alternating tripod stepping pattern during the climb. Black bars represent stance period and white spaces the swing period. R, right side; L, left side. (C) Fore-aft (blue), lateral (green) and normal (red) wall reaction forces produced by the cockroach during a climb. Single-leg forces were measured as the cockroach entered (A, left) and exited the plate (A, right). The black circles correspond to the panels in A. Whole body (center of mass) wall reaction forces were measured while the cockroach was fully on the plate (middle) with at least three legs in contact (horizontal black bar below C). Horizontal broken lines represent average body weight.

View larger version (32K): [in a new window]   Fig. 3. Frequency and phase of wall reaction forces during climbing. (A) Stride frequency increased with increasing average fore-aft velocity (blue circles). Inset: the relationship of stride frequency with speed was similar to the relation found in level ground running (black circles). Level data taken from Full and Tu (Full and Tu, 1990). (B) Power spectra of integrated forces (arbitrary units) while the animal was on the plate averaged over trials from different individuals. Fore-aft and normal forces oscillated at step frequency (average step frequency fstep=17.7±3.7 Hz) while lateral force oscillated at half stepping frequency (fstance=7.8±1.9 Hz), the stride frequency. (C) Integrated forces from all legs during a single constant average velocity stride (two steps) in fore-aft (blue), lateral (green) and normal (red) direction. The data are normalized to the stride period. Error bars on plot represent ± 1 s.e.m. Standard deviations are approximately four times in magnitude (see Results section for a discussion). Black broken line represents average body weight (N=7 individuals). The stepping pattern for a single representative trial is shown below. The schematics of the cockroach indicate the approximate leg configurations at mid-stance. Legs colored black indicate feet that are in contact with the wall.

View larger version (15K): [in a new window]   Fig. 4. (A-E) Fore-aft (blue), lateral (green) and normal (red) wall reaction forces developed by individual legs for one step during vertical climbing. Leg forces were averaged from N=7 individuals and normalized to stride period. Values are means ± s.d. In each panel, the solid black vertical line shows the average, normalized stance period (gray bars indicate s.d.). The crosshatched region in A and B shows the overlap region of middle legs with front legs. Normal forces in this region were estimated from Fig. 3C. Black broken horizontal line represents average body weight.

View larger version (21K): [in a new window]   Fig. 5. Summary of peak single leg wall reaction forces in a cockroach during climbing averaged over different individuals (N=13). (A) Fore-aft forces. (B) Lateral forces. (C) Normal forces. The error bars represent s.d. The broken line in each panel represents average body weight (28.7±11 mN). Forces for the middle left leg were not measured.

View larger version (26K): [in a new window]   Fig. 6. Cockroaches (A,B) and geckos (C,D), with different leg number, morphology and adhesive mechanism, have similar single-leg wall reaction force patterns during climbing. Dorsal (A,C) and sagittal (B,D) views are shown. The arrows represent average peak wall reaction forces for single legs in fore-aft (blue), lateral (green) and normal (red) directions. All legs in both animals pull up the wall. Legs pull in toward the midline, except for the hind cockroach legs where lateral forces were near zero. Front legs pull the head toward the wall, while hind legs push the abdomen (below the COM) away from the wall. In the cockroach, the middle-leg normal forces were small. Black arrows indicate average body weight for the animals studied (30 mN for cockroaches, 20 mN for geckos). Arrows that represent limb reaction forces are scaled relative to the length of the black arrows. Gecko data are from Autumn et al. (2006).

View larger version (21K): [in a new window]   Fig. 7. Fore-aft (blue) and lateral (green) center of mass (COM) wall reaction forces, COM fore-aft and lateral instantaneous velocity for two steps (one stride) during climbing for (A) a cockroach, (B) a gecko and (C) the spring-mass model (template). Cockroaches and geckos show similar COM wall reaction forces and velocities. This pattern can be represented by the template described in Fig. 8. The fore-aft and lateral forces are in-phase and the lateral force is one-half the oscillation frequency of fore-aft force. The velocities are phase-delayed from the corresponding forces by approximately /2. Climbing velocity for the cockroach is 20 cm s-1, the gecko 49 cm s-1, and the template 18 cm s-1. Broken lines indicate body weight. The stepping patterns are shown below for a normalized stride. Black bars represent stance period and white spaces the swing period.

View larger version (26K): [in a new window]   Fig. 8. A dynamic template for climbing. The two degrees of freedom model that generates the template climbing dynamics shown in Fig. 7C. (A) Schematic of the model. (B) Schematic of the motion of the model during two steps (one stride of period T). In the first step with the right leg, at touchdown (t=0) the right actuator is maximally extended, and the spring is un-extended with zero rest length. Touchdown is created by establishment of a rotationally free pin-joint with the wall. As the actuator length L(t) decreases, the spring in the leg extends, the foot freely pivots about the point of contact and the center of mass (COM) is translated vertically and laterally. The cycle repeats for the left leg. The actuator changes length sinusoidally such that L(t)=L0[1+zsin(2ft)], where z is the fractional length change and f=1/T is the stride frequency. The solid vertical line in each panel indicates the fixed lateral position about which the COM laterally oscillates. The angular excursion of the body is exaggerated for clarity. Actual angular excursion of the body relative to vertical is approximately ±3°. The model was coded and integrated in the Working Model 2D (Design Simulation Technologies, Inc) simulation environment. The parameters used to generate Fig. 7C were body mass=2 g, body dimensions=4 cmx0.95 cm, l1=0.71 cm, l2=0.84 cm, ß=10°, L0= 1.54 cm, z=0.6, k=6 N m-1, =0.09 Ns m-1, f=9 Hz. The attachment duty factor in the model is 0.46.

View larger version (88K): [in a new window]   Fig. 9. Climbing gecko (A), cockroach (B) and robot (C). The biologically inspired climbing robot named RiSE (Robots in Scansorial Environment) is using the force generation concepts discovered for cockroaches and geckos (Autumn et al., 2005).