figure 1: obtained from the original paper

## Background:

1. Most researchers at the time of publication(1951) considered that insect movement was accomplished via the alternation of two tripods of support, each composed of the foreleg and hindleg on one side, together with the middle leg on the opposite side. As a result, although insects have six legs their movement could be analysed as if they only had two alternating groups.

2. Demoor in particular extended the dynamics of the alternating groups of diagonal legs to include majority of Arthropods. He concluded that the movement of insects conformed to the general description that walking is a series of checked falls.

3. The concept that walking is a series of checked falls seems to have little meaning except in the case of bipeds or tetrapods that are moving fast and therefore possess dynamic stability.

4. The walking tetrapod may stop at any phase of its walking cycle and not fall over, as the center of gravity lies within the area of support.

5. At the time of publication, a general consensus emerged concerning the roles fulfilled by the three pairs of legs during walking. The forelegs were considered to have a tractive function, the hind pair to propel, while the middle legs act as fulcra.

Finally, in the introduction the authors claim that in the present century the focus of research has moved from the mechanism of movement to a study of the role of the brain and different parts of the nervous system in the co-ordination of locomotory movements. This statement is interesting because the authors then make an original discovery concerning insect movement that is simple, purely biomechanical and yet general. I think it also says something important about the effective complexity of neural circuits controlling the locomotion of terrestrial insects.

## Materials and Methods:

figure 2: A Sinclair ciné camera
1. The authors made detailed studies on the cockroaches Periplaneta americana and Blatta orientalis & various beetles Dysticus marginalis, Hydrophilus piceus, Carbus violaceus, Chrysomala orichalcea and Blaps murconata.
2. According to the authors, the walking movements of the other insects did not appear to differ from their selection of species in any essential feature. I’m not sure whether to take this statement at face value.
3. The insects were usually filmed from above as they walked over graph paper but simultaneous side and ventral views, sustained with the aid of a mirror were most valuable in describing the cycles of individual leg movements.
4. A Sinclair ciné camera was used at speeds of 16-32 frames per second with illumination provided by two Photoflood lights at a distance of 3 ft. According to the authors, this lighting disturbed the cockroaches but their negative phototaxis assisted the photography as they ran towards a dark box placed at one side of the field.

## Results:

figure 3: An analysis of force on the legs of the cockroach

In order to understand the results it’s first necessary to introduce the following terms:

Protraction: the complete movement forwards of the whole limb relative to its articulation with the body.

Retraction: describes the remaining half of the cycle between the instant when the leg is placed on the ground and the time it’s raised and protraction begins

In theory, the duration of protaction and retraction should be equivalent but there’s always a small delay between the protraction of a tripod of limbs. Now, as a result of the authors’ investigation they have discovered the following pair of rules:

1. No fore or middle leg is protracted until the leg behind has taken up its supporting position.
2. Each leg alternates with the contralateral limb of the same segment.

Furthermore, if we define $p$ to be the protraction time and $r$ to be the retraction time the authors make the following general observations:

1. An increase in speed is generally accompanied by a decrease in the times of both protraction(p) and retraction(r). This increase in stride frequency is then accompanied by a reduction in stride length and an increase in the distance between successive points of support. The range of speeds is continuous and no distinction could be made between walking and running.

2. A system of rigidly alternating tripods would result in $\frac{p}{r}=1$ but this is never quite realised as there is always a small delay between the protraction of three legs of a triangle.

3. It’s concluded that insects are the end-product of a process of limb reduction among terrestrial Arthropods in which $\frac{p}{r} \rightarrow 1$ and yet the animal retains static stability throughout the whole cycle.

I find the last point quite ambitious and I think more detailed justifications are desirable although the authors defend this proposition well.

## Remarks:

1. I find this paper very interesting as it suggests that most tripod gaits have a relatively simple physical explanation and suggests that neural mechanisms for control of terrestrial insect locomotion should be relatively simple.
2. I think that numerical experiments with a variety of tripod gaits using the rules given in the results section could provide insight into the special stability advantages of six-limbed organisms. This is something I’ll look into soon but it would require specifying an insect morphology that approximates its biomechanics quite well. I wouldn’t mind doing this for P. endroedyi described in [2] but this would take some time to do properly.
3. There is a lot more in this paper, entire pages, concerning the physiological constraints on Arthropod locomotion that I haven’t included in this review. They aren’t of direct interest to me right now but they are also very well written and I’ll probably return to those sections in the near future.

# References:

1. The co-ordination of insect movements. G.M. Hughes. 1951.
2. A new galloping gait in an insect. Smolka et al. 2013.