Correlation between ranges of leg walking angles and passive rest angles among leg types in stick insects

Because of scaling issues, passive muscle and joint forces become increasingly important as limb size decreases.^1-3 In some small limbs, passive forces can drive swing in locomotion,^4,5 and antagonist passive torques help control limb swing velocity.⁶ In stance, minimizing antagonist muscle and joint passive forces could save energy. These considerations predict that, for small limbs, evolution would result in the angle range over which passive forces are too small to cause limb movement (called "resting-state range" in prior insect work⁴ and "area of neutral equilibrium" in physics and engineering) correlating with the limb's typical working range, usually that in locomotion. We measured the most protracted and retracted thorax-femur (ThF) angles of the pro- (front), meso- (middle), and metathoracic (hind) leg during stick insect (Carausius morosus) walks. This ThF working range differed in the three leg types, being more posterior in more posterior legs. In other experiments, we manually protracted or retracted the denervated front, middle, and hind legs. Upon release, passive forces moved the leg in the opposite direction (retraction or protraction) until it reached the most protracted or most retracted edge of the ThF resting-state range. The ThF resting-state angle ranges correlated with the leg-type working range, being more posterior in more posterior legs. The most protracted ThF walking angles were more retracted than the post-protraction ThF angles, and the most retracted ThF walking angles were similar to the post-retraction ThF angles. These correlations of ThF working- and resting-state ranges could simplify motor control and save energy. These data also provide an example of evolution altering behavior by changing passive muscle and joint properties.⁷.