Modelling torque generation by the mero-carpopodite joint of the american lobster and the snow crab

Abstract

The torque generated by a rotating joint comprises the useful force exerted by the joint on the external environment, and both the magnitude and distribution of torque through the step cycle during walking are important variables in understanding the mechanics of walking. The mechanics of the American lobster (Homarus americanus) and snow crab (Chionoecetes opilio) during walking were modelled to examine the relative roles of flexor versus extensor apodeme–muscle complexes, investigate which legs of these decapods likely contribute the greatest to locomotion, determine scaling effects of torque generation, and assess the relative roles of various model variables on torque production. Force generated along the length of the apodeme by the muscle was modelled based on apodeme surface area, muscle stress, and muscle fibre pinnation angle. Torque was then calculated from this estimated force and the corresponding moment arm. The flexor apodeme–muscle complex is calculated to generate consistently greater forces than the extensor, and generally this results in flexor torque being larger than extensor, though the snow crab does illustrate the opposite in two of its legs. This greater torque generation in flexion suggests that, in addition to the pushing of the trailing legs, the pulling action of the leading legs may play a significant role, at least during lateral walking. Leg 4 of both species appears to generate greater torques and thus provide the greatest forces for locomotion. Torque generation as a function of body size shows a second order response due to the increase in apodeme surface area. The pinnation angle of the muscle fibre is found to be insignificant in force generation, apodeme surface area (representing muscle cross sectional area) likely plays the most influential role in total force production, and moment arm controls the distribution of this force through the step cycle. Muscle stress remain a largely unknown quantity however, and may significantly affect both magnitude and distribution through step cycle of forces, and thus torque. Despite the uncertainty associated with the muscle stress parameter, the modelled results fit well with previously published force measurements.

Keywords:

• Model
• Torque
• Force
• Locomotion
• Lobster
• Crab
• Homarus
• Chionoecetes

Acknowledgements

We would like to acknowledge the assistance and support of Mikio Moriyasu and Marc Lanteigne of the Department of Fisheries and Oceans, Moncton, New Brunswick, and Jim Williams of St. Francis Xavier University, Antigonish, Nova Scotia for early review of the manuscript. Also we thank two anonymous reviewers for their constructive criticism. Funding for this work was provided by a Natural Sciences and Engineering Research Council of Canada grant to E. DeMont.