Gearing for speed slows the predatory strike of a mantis shrimp

The geometry of an animal’s skeleton governs the transmission of force to its appendages. Joints and rigid elements that create a relatively large output displacement per unit input displacement have been considered to be geared for speed, but the relationship between skeletal geometry and speed is largely untested. The present study explored this subject with experiments and mathematical modeling to evaluate how morphological differences in the raptorial appendage of a mantis shrimp ( Gonodactylus smithii ) affect the speed of its predatory strike. Based on morphological measurements and material testing, we computationally simulated the transmission of the stored elastic energy that powers a strike and the drag that resists this motion. After verifying the model’s predictions against measurements of strike impulse, we conducted a series of simulations that varied the linkage geometry, but were provided with a fixed amount of stored elastic energy. We found that a skeletal geometry that creates a large output displacement achieves a slower maximum speed of rotation than a low-displacement system. This is because a large displacement by the appendage causes a relatively large proportion of its elastic energy to be lost to the generation of drag. Therefore, the efficiency of transmission from elastic to kinetic energy mediates the relationship between the geometry and the speed of a skeleton. We propose that transmission efficiency plays a similar role in form–function relationships for skeletal systems in a diversity of animals. * A : scaling constant a–d : position vectors for joint positions in four-bar linkage (m) B : scaling factor B iso : scaling factor predicted by isometry C : chord width of an element of the striking body (m) C d : drag coefficient (dimensionless) C pix : density constant (kg m–3) D : drag torque index (dimensionless) E drag : energy lost to drag (J) E elastic : stored elastic energy (J) E kine : kinetic energy (J) H : length of the striking body (m) h b,d : distance between b and d (m) h dac : position along the dactyl (m) h load : distance between the point of loading and a (m) h out : distance between striking body center of mass and b (m) I SB : moment of inertia of striking body (kg m2) ![Graphic][1] : moment of inertia of striking body (dimensionless) I water : moment of inertia of the water (m4) k linear : linear stiffness of the meral spring (N rad–1) k torsion : torsion stiffness of the meral spring (N m deg–1) l 1– l 4 : lengths of links in the four-bar linkage (m) L max : maximum angular momentum of the striking body (kg m2 deg s–1) l SB : total length of striking body (m) m b : body mass (g) m SB : mass of striking body (g) p : pixel intensity (dimensionless) P : linear momentum of the striking body (g m s–1) r : distance between an element of the striking body and b (m) r vox : distance between a voxel and b (m) t : time (s) T : width of an element of the striking body (m) T k : kinematic transmission (dimensionless) v : volume of voxel xˆ : unit vector (dimensionless) ŷ : unit vector, orthogonal to xˆ (dimensionless) γ : output angle of the linkage system (deg) η : transmission efficiency (dimensionless) θ : input angle of a lever or linkage system (deg) θ0 : initial position of the input angle (deg) θrest : position of the input angle at rest (deg) ρtissue : density of tissue (kg m–3) ρwater : density of water (kg m–3) τapplied : torque applied to the striking body (N m) τdrag : torque generated by drag (N m) τspring : torque generated by meral spring (N m) ν : angle between the direction of the load and the meral-V (deg) Ψ : angle between links 1 and 4 (rad) [1]: /embed/inline-graphic-5.gif