TY - JOUR
T1 - Gearing for speed slows the predatory strike of a mantis shrimp
JF - The Journal of Experimental Biology
JO - J. Exp. Biol.
SP - 1231
LP - 1245
DO - 10.1242/jeb.061465
VL - 215
IS - 7
AU - McHenry, Matthew J.
AU - Claverie, Thomas
AU - Rosario, Michael V.
AU - Patek, S. N.
Y1 - 2012/04/01
UR - http://jeb.biologists.org/content/215/7/1231.abstract
N2 - 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. Ascaling constanta–dposition vectors for joint positions in four-bar linkage (m)Bscaling factorBisoscaling factor predicted by isometryCchord width of an element of the striking body (m)Cddrag coefficient (dimensionless)Cpixdensity constant (kg m–3)Ddrag torque index (dimensionless)Edragenergy lost to drag (J)Eelasticstored elastic energy (J)Ekinekinetic energy (J)Hlength of the striking body (m)hb,ddistance between b and d (m)hdacposition along the dactyl (m)hloaddistance between the point of loading and a (m)houtdistance between striking body center of mass and b (m)ISBmoment of inertia of striking body (kg m2)moment of inertia of striking body (dimensionless)Iwatermoment of inertia of the water (m4)klinearlinear stiffness of the meral spring (N rad–1)ktorsiontorsion stiffness of the meral spring (N m deg–1)l1–l4lengths of links in the four-bar linkage (m)Lmaxmaximum angular momentum of the striking body (kg m2 deg s–1)lSBtotal length of striking body (m)mbbody mass (g)mSBmass of striking body (g)ppixel intensity (dimensionless)Plinear momentum of the striking body (g m s–1)rdistance between an element of the striking body and b (m)rvoxdistance between a voxel and b (m)ttime (s)Twidth of an element of the striking body (m)Tkkinematic transmission (dimensionless)vvolume of voxelxˆunit vector (dimensionless)ŷunit vector, orthogonal to xˆ (dimensionless)γoutput angle of the linkage system (deg)ηtransmission efficiency (dimensionless)θinput angle of a lever or linkage system (deg)θ0initial position of the input angle (deg)θrestposition of the input angle at rest (deg)ρtissuedensity of tissue (kg m–3)ρwaterdensity of water (kg m–3)τappliedtorque applied to the striking body (N m)τdragtorque generated by drag (N m)τspringtorque generated by meral spring (N m)νangle between the direction of the load and the meral-V (deg)Ψangle between links 1 and 4 (rad)
ER -