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First published online October 5, 2007
Journal of Experimental Biology 210, 3677-3688 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.006486

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Linkage mechanics and power amplification of the mantis shrimp's strike

S. N. Patek^1,*, B. N. Nowroozi², J. E. Baio¹, R. L. Caldwell¹ and A. P. Summers²

¹ Department of Integrative Biology, University of California, Berkeley, CA 94720-3140, USA
² Ecology and Evolutionary Biology, University of California–Irvine, Irvine, CA 92697-2525, USA

View larger version (130K): [in this window] [in a new window]   Fig. 1. Odontodactylus scyllarus raptorial appendage. (A) A resting peacock mantis shrimp with the raptorial appendage circled. Raptorial appendages are used either for stabbing (dactyl open and extended) or for hammering (dactyl folded in and bulbous heel exposed, as shown here). (B) Lateral view of an isosurface rendering of segmented CT scan data of the left raptorial appendage. Each skeletal element has been pseudocolored to increase contrast. The isosurface threshold has been optimized for each element to illustrate the morphology and spatial relationships. (C) Ventral view of a shadowless volume rendering of left merus (m). Shading corresponds to degree of radio-opacity (mineralization), with lighter colors corresponding to greater mineralization and darker to poorly mineralized areas. Note the unmineralized region adjacent to the highly mineralized ventral bar (vb) extending proximally from the base of the meral-V. This unmineralized region may permit dorso-proximal flexion of the meral-V (v). (D) Lateral view of the merus using the same rendering technique as in C. s, saddle; c, carpus; p, propodus; d, dactyl. Scale bars, 4 mm.

View larger version (21K): [in this window] [in a new window]   Fig. 2. A four-bar linkage model and the associated points in the proposed mantis shrimp four-bar linkage model. Red circles indicate pivot points; numbers indicate links. Pivots A and D are fixed in space and form Link 1. Link 2 is the input link formed by pivots A and B. Link 3 is the coupler link formed by pivots B and C. Link 4 is the follower link formed by pivots C and D. The input angle (in) and output angle (out) can be calculated using the law of cosines and the length of the diagonal (green broken line connecting pivots B and D). This particular model configuration is not operational when B, C and D are collinear, thereby limiting the input range of in (see Fig. 9 in the Results). (A) A tracing of a high-speed video image of a raptorial appendage that has completed the load phase and is spring-loaded and prepared to strike. The saddle (s) is compressed and the meral-V (v) is rotated proximally. (B) The corresponding linkage model to A. (C) A raptorial appendage in the release phase. The saddle is hyper-extended into a flattened shape. The meral-V is fully rotated and open. (D) The corresponding linkage configuration to C. m, merus; c, carpus; p, propodus; d, dactyl. Beige regions in A and C represent arthrodial membrane; gray regions indicate exoskeleton; yellow area represents the saddle.

View larger version (68K): [in this window] [in a new window]   Fig. 3. CT scans of the internal anatomy of the raptorial appendage and the degree of mineralization of the merus exoskeleton (gray is mineralized; transparent regions represent relatively unmineralized exoskeleton). (A) Medial view of the raptorial appendage (proximal to right of page; ventral toward the bottom of the page) showing the large lateral extensor apodeme (e). Ventrally, the lateral flexor apodeme (f) attaches to sclerite 2 (orange). Medial to sclerite 2 is the small, rod-shaped sclerite 1 (green). (B) An internal perspective of the merus viewed from the distal end (lateral to left). Sclerite 2 (s2) is in its resting, unlocked position such that it hangs externally between the merus and carpus. The surface of the distal meral-V (v) articulation, which loosely articulates with the carpus, contrasts with the large internal joint, which forms the medial carpus joint articulation (j). (C) Same view as in B with sclerite 2 and sclerite 1 (s1) in closed and braced positions. Note that sclerite 1 does not appear to directly articulate with sclerite 2 when in the closed position and instead folds medially relative to the edge of sclerite 2. (D) Sclerites in resting position (medial view; distal to left). (E) Locked positions of the sclerites with the carpus rotated counter-clockwise in preparation to strike (medial view). m, merus; c, carpus; s, saddle; p, propodus; b, ventral infolding of merus. Scale bars, 4 mm.

View larger version (20K): [in this window] [in a new window]   Fig. 4. Sclerite engagement and orientation. (A) Sclerite 2 (red, solid fill) is in the engaged position and braced against the ventral meral infolding. Yellow highlighting indicates the area of ventral meral infolding against which the sclerite is braced. The blue dotted line shows the approximate attachment point and orientation of the lateral flexor muscle that engages the sclerite. Shown from the medial side, with the meral-V (v) behind the sclerite. Ventral is toward the bottom of the page and proximal is to the right. (B) A schematic diagram of the engaged and resting positions of sclerite 2. The darkest sclerite (red) is shown in the engaged position with yellow highlighting the articulating surfaces. When the sclerite is released it rotates distally (to left), to rest with the articulating surface hanging outside the animal (circled). This portion of the sclerite is visible in mantis shrimp specimens and hangs between the merus and carpus. Blue dotted lines show the approximate orientation and attachment of the lateral flexor muscle.

View larger version (95K): [in this window] [in a new window]   Fig. 5. The morphology of the raptorial appendage of the peacock mantis shrimp. Line drawings are presented adjacent to photographs of the corresponding areas of the raptorial appendage. Proximal is to the right of the page. (A) Lateral view highlights the external, loose articulation between the meral-V (v) and carpus (c; inset). A thin strip of exoskeleton forms the bridge (b) between the meral-V and saddle (s). (B) Medial view shows the internal meral-carpal articulation that functions as a sliding channel joint (left inset). Also visible is the proximal saddle notch, into which the saddle is pushed during extensor muscle contraction in the load phase (right inset). (C) Dorsal view (medial toward top of page) shows the orientation of the lateral extensor apodeme (a, pink) extending from the carpus and running beneath the saddle. The bridge (b) runs dorsally from the lateral meral-V (visible in A) and across to the distal horn of the saddle (visible in B). The medial meral-carpal articulation consists of two adjacent articulations (orange circles); the internal medial meral-carpal articulation is a robust sliding channel joint (as shown in B, left inset). (A–C) Orange circles indicate articulations; gray bars indicate internal buttressing; beige regions are arthrodial membrane; gray regions indicate exoskeleton; yellow coloration represents the saddle (s). m, merus; p, propodus; d, dactyl.

View larger version (20K): [in this window] [in a new window]   Fig. 6. A resting (solid outline) and loaded (light-blue overlay) merus segment (m) of the raptorial appendage. Proximal is to the right of the page, dorsal is toward the top of the page. (A) Lateral view of the raptorial appendage. When the extensor muscles contract in preparation for a strike in the load phase, the meral-V (v) rotates proximo-medially (clockwise in this image), which simultaneously causes the bridge (b) to move proximally. When the bridge pushes proximally, it pushes against the saddle (s), which is compressed to form a more concave curve. A mineralized ventral bar (vb) extends proximally from the base of the meral-V. (B) Medial view of the raptorial appendage showing the proximal movement and flexion of the saddle caused by extensor muscle contraction. When seen from the medial view, the saddle is pushed into a notch on the merus. (C) A diagram of the possible areas of elastic energy storage (orange spring icons) during rotation of the merus and flexion of the saddle in preparation for a strike. Here we propose that the meral-V functions as a spring by flexing along its base, similar to a tape spring, to form a tighter curve during extensor muscle contraction. A previous study (Patek et al., 2004) proposed that elastic energy is stored as the saddle compresses into a more concave shape.

View larger version (15K): [in this window] [in a new window]   Fig. 7. The release phase of a smashing raptorial strike, illustrating the flexion and rotation of the raptorial appendage structures. The left axis represents rotation in degrees of the meral-V (green squares), propodus/dactyl unit (filled circles) and carpus (open circles). The right axis shows the length change of the saddle (orange triangles). Time zero is the end of the load phase, during which time the lateral extensor muscle contracted to rotate and close the meral-V and compress the saddle. The initial stages of the raptorial strike begin with a sliding movement in which the carpus rotates but the other segments move only slightly. The sweep phase begins when the meral-V rotates and saddle lengthens concurrently with the greatest angular acceleration of the carpus and propodus/dactyl. When impact occurs, the dactyl/propodus recoil while the saddle and meral-V continue to extend slightly. Data points were digitized from high-speed video images.

View larger version (29K): [in this window] [in a new window]   Fig. 8. A tracing of a typical strike sequence from high-speed video images with the links and pivots of a four-bar linkage mechanism overlaid on the tracings. Shown from left to right, images are 0.4 ms apart with the exception of the final two images, which are 0.2 ms apart. The saddle is colored orange; v, meral-v; c, carpus; p, propodus; d, dactyl. Insets illustrate schematically the compression and release of a spring (orange) and the braced and released position of sclerite 2 (red sclerite, gray brace).

View larger version (38K): [in this window] [in a new window]   Fig. 9. The four-bar model predictions vary depending on relative link lengths and starting angles. The linkage mechanism is operational in two regions between input rotations of 0 and 360° (region from 0 to 180° shown; the range from 180–360° is the mirror image of 0 to 180° and is never used by mantis shrimp). The horizontal lines at output rotations of 0° and 180° indicate that a change in input rotation does not yield any output rotation (i.e. the linkage mechanism is non-operational). (A) An input rotation between 40° and 120° yields an output rotation depending on relative link lengths. Green traces show the predicted behavior based on the link lengths of a relaxed raptorial appendage (i.e. Link 4 extensor muscle is not contracted). Blue traces show the predicted behavior of the relaxed appendages if Link 4 is constrained to the average shortened length observed in video images. Red traces illustrate the range of behaviors given the range of link lengths measured in loaded appendages from video images. The thick black line provides the linkage model behavior given the average link lengths measured from the loaded images (red lines; also shown in Fig. 10). (B) The predicted model behavior of four individuals (each color represents a different individual) given measured inputs and link lengths from high-speed video sequences.

View larger version (6K): [in this window] [in a new window]   Fig. 10. Predicted four-bar model behavior based on the average link lengths of loaded raptorial appendages. For a given input angle, the four-bar linkage mechanism yields an output that varies nonlinearly along the range of input angles. The four-bar model is not operational beyond the range of input angles shown here. Kinematic analyses showed that mantis shrimp typically generate input angles of the meral-V in the range 64–73°, as indicated here (yellow line).

View larger version (12K): [in this window] [in a new window]   Fig. 11. The relationships between input angle rotation (Link 2, meral-V) and output angle rotation (Link 3, propodus rotation) measured in high-speed video sequences. (A) The cumulative change in input and output rotation across video frames (combined data from 23 strikes, five individuals). (B) The net input and output rotation (the total rotation across the full input range) across each strike recorded in the same individuals as in A, with each individual represented by a different symbol. The predicted output based on the four-bar model slope (crosses) is shown.