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Mechanics of cuticular elastic energy storage in leg joints lacking extensor muscles in arachnids

Andrew T. Sensenig^* and Jeffrey W. Shultz

Department of Entomology, University of Maryland, College Park, MD 20742, USA

View larger version (31K): [in a new window]   Fig. 1. Fourth walking legs of arachnids, showing their basic anatomy. Whole legs are shown at approximately the same scale. (A) Heterometrus; left leg, anterior perspective, inset showing posterior perspective. (B) Eremopus; right leg, posterior perspective, inset showing elastic sclerite of patella—tibia joint. (C) Mastigoproctus; left leg, anterior perspective. (D) Aphonopelma; right leg, posterior perspective. (E) Leiobunum; right leg, posterior perspective, inset showing elastic sclerite of tibia—basitarsus joint. bf, basifemur; bt, basitarsus; es, elastic sclerite; ex, extensor muscle; fe, femur; pa, patella; tf, telofemur; ti, tibia; tr, trochanter; tt, telotarsus.

View larger version (26K): [in a new window]   Fig. 2. (A) Diagram of the experimental apparatus used. (B) Changes in torque over time during a simulated cycle of joint movement. Elastic mechanisms resist flexion (Input impulse) but assist extension (Output impulse), the difference representing entropic energy loss. (C) Changes in torque over the range of joint angles used during locomotion. The area under the upper (loading) curve represents input energy; the area under the lower (unloading) curve represents output energy; the difference between them represents lost energy. Output energy divided by input energy multiplied by 100 is the percent efficiency or resilience.

View larger version (28K): [in a new window]   Fig. 4. Torque generated by isolated joints of representative Eremopus and Leiobunum during simulated locomotor cycles. Arrows denote the mean limits of joint excursion measured in walking animals. (A-C) Different internal fluid pressures. (D) Two work loops generated by tibia—basitarsus of Leiobunum at 0 kPa representing typical variation between frequencies and individuals. The heavy line represents the approximation of torque used in the calculation of elastic recoil to forward motion. Values of resilience (%) are shown next to the corresponding work loop.

View larger version (42K): [in a new window]   Fig. 3. Changes in joint angles during walking at typical speeds (representative trials). Speed and step frequencies are noted in parentheses. The contact angle depicted for Eremopus and Leiobunum is the projection onto the sagittal plane of the angle between the substratum and lever arm and was used to calculate potential propulsive work due to elastic recoil. Dotted lines are inferred due to incomplete kinematic information. The basitarsus—telotarsus joint angle is diagrammed as the supplementary angle. Fe—Pa, femur—patella joint; Pa—Ti, patella—tibia joint; Ti—Bt, tibia—basitarsus joint; Bt—Tt, basitarsus—telotarsus joint.

View larger version (24K): [in a new window]   Fig. 5. Scaled midrange torques at applied internal fluid pressures. Midrange torques are those torques generated by a joint at an angle located midway between the maximum and minimum angles observed during locomotion. Values are means ± 2 S.E.M. X indicates that measurements were not taken. No torque was generated by the femur—patella joint of Hadrurus or by the patella—tibia joints of both scorpion species at all pressures tested.

View larger version (41K): [in a new window]   Fig. 6. Torque generated by isolated joints of representative Mastigoproctus and Aphonopelma during a simulated locomotor cycle under different internal fluid pressures. Values of resilience (%) are shown next to the corresponding work loop. Arrows denote the mean limits of joint excursion measured in walking animals.

View larger version (24K): [in a new window]   Fig. 7. Torque generated by isolated joints of representative Hadrurus and Heterometrus during a simulated locomotor cycle under different internal fluid pressures. Values of resilience (%) are shown next to the corresponding work loop. Arrows denote the mean limits of joint excursion measured in walking animals.

View larger version (29K): [in a new window]   Fig. 8. Decay in extension force of elastic joints over time. Each joint was flexed and maintained in a flexed position while recording torque. The absolute magnitudes of initial torque and joint angle are noted.