Fig. 5

Mechanics of the musculoskeletal ovipositor system of Ventuia canescens. a–g, i Kinematics of the musculoskeletal ovipositor system; acting (input) muscle forces are visualized by solid red arrows (b, d, f, g, i) and resulting (output) movements by solid black arrows (c, e, g, i). a–g, j–m 3D model of the ovipositor system (medial view, left is anterior). b m1 potentially serves as a tensor muscle for stabilization of the ovipositor system during oviposition. c, d, i Contraction of both m4a and m4b (F₄ in d, i) moves the 2nd valvifer posteriorly and the female T9 anteriorly towards each other (small number 3 in c, i), thus indirectly causing the 1st valvifer to tilt anteriorly (small number 4 in c, i). This is possible because the 1st valvifer is articulated with both the 2nd valvifer and the female T9 via the intervalvifer and tergo-valvifer articulations that act as rotational joints. The 1st valvifer thereby functions as a lever arm that transfers the movement to the dorsal ramus of the 1st valvula and consequently causes the 1st valvula to slide distally relative to the 2nd valvula (small number 5 in c). These movements might also facilitate the extension of the terebra back towards its resting position (c). m6 thereby stabilizes the ovipositor system by holding the 2nd valvifer and the female T9 in position and preventing them to rotate around the articulations (d). e, f, i Contraction of m5 (F₅ in f, i) moves the 2nd valvifer anteriorly and the female T9 posteriorly apart from each other (small number 6 in e, i), thus causing the 1st valvifer to tilt posteriorly (small number 7 in e,i) and consequently causing the 1st valvula to slide proximally relative to the 2nd valvula (small number 8 in e). These movements might also facilitate the flexion of the terebra (e). g, i Contraction of m3 (F₃ in g, i) causes the bulbs to pivot anteriorly at the basal articulation, thus flexing the 2nd valvula and, therefore, the whole terebra (small number 2 in g, i). Contraction of m2 (F₂ in g, i) extends the terebra back towards its resting position (small number 1 in g, i). h Light microscopical image of the insertion regions of m2 and m3 at the processus articularis and the processus musculares, respectively (lateral view, left is anterior). The duct of the venom gland reservoir of the 2nd valvifer ends at the lateral openings of the bulbous region of the 2nd valvula. i Resulting schematic drawing of the mechanism of the tilting movements of the 1st valvifer and of the flexion/extension of the terebra (lateral view, left is anterior, not to scale). Only the two pairs of antagonistically acting muscles that are mainly responsible for these movements are represented in simplified terms (m2/m3 and m4/m5). The muscles stabilizing the system (m1 and m6) are not depicted here. j–m Simplified mechanical scheme of the leverages of the ovipositor in the resting position; acting (input) muscle forces are visualized by solid red arrows, their horizontal force vector components and the resulting (output) forces by thin red arrows (j, k), the anatomical (in)levers by solid black lines and the effective (= mechanical) levers by thin black lines, and the joint angles (α, β, ε) are given (k, m). j, l Major direction of the acting muscle forces (F₂, F₃, F₄ and F₅) from a muscle’s insertion point to the centre point of its origin. j, k Under the simplified assumption that the 2nd valvifer, which acts as the frame of reference, and the female T9 are guided and cannot twist but only move towards or apart from each other along the horizontal anterior–posterior axis, the input force vectors F_4x and F_5x act horizontally at the 1st valvifer at the tergo-valvifer-articulation. The distance between the tergo-valvifer articulation (where the force is applied) and the intervalvifer articulation (joint axis/pivot point) is the anatomical inlever c; for torques see eqs. 4, 5. The 1st valvifer acts as a lever with the effective outlever d’, resulting in pro- or retraction forces at the dorsal ramus of the 1st valvula F_1vv4 and F_1vv5; see eqs. 6, 7. l, m Input force vectors F₂ and F₃ acting at the proximal end of the 2nd valvula with the basal articulation as joint axis and the anatomical inlevers a and b; for torques see eqs. 2, 3. n Schema of a female wasp flexing its terebra to an active position for oviposition (after [32]) (Additional file 1), which might be supported by the flexible 3rd valvulae (not shown in a–m). Abbreviations: 1vf, 1st valvifer; 1vv, 1st valvula; 2vf, 2nd valvifer; 2vv, 2nd valvula; 3vv, 3rd valvua; ba, Basal articulation; blb, Bulb; dr1, Dorsal ramus of the 1st valvifer; F, Force; F_x, Horizontal vector components of a force; iva, Intervalvifer articulation; m1, 1st valvifer-genital membrane muscle; m2, Anterior 2nd valvifer-2nd valvula muscle; m3, Posterior 2nd valvifer-2nd valvula muscle; m4a, Dorsal T9-2nd valvifer muscle part a; m4b, Dorsal T9-2nd valvifer muscle part b; m5, Ventral T9-2nd valvifer muscle; m6, Posterior T9-2nd valvifer muscle; pra, Processus articularis; prm, Processus musculares; T9, Female T9; trb, Terebra; tva, Tergo-valvifer articulation; vd, Duct of the venom gland reservoir of the 2nd valfiver