Fig 1.
Morphology of the mandibular apparatus of P. americana, kinematics and general experimental setup.
A) Morphology of the cockroach head from a μCT scan with emphasis to the mandibles (coloured light blue) and their driving muscles (light red). 1l-4l: teeth of the left mandible; 1r-3r: teeth of the right mandible; α: opening angle of the right mandible (approx.. 70°); ‘ce’: right complex eye; ‘md’: mandibles; ‘Cleft‘ and ‘Cright’: anterior condyles of the left and right mandible joints; ‘m1’: left mandible closer muscle; ‘m2’: left mandible opener; mf: main direction of the muscle force; ‘mt’: apodeme connecting the mandible closer muscle with the median edge of the mandible; mr: molar region B) Camera view onto the mandibles (light blue) and the sensor tip (light red) during the bite experiments. The horizontal line is defined by the anterior condyles of the left and right mandible joints Cleft and Cright; ‘1r’ depicts the distal tip of the right mandible and α is the mandible angle with respect to the horizontal line, i.e. the opening angle of the right mandible before mathematical correction (see methods). C) Side view of the general setup with the fixated specimen at the right and the force transducer at the left side.
Fig 2.
Finite element model of the force sensor’s general structure loaded laterally (Colours encode deformation of the structure; blue: no deformation and red: high deformation).
The structural basis of the force transducer consisted of stereolithographically hardened PVC and provided two cantilever beam springs aligned perpendicular to each other; this way allowing for spatial resolution in two directions. The cross talk was very low in all loading situations. The sensitive structure was equipped with two semiconductor strain gages and integrated in a CNC-fabricated aluminium housing (see Fig 1c). For simplicity the bevelled sensor tip, i.e. the tip of the hypodermic needle that engaged with the mandible teeth was modelled as a cylinder.
Fig 3.
Example sequence of measured Ftot.
The residual forces Fres changed little during a trial and are generated by slow muscle fibres and passive elasticity of the muscle-joint complex while the changes on top of this basis (Fact) are generated by faster muscle fibres.
Fig 4.
Resulting forces at the position of the second right and third left teeth over the functional range of the mandibles.
A) Fact, i.e. forces generated by the faster muscle fibres (for details see text). B) Ftot, i.e. total bite forces including tonic and passive contributions. C) Residual forces at the position of the second right and third left teeth over the functional range of the mandibles. Residual forces represent the sum of passive joint forces and tonic contributions while their effective contributions depend on the opening angle. Forces were determined for the instances directly prior to a contraction and are consequently restricted to medium and large opening angles. In B and C, the red lines show the mean (solid), ± standard error (s.e.m.; dashed) and ± standard deviation (s.d.; dotted) of the passive forces, i.e. those forces necessary to open the mandibles of freshly killed specimens. At small and medium opening angles, the residual forces (Fres) are primarily generated by tonic muscle fibres while at high opening angles passive forces dominate.
Fig 5.
Contraction forces of the mandible closer muscle over the functional range of the mandibles in degrees (lower abscissa) and the mean fibre length of the closer muscle in mm (upper abscissa).
A)Fm,act i.e. forces generated by faster muscle fibres. The values for left (red) and right mandibles are highly concordant B)Fm,tot. i.e. total muscular forces. Mean passive forces (see Figs 4b and 5) were subtracted from the residual forces prior to the calculation of Fm,tot. Mean muscle fibre lengths and length changes were described in [14].