Abstract
The elephant trunk is a highly dexterous muscular hydrostat whose continuous, distributed deformations pose significant challenges for mathematical modeling. We introduce linear "stereotypical" laws that map desired trunk configurations, parameterized by curvature and length, directly to the internal muscle-analogue forces required in our rod-based dynamic model. The trunk is represented as a simplified multi-segment structure of point masses linked through longitudinal and radial muscle analogues and connective tissue, all modeled using rods. Using these laws, the model predicts biological reaching trajectories with tip-position errors below 8% while maintaining hydrostatic volume across trials. The resulting force-shape mappings reveal consistent, repeatable internal force patterns underlying trunk postures, providing a compact representation of actuation strategies that generate specific planar shapes. By reducing high-dimensional continuum dynamics to simple linear relationships, this framework preliminarily enables the inference of muscle-force distributions from shape configurations, laying the groundwork for deeper exploration of the elephant trunk motion strategies and their translation into advanced robotic systems control.