The problem of wrapping of a strand over a surface is ubiquitous, such as in biomechanics for muscle length and muscle length rate estimation, or in robotics when wires are guided over non-circular surfaces. Hereby, continuous solutions are sought, as discrete solutions generate jumps in the position which lead to spikes in velocity and acceleration transmission. Up to now, the continuous problem has been solved only for infinitesimally thin lines using a chain of geodesics. In continuation of previous papers on a completely novel approach for continuous wrapping of thick strands of constant length, this paper regards now the problem of extendible midlines including cross-contraction, which is shown to generate again fundamentally new transmission equations including perturbation theory. Due to the complexity of the ensuing differential equations, only the 2D case is regarded, i.e. where the “surface” is a curve. However, the results can be transferred to the 3D case with general surfaces as the normal curvature along the geodesic line. The effectiveness of the approach is shown for the case of a parabolic convex muscle on an elliptical surface.
Smooth Wrapping of Stretchable Thick Strands Over a Surface - The 2D Case
Springer Proceedings in Advanced Robotics
International Symposium on Advances in Robot Kinematics ; 2022 ; Bilbao, Spain June 26, 2022 - June 30, 2022
2022-06-18
8 pages
Article/Chapter (Book)
Electronic Resource
English
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