Abstract
An elastic rod is clamped at one end and has a dead load attached to the other (free) end. The rod is then slowly rotated using the clamp. When the load is smaller than the buckling value, the rod describes a continuous set of quasi-static forms and its end traces a (smooth, convex and simple) closed curve, which would be a circle if the rod were rigid. The closed curve is analytically determined through the integration of the Euler’s elastica, so that for sufficiently small loads the mechanical system behaves as an ‘elastica compass’. For loads higher than that of buckling, the elastica reaches a configuration from which a snap-back instability occurs, realizing a sort of ‘elastica catapult’. The whole quasi-static evolution leading to the critical configuration for snapping is calculated through the elastica and the subsequent dynamic motion simulated using two numerical procedures, one ad hoc developed and another based on a finite-element scheme. The theoretical results are then validated on a specially designed and built apparatus. An obvious application of the present model would be in the development of soft robotic limbs, but the results are also of interest for the optimization analysis in pole vaulting.
Highlights
The design of innovative devices for advanced applications is being driven by the need for compliant mechanisms, which are usually inspired by nature [1,2] and is part of a transition from traditional robotics to soft robotics [3,4,5]
When the load is higher than that which would lead to buckling for the straight rod, an unstable configuration is quasi-statically reached, at which the rod suffers a snapback instability and dynamically approaches another configuration, so that the system behaves as an ‘elastica catapult’
In the simplest set-up for a flexible robot arm, an elastic rod is subject to a prescribed slow rotation at one end and to a concentrated mass in a gravity field at the other
Summary
The design of innovative devices for advanced applications is being driven by the need for compliant mechanisms, which are usually inspired by nature [1,2] and is part of a transition from traditional robotics to soft robotics [3,4,5]. The set-up of a numerical technique is a complex problem, which was analysed from several points of view, but not still completely solved [16,17,18,19,20,21] To this purpose, two approaches are presented, one is a standard use of a finite-element software (Abaqus), whereas the other is developed as a perfection of a technique introduced for pneumatic soft robot arms [22]. Two approaches are presented, one is a standard use of a finite-element software (Abaqus), whereas the other is developed as a perfection of a technique introduced for pneumatic soft robot arms [22] The latter approach, in which the elastic rod is reduced to a nonlinear spring governed by the elastica, is elegant, but the kinematics is limited to the first deformation mode and an axial deformation and viscous damping have to be added to prevent spurious numerical instabilities, issues which may be circumvented through the finite-element approach. These results open the way to a rational design of deformable robot arms and, as a side development, may find application in the analysis of the pole vault dynamics and the optimization of athletes’ performance [23,24]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
