The vibro-impact capsule system in millimetre scale: numerical optimisation and experimental verification
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The vibro-impact capsule system in millimetre scale: numerical optimisation and experimental verification Yang Liu . Joseph Pa´ez Cha´vez . Jiajia Zhang . Jiyuan Tian . Bingyong Guo . Shyam Prasad
Received: 29 June 2020 / Accepted: 28 August 2020 / Published online: 18 September 2020 Ó The Author(s) 2020
Abstract The vibro-impact capsule system has been studied extensively in the past decade because of its research challenges as a piecewise-smooth dynamical system and broad applications in engineering and healthcare technologies. This paper reports our team’s first attempt to scale down the prototype of the vibroimpact capsule to millimetre size, which is 26 mm in length and 11 mm in diameter, aiming for small-bowel endoscopy. Firstly, an existing mathematical model of the prototype and its mathematical formulation as a piecewise-smooth dynamical system are reviewed in order to carry out numerical optimisation for the prototype by means of path-following techniques. Our numerical analysis shows that the prototype can Y. Liu (&) J. Zhang J. Tian B. Guo College of Engineering, Mathematics, and Physical Sciences, University of Exeter, Exeter EX4 4QF, UK e-mail: [email protected] J. Zhang e-mail: [email protected] J. Tian e-mail: [email protected]
achieve a high progression speed up to 14.4 mm/s while avoiding the collision between the inner mass and the capsule which could lead to less propulsive force on the capsule so causing less discomfort on the patient. Secondly, the experimental rig and procedure for testing the prototype are introduced, and some preliminary experimental results are presented. Finally, experimental results are compared with the numerical results to validate the optimisation as well as the feasibility of the vibro-impact technique for the potential of a controllable endoscopic procedure.
J. Pa´ez Cha´vez Center for Dynamics, Department of Mathematics, TU Dresden, 01062 Dresden, Germany S. Prasad Royal Devon and Exeter NHS Foundation Trust, Barrack Road, Exeter EX2 5DW, UK e-mail: [email protected]
B. Guo e-mail: [email protected] J. Pa´ez Cha´vez Center for Applied Dynamical Systems and Computational Methods (CADSCOM), Faculty of Natural Sciences and Mathematics, Escuela Superior Polite´cnica del Litoral, 09-01-5863 Guayaquil, Ecuador e-mail: [email protected]
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Keywords Vibro-impact Nonsmooth dynamics Numerical continuation Experiment Capsule endoscopy
1 Introduction Inspired from inchworm’s locomotion, self-propelled mobile mechanisms driven by autogenous internal force and environmental resistance have attracted great attention from applied mathematicians, experimentalists and engineers because of their theoretical challenges as piecewise-smooth dynamical systems and broad applications in robotics, e.g. [1]. The original idea of the self-propelled driving was pioneered by Chernousko [2, 3]. He proposed a twomass system to move progressively in a resistive medium when the two bodies performed periodic motions r
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