Table of Contents
Journal of Nonlinear Dynamics
Volume 2016, Article ID 8124015, 15 pages
Research Article

Two-Dimensional Kinetic Shape Dynamics: Verification and Application

1Tao Life Sciences, Greenville, SC, USA
2The University of South Florida, Tampa, USA

Received 4 May 2016; Accepted 25 September 2016

Academic Editor: Thordur Runolfsson

Copyright © 2016 Ismet Handzic et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A kinetic shape (KS) is a smooth two- or three-dimensional shape that is defined by its predicted ground reaction forces as it is pressed onto a flat surface. A KS can be applied in any mechanical situation where position-dependent force redirection is required. Although previous work on KSs can predict static force reaction behavior, it does not describe the kinematic behavior of these shapes. In this article, we derive the equations of motion for a rolling two-dimensional KS (or any other smooth curve) and validate the model with physical experiments. The results of the physical experiments showed good agreement with the predicted dynamic KS model. In addition, we have modified these equations of motion to develop and verify the theory of a novel transportation device, the kinetic board, that is powered by an individual shifting their weight on top of a set of KSs.