On some geometric properties of extremals in the optimal retargeting problem for spherically symmetric rigid bodies

2009 ◽  
Vol 44 (5) ◽  
pp. 663-670 ◽  
Author(s):  
A. N. Sirotin
Author(s):  
Peter Mann

This chapter discusses the work–energy theorem, which is developed from Newton’s second law, and defines the kinetic and potential energies of the system. While there is some vector calculus involved, it has been kept to the bare minimum and the reader should not require in-depth knowledge to understand the salient points. If there is a net force on the particle, it accelerates in the direction of the unbalanced force. The force is a central force if it depends only on the distance between the point on which the force acts and the coordinate origin. Using Stokes’s theorem, potential energies are thoroughly discussed. The chapter also discusses spherically symmetric potentials, isotropic force, force on systems of particles, centre of mass coordinates and rigid bodies.


2021 ◽  
Author(s):  
Kanata Warisaya ◽  
Hiroaki Hamanaka ◽  
Asao Tokolo ◽  
Tomohiro Tachi

Abstract Auxetic material using corner-connected kinematic tiles has been applied to different kinematic designs. However, existing works rely on the connectivity of regular polygonal tilings because of the overconstraining nature of kinematic tiling. This study proposes a new family of auxetic structures based on non-regular and aperiodic rhombic tiling inspired by the Tokyo 2020 Emblems. We convert emblem-like patterns on rhombic tilings into kinematic structures by regarding the rectangular figure as voids and the region between rectangles as rigid bodies. Due to the geometric properties of rhombic tiling, the structure forms a one-degree-of-freedom planar mechanism with a constant Poisson’s ratio of −1. The large combinatorial family of rhombic tilings provides design variations of kinematic structures with non-regular topology. Furthermore, we show a kirigami-based method for fabricating the structure as a compliant mechanism. This connection between math and art potentially broadens the range of architected materials based on folding, kirigami, and tessellation.


Sign in / Sign up

Export Citation Format

Share Document