Kinetic Shapes: Analysis, Verification, and Applications

Abstract

A circular shape placed on an incline will roll; similarly, an irregularly shaped object, such as the Archimedean spiral, will roll on a flat surface when a force is applied to its axle. This rolling is dependent on the specific shape and the applied force (magnitude and location). In this paper, we derive formulas that define the behavior of irregular 2D and 3D shapes on a flat plane when a weight is applied to the shape's axle. These kinetic shape (KS) formulas also define and predict shapes that exert given ground reaction forces when a known weight is applied at the axle rotation point. Three 2D KS design examples are physically verified statically with good correlation to predicted values. Motion simulations of unrestrained 2D KS yielded expected results in shape dynamics and self-stabilization. We also put forth practical application ideas and research for 2D and 3D KS such as in robotics and gait rehabilitation.

The musical kinetic shape: A variable tension string instrument

“…While our prototype only utilizes one revolution around a kinetic shape, it is possible to design a very similar instrument with a greater range by creating a kinetic shape with more than one revolution, or even a 3D kinetic shape [15] that is attached to two string with two independent tensions. Although this prototype is used to generate music, the same concept can be applied to manufacture strain gages that have adjustable sensitivity.…”

“…It is possible to mechanically vary a force creating variable string tension through the use of a kinetic shape [15] attached to the string. To understand this concept, the kinetic shape is explained as follows.…”

“…A two-dimensional shape can be derived which when a known weight is applied to the shape, will exert a predicted horizontal force. This 2D kinetic shape equation as described in [15] is Equation 2.…”

“…The 2D kinetic shape equation (Equation 2) [15] indicates that the total dimensions of a kinetic shape are irrelevant, while only the curvature of the shape contributes to its behavior. However, preliminary tests concluded that in practice, a larger kinetic shape will produce more accurate results than an overall smaller one due to the fact that a smaller kinetic shape will be more a↵ected by fabrication/surface imperfections and misalignment during use.…”

Two-Dimensional Kinetic Shape Dynamics: Verification and Application

“…The concept and approach of the kinetic shape (KS) [1] offer a way to analyze these types of dynamics problems. The KS equation defines a smooth shape in static equilibrium that can produce exact and predictable reaction forces when forced onto a flat surface.…”