Research Papers

Kinetic Shapes: Analysis, Verification, and Applications

[+] Author and Article Information
Ismet Handz̆ić

Department of Mechanical Engineering,
University of South Florida,
Tampa, FL 33620
e-mail: ihandzic@mail.usf.edu

Kyle B. Reed

Department of Mechanical Engineering,
University of South Florida,
Tampa, FL 33620
e-mail: kylereed@mail.usf.edu

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 1, 2013; final manuscript received March 3, 2014; published online April 11, 2014. Assoc. Editor: Oscar Altuzarra.

J. Mech. Des 136(6), 061005 (Apr 11, 2014) (8 pages) Paper No: MD-13-1500; doi: 10.1115/1.4027168 History: Received November 01, 2013; Revised March 03, 2014

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.

Copyright © 2014 by ASME
Topics: Shapes
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Fig. 1

A circular wheel on a decline and a shape with a negatively changing radius are instantaneously equivalent in rolling dynamics

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Fig. 2

(a) Static equilibrium of a kinetic shape. (b) Kinetic shape geometric parameters.

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Fig. 3

Schematic of test structure for 2D kinetic shapes

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Fig. 4

(a) 2D Shape 1 forms a spiral with a steadily increasing radius as it is defined by a constant vertical force input and a constant RGRF output all around the shape. (b) 2D Shape 2 forms a monotonically increasing radius spiral, however when a constant weight is applied, it reacts with a sinusoidal RGRF around its perimeter. (c) 2D Shape 3 forms a continuous shape because, when a constant weight input is applied, it initially reacts with a positive reaction force and then switches directions to form a negative RGRF. All physical measurements are in good agreement.

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Fig. 5

A flat plate with a known mass is dispensed with a predicted linear acceleration

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Fig. 6

Dynamic interaction of 2D Shape 2 onto a flat plate (0.5 kg). The applied weight is constant as the kinetic shape pushes the plate.

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Fig. 7

When disturbed or placed at an unstable position, a two-dimensional kinetic shape settles at its equilibrium point

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Fig. 8

While a cylinder only produces a RGRF force to keep it from slipping, a helix curve produces an additional TGRF for sideways rolling, as illustrated in this figure

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Fig. 9

Free body force diagram of a 3D kinetic shape

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Fig. 10

Geometric parameters at 3D shape ground contact

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Fig. 11

(a) Radial and tangential ground reaction force definition of 3D KS. (b) Derived 3D surface and 3D curve KS, where the curve is the surface center.

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Fig. 12

A kinetic shape derived to react with a constant 100 N radial force when nonconstant walking weight is applied




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