Kinetic Shape Equations for Target Ground Reaction Forces
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Solution Overview
Problem
There is a need to determine the optimal kinetic shape for a given application to achieve a desired reactive force, as existing technologies lack methods to design and analyze two- and three-dimensional kinetic shapes that produce specific ground reaction forces when loaded with a known weight.
Innovation Solution
The development of equations for two- and three-dimensional kinetic shapes allows for the derivation of shapes that generate desired radial and tangential ground reaction forces by solving for variables such as radius, angle, and force functions, enabling the creation of shapes that produce consistent or varying reaction forces based on applied weights.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If kinetic shapes are designed to produce specific ground reaction forces, then force control precision is improved, but design complexity increases due to the need to solve complex differential equations for two- and three-dimensional shapes
Solution Approach 1:
The patent transforms the complex shape design problem into a parameter-based solution by defining kinetic shapes through mathematical parameters in differential equations. By changing the force function parameters and boundary conditions, different kinetic shapes can be generated to achieve desired ground reaction forces without redesigning the entire shape geometry each time.
Solution Approach 2:
The patent replaces traditional mechanical shape design with a mathematical modeling approach. Instead of iteratively designing and testing physical shapes, the system uses differential equations to directly calculate the kinetic shape parameters that produce the desired force profiles, substituting mechanical trial-and-error with computational mathematics.
2Force
If kinetic shapes are used to generate desired reactive forces, then force generation capability is improved, but the lack of existing design methods for two- and three-dimensional shapes limits design versatility
Solution Approach 1:
The patent creates a universal design framework that can generate kinetic shapes for various applications by solving a general differential equation. The same mathematical approach works for both two-dimensional and three-dimensional shapes, and can be adapted to different force requirements (radial, tangential, or combined), making the method versatile across multiple applications.
Solution Approach 2:
The patent extends the kinetic shape design from two-dimensional to three-dimensional by adding dimensional parameters to the differential equations. This allows the generation of complex 3D kinetic shapes that can produce ground reaction forces in multiple directions, significantly expanding design versatility while maintaining the same mathematical foundation.
3Manufacturing precision
If complex differential equations are solved to derive kinetic shapes, then manufacturing precision of force profiles is improved, but computational time and analysis complexity increase
Solution Approach 1:
The patent performs preliminary mathematical analysis to establish the differential equations and boundary conditions before actual shape generation. By pre-defining the mathematical framework and force function forms, the system reduces the computational burden during the actual shape derivation process, allowing for precise force profiles without excessive computational time for each new design.
Data Source
Figure 1~2B
Figure 3
Figure 4A~4C
AI summary
In one embodiment, a kinetic shape is designed by determining an applied force to be applied to an object that is to incorporate the kinetic shape, determining a reactive force that is desired to be produced in response to the applied force, inputting the applied force and the reactive force into a kinetic shape equation, and solving the equation to obtain the kinetic shape.