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Liferider

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- Thread starter Liferider
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In summary: I need something that is easier to use and understand. That being said, I am open to suggestions.In summary, the author is working on a robot that can move deformable objects. He is looking for references on the subject and would like some suggestions on how to calculate the deformation.

- #1

Liferider

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- #2

Ben Niehoff

Science Advisor

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The bending of a beam (and similar objects) is determined by a 4th-order equation:

http://en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory

But if you're talking about solid objects that extend generically in all directions, I don't have a good answer.

- #3

AlephZero

Science Advisor

Homework Helper

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There are lots of software packages that can do that numerically - google for "finite element analysis."

On the other hand, if you really "want to form a differential equation", you will end up with maybe 12 or more coupled partial differential equations, which usually don't have a closed-form solution.

I think what you really need to first is get clear in your mind

- #4

Liferider

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I am basically only concerned with the deformation in one dimension, the one along the gripper displacement. I also want to express a reactive force from the object, acting on the gripper fingers. Maybe I can model the reactive force as a spring (linear or not). And I would also like to include some dynamics such that the object does not retain its shape instantaneously (after a finger release).

Last edited:

- #5

Liferider

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Here are some math:

Force from object

\begin{equation}

F_{ob} = k_s (x_{ob,0} - x_{ob})

\end{equation}

\begin{equation}

\ddot{x}_{ob} = ?

\end{equation}

where $x_{ob,0}$: Equilibrium width, $x_{ob}$: Actual width. I just need to be pointed in the right direction. Regarding FEM methods, I just think it would not serve my simple purpose.

Force from object

\begin{equation}

F_{ob} = k_s (x_{ob,0} - x_{ob})

\end{equation}

\begin{equation}

\ddot{x}_{ob} = ?

\end{equation}

where $x_{ob,0}$: Equilibrium width, $x_{ob}$: Actual width. I just need to be pointed in the right direction. Regarding FEM methods, I just think it would not serve my simple purpose.

Last edited:

A differential equation for a deformable object is a mathematical equation that describes the relationship between the deformation of an object and the forces acting upon it. It is used to model the behavior of materials under external forces, such as stress and strain.

A differential equation for a deformable object is solved by using various mathematical techniques, such as separation of variables, integration, and substitution. These techniques allow us to find a general solution that describes the behavior of the object.

Differential equations for deformable objects have many applications in engineering, physics, and other scientific fields. They are used to model the behavior of materials in structures, design new materials, and understand the mechanics of various objects, such as bones, muscles, and other biological tissues.

Some common types of differential equations for deformable objects include the Navier-Stokes equations, the elasticity equations, and the wave equation. These equations have different forms and are used to model different types of deformations, such as flow, stress, and vibrations.

Differential equations for deformable objects are used to model and describe real-world scenarios, such as the behavior of bridges, buildings, and other structures under external forces. They also help us understand the behavior of biological tissues and how they respond to different types of stress and strain.

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