A toy-inspired kirigami pattern and its kinematic performance by applying mechanisms and machine theory

Weiwei Lin; Kunjing Chen; Yuan Gao; Aihua Chen; Fufu Yang; Huijuan Feng

doi:10.5194/ms-12-933-2021

A toy-inspired kirigami pattern and its kinematic performance by applying mechanisms and machine theory

Mechanical Sciences ◽

10.5194/ms-12-933-2021 ◽

2021 ◽

Vol 12 (2) ◽

pp. 933-943

Author(s):

Weiwei Lin ◽

Kunjing Chen ◽

Yuan Gao ◽

Aihua Chen ◽

Fufu Yang ◽

...

Keyword(s):

Inverse Problem ◽

Degree Of Freedom ◽

Machine Theory ◽

Inverse Folding ◽

Kinematic Performance

Abstract. Origami that can form various shapes by setting simple creases on the paper and folding along these creases has a lot of applications from the fields of art to engineering. The inverse problem of origami that determines the distribution of creases based on the desired shape is very complicated. In this paper, we use theoretical kinematics to systematically analyse an inverse folding problem of a toy about how to fold a piece of paper into a disc through a smaller hole without breaking it. The results show that some four-crease and six-crease patterns can achieve the expected function, and they can be easily folded with 1 degree of freedom (DOF). It not only opens up a new way to solve the inverse folding problem but also helps students to understand mechanisms and machine theory.

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Development and evaluation of a handheld type 6 DoF midair haptic device using asymmetric vibration and a presentation force vectoring mechanism

10.21203/rs.3.rs-147091/v1 ◽

2021 ◽

Author(s):

Yuto Okuda ◽

Shunsuke Komizunai ◽

Atsushi Konno

Keyword(s):

Inverse Problem ◽

Problem Solving ◽

Degree Of Freedom ◽

Haptic Device ◽

Input And Output ◽

User Test ◽

Original Presentation ◽

Force Sense ◽

Asymmetric Vibration

Abstract This paper describes a handheld type aerial haptic device with 6 DoF (degree of freedom) using pseudo-haptics by asymmetric vibration. By introducing a original presentation force vectoring mechanism, 6 DoF force sense presentation and compactness suitable for handheld use with a small number of vibrators are realized together. In addition, a relationship between the drive input and output (presentation force sense) of the developed device is formulated, and its inverse problem solving method for obtaining the drive input that realizes a desired presentation force sense is derived. Furthermore, a user test clarified the direction in which this device can / cannot effectively exert force.

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Lagrangians for Damped Linear Multi-Degree-of-Freedom Systems

Journal of Applied Mechanics ◽

10.1115/1.4023019 ◽

2013 ◽

Vol 80 (4) ◽

Cited By ~ 6

Author(s):

Firdaus E. Udwadia ◽

Hancheol Cho

Keyword(s):

Inverse Problem ◽

Conservation Laws ◽

Degree Of Freedom ◽

Linear Vibration ◽

Gyroscopic System ◽

Simple Manner ◽

Vibration Theory ◽

Stiffness Matrices ◽

Two Degree Of Freedom ◽

Special Case

This paper deals with finding Lagrangians for damped, linear multi-degree-of-freedom systems. New results for such systems are obtained using extensions of the results for single and two degree-of-freedom systems. The solution to the inverse problem for an n-degree-of-freedom linear gyroscopic system is obtained as a special case. Multi-degree-of-freedom systems that commonly arise in linear vibration theory with symmetric mass, damping, and stiffness matrices are similarly handled in a simple manner. Conservation laws for these damped multi-degree-of-freedom systems are found using the Lagrangians obtained and several examples are provided.

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Trajectory optimisation of six degree of freedom aircraft using differential flatness

The Aeronautical Journal ◽

10.1017/aer.2018.99 ◽

2018 ◽

Vol 122 (1257) ◽

pp. 1788-1810 ◽

Cited By ~ 5

Author(s):

P. Elango ◽

R. Mohan

Keyword(s):

Inverse Problem ◽

Inverse Problems ◽

Computational Efficiency ◽

Degree Of Freedom ◽

Differential Flatness ◽

Thrust Vectoring ◽

Dynamic Soaring ◽

Six Degree Of Freedom ◽

Control Surfaces ◽

Trajectory Optimisation

ABSTRACTThe flatness of a six-degree-of-freedom (6DoF) aircraft model with conventional control surfaces – aileron, flap, rudder and elevator, along with thrust vectoring ability is established in this work. Trajectory optimisation of an aircraft can be cast as an inverse problem where the solution for control inputs that yield desired trajectories for certain states is sought. The solution to the inverse problems for certain systems is made tractable when they exhibit differential flatness. Flatness-based trajectory optimisation has a significant advantage over an equivalent collocation-based method in terms of computational efficiency and viability for real-time implementation. An application for the flatness of 6DoF aircraft is shown in the trajectory optimisation for dynamic soaring, and its connection with an equivalent 3DoF flatness-based implementation is also brought out. The results are compared with that from a collocation-based approach.

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Kinematic performance of a six degree-of-freedom hand model (6DHand) for use in occupational biomechanics

Journal of Biomechanics ◽

10.1016/j.jbiomech.2011.04.003 ◽

2011 ◽

Vol 44 (9) ◽

pp. 1805-1809 ◽

Cited By ~ 25

Author(s):

Frank L. Buczek ◽

Erik W. Sinsel ◽

Daniel S. Gloekler ◽

Bryan M. Wimer ◽

Christopher M. Warren ◽

...

Keyword(s):

Degree Of Freedom ◽

Hand Model ◽

Kinematic Performance ◽

Six Degree Of Freedom

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Kinematic performance evaluation of 2-degree-of-freedom parallel mechanism applied in multilayer garage

Advances in Mechanical Engineering ◽

10.1177/1687814018791712 ◽

2018 ◽

Vol 10 (8) ◽

pp. 168781401879171

Author(s):

Tianhua He ◽

Junpeng Shao ◽

Yongde Zhang ◽

Jingang Jiang

Keyword(s):

Parallel Mechanism ◽

Evaluation Method ◽

Degree Of Freedom ◽

Evaluation Index ◽

Global Symmetry ◽

Symmetric Structure ◽

Lower Mobility ◽

Translational Degree ◽

Kinematic Performance ◽

Simulation Results

In this article, our recent work on a kind of 2-degree-of-freedom lower-mobility parallel mechanism, which has one rotation degree of freedom and one translational degree of freedom, used in multilayer garage is presented. It has the following characteristics: lower-mobility, non-symmetric structure but can realize symmetric movement and a good compatibility for different kinds of lifting work. Kinematic performance should be considered in the first of designing a new kind of mechanism, the optimal kinematic design and analysis of this lower-mobility parallel mechanism are primarily investigated. In process of study, the global conditioning index over workspace is adopted, we establish a new evaluation method for the lower-mobility parallel mechanism, called global symmetry index and simulation results are shown. In addition, the flexible workspace of this lower-mobility parallel mechanism is also proposed. The evaluation index can be also applied on other lower-mobility parallel mechanism, which needs steady and symmetric movement.

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Inverse Problem for Lagrangian Dynamics for Multi-Degree-of-Freedom Systems With Linear Damping

Volume 4: Dynamics, Control and Uncertainty, Parts A and B ◽

10.1115/imece2012-87196 ◽

2012 ◽

Cited By ~ 1

Author(s):

Hancheol Cho ◽

Firdaus E. Udwadia

Keyword(s):

Inverse Problem ◽

Simple Procedure ◽

Degree Of Freedom ◽

Lagrangian Dynamics ◽

Mass Matrices ◽

Helmholtz Conditions ◽

Linear Damping ◽

Damped Systems ◽

Stiffness And Damping ◽

Two Degree Of Freedom

This paper deals with the inverse problem for Lagrangian dynamics for linear multi-degree-of-freedom systems. New results for linearly damped systems are obtained using extensions of results for single-degree-of-freedom systems. First, for a two-degree-of-freedom linear system with linear damping, the conditions for the existence of a Lagrangian are explicitly obtained by solving the Helmholtz conditions. Next, since the Helmholtz conditions are near-impossible to solve for general n-degree-of-freedom systems, a new simple procedure that does not require the use of the Helmholtz conditions and that is easily extended to n-degree-of-freedom linear systems, is developed. The emphasis is on obtaining the Lagrangians for these multi-degree-of-freedom systems in a simple manner, using insights obtained from our understanding of the inverse problem for single- and two-degree-of-freedom systems. Specifically we include systems that commonly arise in linear vibration theory with positive definite mass matrices, and symmetric stiffness and damping matrices. This method yields several new Lagrangians for linear multi-degree-of-freedom systems. Finally, conservation laws for these damped multi-degree-of-freedom systems are found using the Lagrangians obtained.

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Inverse Problem in Vibration for Generating Symmetric Coefficient Matrices

13th Biennial Conference on Mechanical Vibration and Noise: Vibration Analysis — Analytical and Computational ◽

10.1115/detc1991-0313 ◽

1991 ◽

Author(s):

Ladislav Starek ◽

Daniel J. Inman

Keyword(s):

Inverse Problem ◽

Eigenvalue Problem ◽

Differential Equations ◽

Spectral Data ◽

Symmetric Solution ◽

Second Order ◽

Inverse Eigenvalue Problem ◽

Degree Of Freedom ◽

Mass Damper ◽

Inverse Eigenvalue

Abstract This paper provides a symmetric solution to the inverse eigenvalue problem for systems defined by second order vector differential equations representing a multiple degree of freedom spring-mass damper system. Formulations are provided for calculating real symmetric coefficient matrices from spectral data. These relations are also defined for both simple and Jordan systems.

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