Mobility and Kinematic Analysis of Foldable Plate Structures Based on Rigid Origami

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Jianguo Cai ◽  
Zelun Qian ◽  
Chao Jiang ◽  
Jian Feng ◽  
Yixiang Xu
Keyword(s):  
Kinematic Analysis ◽  
Jacobian Matrix ◽  
Null Space ◽  
Building Structures ◽  
Rigid Plate ◽  
Deployable Structures ◽  
Plate Structures ◽  
Constraint Equations ◽  
New Type ◽  
System Constraint

As one new type of deployable structures, foldable plate structures based on origami are more and more widely used in aviation and building structures in recent years. The mobility and kinematic paths of foldable origami structures are studied in this paper. Different constraints including the rigid plate, spherical joints, and the boundary conditions of linkages were first used to generate the system constraint equations. Then, the degree-of-freedom (DOF) of the foldable plate structures was calculated from the dimension of null space of the Jacobian matrix, which is the derivative of the constraint equations with respect to time. Furthermore, the redundant constraints were found by using this method, and multiple kinematic paths existing in origami structures were studied by obtaining all the solutions of constraint equations. Different solutions represent different kinematic configurations. The DOF and kinematic paths of a Miura-ori and a rigid deployable antenna were also investigated in detail.

Mobility and Kinematic Paths of Foldable Origami Structures

2016 ◽  
Author(s):  
Jianguo Cai ◽  
Zelun Qian ◽  
Jian Feng ◽  
Chao Jiang ◽  
Yixiang Xu
Keyword(s):  
Jacobian Matrix ◽  
Null Space ◽  
Degree Of Freedom ◽  
Building Structures ◽  
Deployable Structures ◽  
Plate Structures ◽  
Constraint Equations ◽  
All Solutions ◽  
New Type ◽  
System Constraint

As one new type of deployable structures, foldable plate structures based on origami are more and more widely used in aviation and building structures in recent years. The mobility and kinematic paths of foldable origami structures are studied in this paper. Different constraints including the rigid plate, pin joints and the boundary conditions of linkages were firstly used to generate the system constraint equations. Then the degree of freedom (DOF) of the foldable plate structures was calculated from the dimension of null space of the Jacobian matrix, which is the derivative of the constraint equations with respect to time. Furthermore, the redundant constraints were found by using this method and multiple kinematic paths existing in origami structures were studied by obtaining all solutions of constraint equations. Different solutions represent different kinematic configurations. The degree of freedom and kinematic paths of a Miura-ori and a rigid deployable antenna were also investigated in details.

scholarly journals Constraint Analysis and Redundancy of Planar Closed Loop Double Chain Linkages

2014 ◽  
Vol 6 ◽  
pp. 635423 ◽  
Author(s):  
Jianguo Cai ◽  
Xiaowei Deng ◽  
Yixiang Xu ◽  
Jian Feng
Keyword(s):  
Boundary Conditions ◽  
Closed Loop ◽  
Jacobian Matrix ◽  
Null Space ◽  
Degree Of Freedom ◽  
Double Chain ◽  
Constraint Equations ◽  
System Constraint ◽  
Natural Coordinate ◽  
Planar Linkages

This paper studies the kinematics of planar closed double chain linkages using the natural coordinate method. Different constraints including the rigid bar, pin joint, generalized angulated element (GAE) joint, and the boundary conditions of linkages were firstly used to form the system constraint equations. Then the degree of freedom of the linkages was calculated from the dimension of null space of the Jacobian matrix, which is the derivative of the constraint equations with respect to time. Furthermore, the redundant constraints can also be given by this method. Many types of planar linkages, such as the Hoberman linkage, Types I and II GAEs, nonintersecting GAEs, and linkages with the loop parallelogram condition, were investigated in this paper. It is found that when three boundary conditions are added to the system, the global motion of the system is lost. The results show that these linkages have only one degree of freedom. Moreover, the last two GAE constraints of the numerical examples given in this paper are redundant.

A New Simplified Approach to the Kinematic Analysis and Design of Epicyclic Gearboxes

1995 ◽  
Vol 209 (1) ◽  
pp. 49-53 ◽  
Author(s):  
A A Fogarasy ◽  
M R Smith
Keyword(s):  
Kinematic Analysis ◽  
Building Blocks ◽  
Kinematic Constraint ◽  
Simplified Approach ◽  
Analysis And Design ◽  
Constraint Equations ◽  
Epicyclic Gear ◽  
Simplified Method ◽  
New Type ◽  
Gear Drives

The present paper introduces a much simplified method for the kinematic analysis of epicyclic gear drives. It is based on the concept of the existence of only two basic building blocks and their kinematic constraint equations. These can easily be found by inspection of the relevant kinematic structural diagram. A new type of notation is used which is simpler and more versatile than those of previous methods and is adaptable to depicting the kinematic alternatives of any particular drive without the need for drawing structural diagrams.

Kinematic Analysis of a Three-DOF Parallel Mechanism for Telescope Applications

1997 ◽  
Author(s):  
J. A. Carretero ◽  
M. Nahon ◽  
B. Buckham ◽  
C. M. Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Constraint Equations ◽  
Forward And Inverse Kinematics ◽  
Position And Orientation ◽  
Three Degree Of Freedom ◽  
Three Degrees Of Freedom

Abstract This paper presents a kinematic analysis of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described and its forward and inverse kinematics solutions are derived. Because the mechanism has only three degrees of freedom, constraint equations must be generated to describe the inter-relationship between the six Cartesian coordinates which describe the position and orientation of the moving platform. Once these constraints are incorporated into the kinematics model, a constrained Jacobian matrix is obtained. The stiffness and dexterity properties of the mechanism are then determined based on this Jacobian matrix. The mechanism is shown to exhibit desirable properties in the region of its workspace of interest in the telescope focussing application.

Natural Dynamics of Robot Manipulators in the Presence of Obstacles

1991 ◽  
Vol 113 (1) ◽  
pp. 170-174
Author(s):  
T. Jia ◽  
F. M. L. Amirouche
Keyword(s):  
Collision Detection ◽  
Jacobian Matrix ◽  
Null Space ◽  
Robot Manipulators ◽  
Dynamic Control ◽  
Inequality Constraints ◽  
Dimensional Problem ◽  
Constraint Equations ◽  
Natural Dynamics ◽  
Natural Dynamic

This paper presents the natural dynamic control problem of robot manipulators and its application to collision avoidance and path planning. A set of moving convex obstacles (or polyhedron) are modeled to achieve the desired conditions for collision detection and avoidance. The conditions represent a set of inequality constraints which are automatically incorporated to assure collision free motion. A minimum dimensional problem is achieved through the use of the null space of the Jacobian matrix associated with the constraint equations. A simple example to illustrate the procedures developed above is given.

Symmetry-Based Transformable and Foldable Plate Structures

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Valentina Beatini
Keyword(s):  
The Other ◽  
Rigid Plate ◽  
Plate Structures ◽  
Symmetry Operations

This paper presents a novel family of modular flat-foldable rigid plate structures composed by assemblies of 4R-linkages. First, in the field of foldable plates, the proposed system is characterized by being not only foldable but also transformable: the slope of one module over the other is capable of changing not only magnitude but also sign. This transformable behavior extends the range of application of foldable plates from simply larger–smaller configurations to substantially different configurations and usages. The transformable curve is obtained by means of symmetry operations on the spherical length of links. For each module, three configurations can be designed. Various examples are illustrated.

Kinematic Analysis and Synthesis of Three-Input, Eight-Bar Mechanisms Driven by Relatively Small Cranks

1992 ◽  
Author(s):  
Kambiz Farhang ◽  
Partha Sarathi Basu
Keyword(s):  
Nonlinear Equations ◽  
Kinematic Analysis ◽  
Linear Equations ◽  
Output Link ◽  
Analysis And Design ◽  
Constraint Equations ◽  
Analysis And Synthesis ◽  
The Mean ◽  
Approximate Equations

Abstract Approximate kinematic equations are developed for the analysis and design of three-input, eight-bar mechanisms driven by relatively small cranks. Application of a method in which an output link is presumed to be comprised of a mean and a perturbational motions, along with the vector loop approach facilitates the derivation of the approximate kinematic equations. The resulting constraint equations are, (i) in the form of a set of four nonlinear equations relating the mean link orientations, and (ii) a set of four linear equations in the unknown perturbations (output link motions). The latter set of equations is solved, symbolically, to obtain the output link motions. The approximate equations are shown to be effective in the synthesis of three-input, small-crank mechanisms.

Architecture Optmization of a 3-DOF Parallel Mechanism

1998 ◽  
Author(s):  
J. A. Carretero ◽  
R. P. Podhorodeski ◽  
M. Nahon
Keyword(s):  
Parallel Mechanism ◽  
Architectural Design ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Design Parameters ◽  
Objective Functions ◽  
Constraint Equations ◽  
Three Degree Of Freedom ◽  
Architecture Optimization ◽  
Three Degrees Of Freedom

Abstract This paper presents a study of the architecture optimization of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described. Since the mechanism has only three degrees of freedom, constraint equations describing the inter-relationship between the six Cartesian coordinates are given. These constraints allow us to define the parasitic motions and, if incorporated into the kinematics model, a constrained Jacobian matrix can be obtained. This Jacobian matrix is then used to define a dexterity measure. The parasitic motions and dexterity are then used as objective functions for the optimizations routines and from which the optimal architectural design parameters are obtained.

Forward/Reverse Velocity and Acceleration Analysis for a Class of Lower-Mobility Parallel Mechanisms

2006 ◽  
Vol 129 (4) ◽  
pp. 390-396 ◽  
Author(s):  
Si J. Zhu ◽  
Zhen Huang ◽  
Hua F. Ding
Keyword(s):  
Kinematic Analysis ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Rear Part ◽  
Lower Mobility ◽  
Acceleration Analysis

This paper proposes a novel kinematic analysis method for a class of lower-mobility mechanisms whose degree-of-freedom (DoF) equal the number of single-DoF kinematic pairs in each kinematic limb if all multi-DoF kinematic pairs are substituted by the single one. For such an N-DoF (N<6) mechanism, this method can build a square (N×N) Jacobian matrix and cubic (N×N×N) Hessian matrix. The formulas in this method for different parallel mechanisms have unified forms and consequently the method is convenient for programming. The more complicated the mechanism is (for instance, the mechanism has more kinematic limbs or pairs), the more effective the method is. In the rear part of the paper, mechanisms 5-DoF 3-R(CRR) and 5-DoF 3-(RRR)(RR) are analyzed as examples.

Coordinate Reduction in the Dynamics of Constrained Multibody Systems—A New Approach

1988 ◽  
Vol 55 (4) ◽  
pp. 899-904 ◽  
Author(s):  
S. K. Ider ◽  
F. M. L. Amirouche
Keyword(s):  
Null Space ◽  
Computationally Efficient ◽  
New Approach ◽  
Constraint Equations ◽  
Kane’S Equations ◽  
Linearly Independent ◽  
Kane's Equations ◽  
Constrained Dynamical Systems ◽  
Coordinate Reduction ◽  
Algebraic Constraint

In this paper a new theorem for the generation of a basis for the null space of a rectangular matrix, with m linearly independent rows and n (n > m) columns is presented. The method is based on Gaussian row operations to transform the constraint Jacobian matrix to an uptriangular matrix. The Gram-Schmidt process is then utilized to identify basis vectors orthogonal to the uptriangular matrix. A complement orthogonal array which forms the basis for the null space for which the algebraic constraint equations are satisfied is then formulated. An illustration of the theorem application to constrained dynamical systems for both Lagrange and Kane’s equations is given. A numerical computer algorithm based on Kane’s equations with embedded constraints is also presented. The method proposed is well conditioned and computationally efficient and inexpensive.

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