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.

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.

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.

Kinematics Analysis and Simulation of a New Type of Mechanical Excavator with Controllable Mechanism

2011 ◽  
Vol 201-203 ◽  
pp. 220-224 ◽  
Author(s):  
Gan Wei Cai ◽  
Zhuan Zhang ◽  
Yu Chen Pan ◽  
Du Chao Wu ◽  
Xi Yong Xu
Keyword(s):  
Simulation Study ◽  
Inverse Kinematics ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Maintenance Cost ◽  
Hydraulic Excavator ◽  
Kinematics Analysis ◽  
Constraint Equations ◽  
New Type

A new type of excavator is introduced in this paper aiming at solving the problems the hydraulic excavator and traditional mechanical excavator (also called Electric Shovel) have respectively, which are hydraulic leaks and high maintenance cost of the former one and the lack of flexibility of the latter one. The analysis of the proposed novel excavator is carried out including: Degree-of-Freedom (DOF) of the new mechanism by constraint screw theory, inverse kinematics using the method of constraint equations, velocities and acceleration. A simulation study is proposed based on the analysis above. Results show that: the new type of mechanical excavator has the ability to achieve flexible trajectory output within its workspace.

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.

New Type of Two Degree of Freedom Motor Three-Dimensional Tooth Layer Field Application and Solution

2013 ◽  
Vol 391 ◽  
pp. 232-236
Author(s):  
Wen Huan Yang ◽  
Hai Xu Chen ◽  
Shuang Xie ◽  
Chun Ren Fang
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Field Application ◽  
Degree Of Freedom ◽  
Refined Method ◽  
New Type ◽  
Type Motor ◽  
Quasi Newton ◽  
Two Degree Of Freedom ◽  
Non Linear Equations

A new Multi-degree of freedom motor and its establishing of teeth layer parameters have been introduced in the paper, also including application method of database, namely using Quasi-Newton methods to solve the non-linear equations of the new motors magnetic circuit net, formed a refined method for designing and analyzing of motor. The establishment of 3d tooth layer parameters database, is provided for the calculation in the design of the new type motor conveniently.

A Mobile Bennett Network Constructed with Identical Square Panels

2021 ◽  
pp. 1-23
Author(s):  
Fufu Yang ◽  
Yuan Gao ◽  
Shuailong Lu ◽  
Kunjing Chen
Keyword(s):  
Mobile Networks ◽  
Design Parameter ◽  
Degree Of Freedom ◽  
Deployable Structures ◽  
Geometric Conditions ◽  
Application Potential

Abstract Mobile networks, constructed with simple linkages by tessellation, have great application potential in engineering as they could change their shapes according to the need of working state by one degree of freedom (DOF). However, the existing one-DOF networks are always composed of bar-like links, and cooperated membranes should be designed and fabricated additionally, which makes the design and the realization more complicated. This paper is to construct a one-DOF network of Bennett linkages with identical square panels. Geometric conditions to construct the network are derived by investigating the kinematic compatibility, kinematics is carried out to show the relationships among all Bennett linkages, and the discussion on the design parameter shows the extensibility and the deploying performance, which is validated by two physical prototypes. This work initials the construction of mobile networks with identical polygon-like links, which will simplify the fabrication and realization of deployable structures.

scholarly journals A singularity handling algorithm based on operational space control for six-degree-of-freedom anthropomorphic manipulators

2019 ◽  
Vol 16 (3) ◽  
pp. 172988141985891
Author(s):  
Zhi-Hao Kang ◽  
Ching-An Cheng ◽  
Han-Pang Huang
Keyword(s):  
Null Space ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Control Input ◽  
Real Time Control ◽  
Time Control ◽  
Operational Space ◽  
Industrial Manipulators ◽  
Space Motion ◽  
Six Degree Of Freedom

In this article, we analyze the singularities of six-degree-of-freedom anthropomorphic manipulators and design a singularity handling algorithm that can smoothly go through singular regions. We show that the boundary singularity and the internal singularity points of six-degree-of-freedom anthropomorphic manipulators can be identified through a singularity analysis, although they do not possess the nice kinematic decoupling property as six-degree-of-freedom industrial manipulators. Based on this discovery, our algorithm adopts a switching strategy to handle these two cases. For boundary singularities, the algorithm modifies the control input to fold the manipulator back from the singular straight posture. For internal singularities, the algorithm controls the manipulator with null space motion. We show that this strategy allows a manipulator to move within singular regions and back to non-singular regions, so the usable workspace is increased compared with conventional approaches. The proposed algorithm is validated in simulations and real-time control experiments.

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.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

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