A Novel Ortho-Triplex Tensegrity Derived by the Linkage-Truss Transformation With Prestress-Stability Analysis Using Screw Theory

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Liheng Wu ◽  
Jian S. Dai
Keyword(s):  
Stability Analysis ◽  
Quadratic Form ◽  
Screw Theory ◽  
Structural Parameters ◽  
Triangular Prism ◽  
Tensegrity Structures ◽  
Tensegrity Structure ◽  
Revolute Joints ◽  
Rigidity Analysis

Abstract This paper presents a novel tensegrity structure derived from the tensegrity triplex (also called the simplex or regular triangular prism) by using the linkage-truss transformation. In this paper, the tensegrity triplex is first transformed into a 6R linkage with vertical members as revolute joints and is coined the triplex linkage. With this, a novel 6R linkage was derived, whose joint axes are perpendicular to the joint axes of the triplex linkage and is coined the ortho-triplex linkage. Rigidity analysis based on screw theory demonstrates that both obtained linkages with infinitesimal mobility are prestress stable. Finally, transforming the ortho-triplex linkage to a truss, by using cables for tensional members and struts for compressional members, leads to a novel tensegrity that is coined ortho-triplex tensegrity. A non-dimensional quadratic form is further provided to analyze the sensitivity of prestress-stability in terms of the structural parameters. The process of derivation of this novel tensegrity presents a new way of designing tensegrity structures with prestress-stability analysis based on screw theory.

scholarly journals Closed-Form Solutions for the Form-Finding of Regular Tensegrity Structures by Group Elements

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 374 ◽  
Author(s):  
Qian Zhang ◽  
Xinyu Wang ◽  
Jianguo Cai ◽  
Jingyao Zhang ◽  
Jian Feng
Keyword(s):  
Closed Form ◽  
The Self ◽  
Eigenvalue Decomposition ◽  
Force Density ◽  
Triangular Prism ◽  
Form Finding ◽  
Tensegrity Structures ◽  
Closed Form Solutions ◽  
Tensegrity Structure ◽  
Stable Conditions

An analytical form-finding method for regular tensegrity structures based on the concept of force density is presented. The self-equilibrated state can be deduced linearly in terms of force densities, and then we apply eigenvalue decomposition to the force density matrix to calculate its eigenvalues. The eigenvalues are enforced to satisfy the non-degeneracy condition to fulfill the self-equilibrium condition. So the relationship between force densities can also be obtained, which is followed by the super-stability examination. The method has been developed to deal with planar tensegrity structure, prismatic tensegrity structure (triangular prism, quadrangular prism, and pentagonal prism) and star-shaped tensegrity structure by group elements to get closed-form solutions in terms of force densities, which satisfies the super stable conditions.

Dimensional Synthesis of a Novel 2T2R Parallel Manipulator for Medical Applications

2014 ◽  
Author(s):  
Nitish Kumar ◽  
Olivier Piccin ◽  
Bernard Bayle
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Structural Parameters ◽  
Geometric Analysis ◽  
Medical Applications ◽  
Dimensional Synthesis ◽  
Synthesis Algorithm ◽  
Percutaneous Procedures ◽  
Actuated Joints

This paper deals with the dimensional synthesis of a novel parallel manipulator for medical applications. This parallel mechanism has a novel 2T2R mobility derived from the targeted application of needle manipulation. The kinematic design of this 2T2R manipulator and its novelty are illustrated in relation to the percutaneous procedures. Due to the demanding constraints on its size and compactness, achieving a large workspace especially in orientation, is a rather difficult task. The workspace size and kinematic constraint analysis are considered for the dimensional synthesis of this 2T2R parallel mechanism. A dimensional synthesis algorithm based on the screw theory and the geometric analysis of the singularities is described. This algorithm also helps to eliminate the existence of voids inside the workspace. The selection of the actuated joints is validated. Finally, the dimensions of the structural parameters of the mechanism are calculated for achieving the required workspace within the design constraints of size, compactness and a preliminary prototype without actuators is presented.

A 2(3-RRPS) parallel manipulator inspired by Gough–Stewart platform

Robotica ◽  
2012 ◽  
Vol 31 (3) ◽  
pp. 381-388 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mario A. García-Murillo ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Triangular Prism ◽  
Input Output ◽  
Six Degrees Of Freedom ◽  
Moving Platform

SUMMARYThis study addresses the kinematics of a six-degrees-of-freedom parallel manipulator whose moving platform is a regular triangular prism. The moving and fixed platforms are connected to each other by means of two identical parallel manipulators. Simple forward kinematics and reduced singular regions are the main benefits offered by the proposed parallel manipulator. The Input–Output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. A case study, which is verified with the aid of commercially available software, is included with the purpose to exemplify the application of the method of kinematic analysis.

scholarly journals Type Synthesis Principle and Practice of Flexure Systems in the Framework of Screw Theory: Part II—Numerations and Synthesis of Complex Flexible Joints

2010 ◽  
Author(s):  
J. J. Yu ◽  
X. Pei ◽  
S. Z. Li ◽  
Hai-jun Su ◽  
J. B. Hopkins ◽  
...  
Keyword(s):  
High Performance ◽  
Screw Theory ◽  
Companion Paper ◽  
Synthesis Process ◽  
Type Synthesis ◽  
Flexible Joints ◽  
Flexible Joint ◽  
Modeling And Analysis ◽  
Revolute Joints ◽  
Application Requirements

In recent years, the increasing of application requirements call for development of a variety of high-performance (e.g. large-displacement, high-precision) flexible joints. In this paper we demonstrate how to use the proposed methodology for the type synthesis of flexure systems given in the companion paper to synthesize concepts for complex flexible joints. According to the joint characteristics other than other flexure systems, a basic design philosophy and a general type synthesis process for flexible joints are presented firstly. The numerations and type synthesis for four commonly used flexible joint types, i.e. flexible revolute joints (FRJs), flexible translational joints (FTJs), flexible universal joints (FUJs), and flexible spherical joints (FSJs) are investigated in detail. As a result, not only a variety of known flexible joints are systematically surveyed and classified, but also are some new flexible joints developed. The output of this process is the derivation of a multiple of flexible joint concepts that would then be modeled and optimized by existing modeling and analysis methods.

Design of a Statically Balanced Tensegrity Mechanism

2006 ◽  
Author(s):  
Mark Schenk ◽  
Just L. Herder ◽  
Simon D. Guest
Keyword(s):  
Prototype Model ◽  
Static Balancing ◽  
Tensegrity Structures ◽  
New Class ◽  
Tensegrity Structure ◽  
Wide Range ◽  
Prestressed Structures

The combination of static balancing and tensegrity structures has resulted in a new class of mechanisms: Statically Balanced Tensegrity Mechanisms. These are prestressed structures that are in equilibrium in a wide range of positions, and thus exhibit mechanism-like properties. This paper describes the design of a prototype model of a statically balanced tensegrity mechanism based on a classic tensegrity structure.

Effects of the prestress levels on the stiffness of prismatic and star-shaped tensegrity structures

2016 ◽  
Vol 22 (9) ◽  
pp. 1866-1875 ◽  
Author(s):  
Jianguo Cai ◽  
Yuhang Zhou ◽  
Jian Feng ◽  
Xiaowei Deng ◽  
Yongming Tu
Keyword(s):  
Stiffness Matrix ◽  
Eigenvalue Analysis ◽  
Numerical Examples ◽  
Tensegrity Structures ◽  
Tensegrity Structure ◽  
Geometric Stiffness ◽  
Analytical Results ◽  
Material Stiffness

On the basis of the introduction of the stiffness matrix of tensegrity structures, the eigenvalue analysis is carried out to study the influence of the prestress level on the stiffness of tensegrity structures. The triangular prismatic tensegrity structure, the star-shaped tensegrity structure and the star-shaped tensegrity structure with a central strut are selected as the numerical examples. The analytical results show that some eigenvalues increase linearly with the prestress level, whereas other eigenvalues firstly increase and then decrease or firstly decrease and then increase with the increase of the prestress level. This is because the stiffness matrix of the tensegrity structures is mainly composed of the material stiffness matrix and geometric stiffness matrix. As the contribution of these two parts of stiffness to eigenvalue models is different, the trends of eigenvalue variations are different with the increase of the prestressed level.

scholarly journals Research on Stiffness of Multibackbone Continuum Robot Based on Screw Theory and Euler-Bernoulli Beam

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Bin He ◽  
Shoulin Xu ◽  
Zhipeng Wang
Keyword(s):  
Numerical Analysis ◽  
External Load ◽  
Screw Theory ◽  
Structural Parameters ◽  
Bernoulli Beam ◽  
Continuum Robots ◽  
Single Section ◽  
Stiffness Model ◽  
Continuum Robot ◽  
Euler Bernoulli Beam

Continuum robots have become a focus for extensive research, since they can work well in complex and confined environments. The main contribution of this paper is to establish a stiffness model of a single section multibackbone continuum robot and analyze the effect of the structural parameters of continuum robot on the overall rotation and translation stiffness. First, a stiffness model which indicates the end configuration of continuum robot under external load is deduced by the screw theory and Euler-Bernoulli beam. Then, the stiffness elements are fully analyzed, therefore, obtaining the influence of the structural parameters of continuum robot on the stiffness elements. Meanwhile, a numerical analysis of stiffness elements is given. Furthermore, the minimum and maximum rotation/translation stiffness are introduced to analyze the effect of the structural parameters of continuum robot on the overall rotation and translation stiffness. Finally, the experiments are used to validate the proposed stiffness model. The experimental results show that the proposed stiffness model of continuum robot is correct and the errors are less than 7%.

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