Synthesis and Construction of a Family of One-DOF Highly Overconstrained Deployable Polyhedral Mechanisms (DPMs)

2012 ◽  
Author(s):  
Guowu Wei ◽  
Jian Dai
Keyword(s):  
Equation Method ◽  
Reciprocating Motion ◽  
Mobility Analysis ◽  
Plane Symmetric ◽  
Kinematic Chains ◽  
Loop Equation ◽  
Euler’S Formula ◽  
The Family

This paper presents a family of one-DOF highly overconstrained regular and semi-regular deployable polyhedral mechanisms (DPMs) that perform radially reciprocating motion. Based on two fundamental kinematic chains with radially reciprocating motion, i.e. the PRRP chain and a novel plane/semi-plane-symmetric spatial eight-bar linkage, two methods, i.e. the virtual-axis-based (VAB) method and the virtual-centre-based (VCB) method are proposed for the synthesis of the family of regular and semi-regular DPMs. Procedure and principle for synthesizing the mechanisms are presented and selected DPMs are constructed based on the five regular Platonic polyhedrons and the semi-regular Archimedean polyhedrons, Prism polyhedrons and Johnson polyhedrons. Mobility of the mechanisms is then analysed and verified using screw-loop equation method and degree of overconstraint of the mechanisms are investigated by combing the Euler’s formula for polyhedrons and the Grübler-Kutzbach formula for mobility analysis of linkages.

Synthesis, Mobility, and Multifurcation of Deployable Polyhedral Mechanisms With Radially Reciprocating Motion

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Guowu Wei ◽  
Yao Chen ◽  
Jian S. Dai
Keyword(s):  
Geometric Constraints ◽  
Reciprocating Motion ◽  
Single Plane ◽  
Plane Symmetric ◽  
Loop Equation ◽  
Dual Plane ◽  
Potential Applications ◽  
Number Synthesis ◽  
First Time ◽  
Geometry And Kinematics

Extending the method coined virtual-center-based (VCB) for synthesizing a group of deployable platonic mechanisms with radially reciprocating motion by implanting dual-plane-symmetric 8-bar linkages into the platonic polyhedron bases, this paper proposes for the first time a more general single-plane-symmetric 8-bar linkage and applies it together with the dual-plane-symmetric 8-bar linkage to the synthesis of a family of one-degree of freedom (DOF) highly overconstrained deployable polyhedral mechanisms (DPMs) with radially reciprocating motion. The two 8-bar linkages are compared, and geometry and kinematics of the single-plane-symmetric 8-bar linkage are investigated providing geometric constraints for synthesizing the DPMs. Based on synthesis of the regular DPMs, synthesis of semiregular and Johnson DPMs is implemented, which is illustrated by the synthesis and construction of a deployable rectangular prismatic mechanism and a truncated icosahedral (C60) mechanism. Geometric parameters and number synthesis of typical semiregular and Johnson DPMs based on the Archimedean polyhedrons, prisms and Johnson polyhedrons are presented. Further, movability of the mechanisms is evaluated using symmetry-extended rule, and mobility of the mechanisms is verified with screw-loop equation method; in addition, degree of overconstraint of the mechanisms is investigated by combining the Euler's formula for polyhedrons and the Grübler–Kutzbach formula for mobility analysis of linkages. Ultimately, singular configurations of the mechanisms are revealed and multifurcation of the DPMs is identified. The paper hence presents an intuitive and efficient approach for synthesizing PDMs that have great potential applications in the fields of architecture, manufacturing, robotics, space exploration, and molecule research.

Linkages That Transfer Rotations to Radially Reciprocating Motion

2010 ◽  
Author(s):  
Guowu Wei ◽  
Jian S. Dai
Keyword(s):  
Constraint Equation ◽  
Equation Method ◽  
Reciprocating Motion ◽  
Loop Equation ◽  
Revolute Joints ◽  
Kinematic Characteristics ◽  
Overconstrained Linkages ◽  
Geometry And Kinematics

Stemming from study of polyhedral and spheroidal linkages and investigation of reciprocating motion of the PRRP chain, this paper presents four overconstrained linkages that are capable of transferring rotations to radially reciprocating motion. The linkages connected by revolute joints are of symmetrical arrangement and mobility one and are analysed by using the screw-loop equation method. The paper further investigates geometry and kinematics of the linkages and reveals their kinematic characteristics, leading to the constraint equation.

Protein Molecules as Natural Nano Bio Devices: Mobility Analysis

2010 ◽  
Author(s):  
Zahra Shahbazi ◽  
Horea T. Ilies¸ ◽  
Kazem Kazerounian
Keyword(s):  
Degrees Of Freedom ◽  
Conformational Transitions ◽  
Living Cells ◽  
Mobility Analysis ◽  
Folding Process ◽  
Kinematic Chains ◽  
Protein Molecules ◽  
Kinematic Models ◽  
Lower Mobility ◽  
Molecular Components

Proteins are nature’s nano-robots in the form of functional molecular components of living cells. The function of these natural nano-robots often requires conformational transitions between two or more native conformations that are made possible by the intrinsic mobility of the proteins. Understanding these transitions is essential to the understanding of how proteins function, as well as to the ability to design and manipulate protein-based nano-mechanical systems [1]. Modeling protein molecules as kinematic chains provides the foundation for developing powerful approaches to the design, manipulation and fabrication of peptide based molecules and devices. Nevertheless, these models possess a high number of degrees of freedom (DOF) with considerable computational implications. On the other hand, real protein molecules appear to exhibits a much lower mobility during the folding process than what is suggested by existing kinematic models. The key contributor to the lower mobility of real proteins is the formation of Hydrogen bonds during the folding process.

Design and Mobility Analysis of Large Deployable Mechanisms Based on Plane-Symmetric Bricard Linkage

2016 ◽  
Author(s):  
Xiaozhi Qi ◽  
Bing Li ◽  
Zhihuai Miao ◽  
Hailin Huang
Keyword(s):  
Computer Aided Design ◽  
Closed Loop ◽  
Degree Of Freedom ◽  
Mobility Analysis ◽  
Plane Symmetric ◽  
Analysis And Design ◽  
Geometric Conditions ◽  
Deployable Mechanism ◽  
Vertical Bars ◽  
Aided Design

In this paper, a class of large deployable mechanisms constructed by plane-symmetric Bricard linkage is presented. The plane-symmetric Bricard linkage is a closed-loop over-constrained spatial mechanism composed of six hinge-jointed bars, which has one plane of symmetry during its deployment process. The kinematic analysis of the linkage is presented from the perspectives of geometric conditions, closure equations and degree of freedom. The results illustrates that the linkage has one degree of freedom, and it can be deployed from the folded configuration to one rectangle plane. Therefore, the plane-symmetric Bricard linkage can be used to construct lager deployable mechanism as basic deployable unit. Four plane-symmetric Bricard linkages can be assembled to a quadrangular module by sharing the vertical bars of adjacent units. The module is a multi-loop deployable mechanism and has one degree of freedom by the mobility analysis. Large deployable mast, deployable plane truss and deployable ring are built by a plurality of plane-symmetric Bricard linkages. The computer-aided design models for typical examples are built to illustrate their feasibility and validate the analysis and design methods.

Identification of kinematic chains and distinct mechanisms using extended adjacency matrix

2007 ◽  
Vol 221 (1) ◽  
pp. 81-88 ◽  
Author(s):  
A Mohammad ◽  
R A Khan ◽  
V P Agrawal
Keyword(s):  
Adjacency Matrix ◽  
Kinematic Chain ◽  
Theoretic Approach ◽  
Kinematic Chains ◽  
Graph Theoretic ◽  
The Past ◽  
Graph Theoretic Approach ◽  
The Family ◽  
Eigen Value ◽  
Eigen Values

Development of the methods for generating distinct mechanisms derived from a given family of kinematic chains has been persued by a number of researchers in the past, as the distinct kinematic structures provide distinct performance characteristics. A new method is proposed to identify the distinct mechanisms derived from a given kinematic chain in this paper. Kinematic chains and their derived mechanisms are represented in the form of an extended adjacency matrix [EA] using the graph theoretic approach. Two structural invariants derived from the eigen spectrum of the [EA] matrix are the sum of absolute eigen values EA∑ and maximum absolute eigen value EAmax. These invariants are used as the composite identification number of a kinematic chain and mechanism and are tested to identify the all-distinct mechanisms derived from the family of 1-F kinematic chains up to 10 links. The identification of distinct kinematic chains and their mechanisms is necessary to select the best possible mechanism for the specified task at the conceptual stage of design.

Design and locomotion analysis of a novel deformable mobile robot with two spatial reconfigurable platforms and three kinematic chains

2016 ◽  
Vol 231 (8) ◽  
pp. 1481-1499 ◽  
Author(s):  
Wan Ding ◽  
Qiang Ruan ◽  
Yan-an Yao
Keyword(s):  
Mobile Robot ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Three Dimensional Model ◽  
Dynamic Simulations ◽  
Gait Planning ◽  
Plane Symmetric ◽  
Kinematic Chains ◽  
Reconfigurable Platforms ◽  
Actuation Systems

A novel five degrees of freedom deformable mobile robot composed of two spatial reconfigurable platforms and three revolute–prismatic–spherical kinematic chains acting in parallel to link the two platforms is proposed to realize large deformation capabilities and multiple locomotion modes. Each platform is an improved deployable single degrees of freedom three-plane-symmetric Bricard linkage. By taking advantage of locomotion collaborating among platforms and kinematic chains, the mobile robot can fold into stick-like shape and possess omnidirectional rolling and worm-like motions. The mechanism design, kinematics, and locomotion feasibility are the main focus. Through kinematics and gait planning, the robot is analyzed to have the capabilities of rolling and turning. Based on its deformation, the worm-like motion performs the ability to overcome narrow passages (such as pipes, holes, gaps, etc.) with large range of variable size. Dynamic simulations with detailed three-dimensional model are carried out to verify the gait planning and provide the variations of essential motion and dynamic parameters in each mode. An experimental robotic system with servo and pneumatic actuation systems is built, experiments are carried out to verify the validity of the theoretical analysis and the feasibility of the different locomotion functions, and its motion performances are compared and analyzed with collected data.

Critical Review of Existing Degeneracy Testing and Mobility Type Identification Algorithms for Kinematic Chains

2005 ◽  
Author(s):  
Rajesh Pavan Sunkari ◽  
Linda C. Schmidt
Keyword(s):  
Critical Review ◽  
Kinematic Chain ◽  
Structural Studies ◽  
Mobility Analysis ◽  
Structural Synthesis ◽  
Common Error ◽  
Kinematic Chains ◽  
The Individual ◽  
Almost All ◽  
Mathematical Justification

Mobility analysis is one of the fundamental problems of structural studies of kinematic chains. Degeneracy testing, an important step in structural synthesis, can be considered as a part of the mobility analysis due to the similarity of the two problems. One common error in the algorithms for these two problems is the assumption that the graph of a planar kinematic chain is a planar graph. This work shows that almost all the mobility analysis algorithms, except that of Lee and Yoon, have this error. This work also critically reviews the two most efficient algorithms on degeneracy testing, those by Hwang and Hwang, and Lee and Yoon. It is shown that due to the errors in the Hwang and Hwang’s algorithm, it failed to identify some of the degenerate chains. Furthermore, the accuracy of the Lee and Yoon’s algorithms for mobility analysis and degeneracy testing is proved by providing the mathematical justification of the individual steps of the algorithms.

Mobility of Single Loop Linkages: A Final Word?

2007 ◽  
Author(s):  
Jose´ Mari´a Rico ◽  
J. Jesu´s Cervantes ◽  
Juan Rocha ◽  
Jaime Gallardo ◽  
Luis Daniel Aguilera ◽  
...  
Keyword(s):  
Mobility Analysis ◽  
Additional Insight ◽  
Final Word ◽  
Single Loop ◽  
Kinematic Chains ◽  
Recent Developments ◽  
The Subject ◽  
Insight Into

Setting aside paradoxical linkages such as Bennett’s, Bricard’s or Goldberg’s, the mobility of single loop linkages seemed, with the developments on mobility analysis carried out in the last five years, a closed chapter in kinematic research. However, recent developments on the mobility of parallel platforms have shed additional insight into the problem. This contribution attempts to unify the results obtained in the last five years in the area of mobility of single-loop kinematic chains to state what appears to be a final word on the subject.

Reconfiguration of the plane-symmetric double-spherical 6R linkage with bifurcation and trifurcation

2015 ◽  
Vol 230 (3) ◽  
pp. 473-482 ◽  
Author(s):  
Ketao Zhang ◽  
Jian S Dai
Keyword(s):  
System Theory ◽  
Geometric Constraints ◽  
Plane Symmetric ◽  
Kinematic Chains ◽  
Constraint Analysis ◽  
Motion Parameters

This study presents a double-spherical 6R overconstrained linkage which is a variant of the Sarrus linkage and investigates its constraint-induced bifurcation and trifurcation. In light of the unique geometry of the double-spherical 6R linkage, which is also a typical plane-symmetric Bricard 6R loop, its parametric constraints are explored. Based on constraint analysis in screw system theory, both design and motion parameters that lead to constraint singularities are revealed and the transitory positions for bifurcation and trifurcation are identified among geometric constraints induced singular positions. The analysis reveals that the presented 6R overconstrained linkage is able to reconfigure its configurations by passing transitory positions and to evolve to distinct motion branches including spherical 4R linkages and serial kinematic chains.

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