scholarly journals Mobility and Constraint Analysis of Interconnected Hybrid Flexure Systems Via Screw Algebra and Graph Theory

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Frederick Sun ◽  
Jonathan B. Hopkins
Keyword(s):  
Graph Theory ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Mobility Analysis ◽  
Element Analysis ◽  
Constraint Analysis ◽  
Computationally Expensive ◽  
Precision Motion ◽  
Automated Tool ◽  
General Method

This paper introduces a general method for analyzing flexure systems of any configuration, including those that cannot be broken into parallel and serial subsystems. Such flexure systems are called interconnected hybrid flexure systems because they possess limbs with intermediate bodies that are connected by flexure systems or elements. Specifically, the method introduced utilizes screw algebra and graph theory to help designers determine the freedom spaces (i.e., the geometric shapes that represent all the ways a body is permitted to move) for all the bodies joined together by compliant flexure elements within interconnected hybrid flexure systems (i.e., perform mobility analysis of general flexure systems). This method also allows designers to determine (i) whether such systems are under-constrained or not and (ii) whether such systems are over-constrained or exactly constrained (i.e., perform constraint analysis of general flexure systems). Although many flexure-based precision motion stages, compliant mechanisms, and microarchitectured materials possess topologies that are highly interconnected, the theory for performing the mobility and constraint analysis of such interconnected flexure systems using traditional screw theory does not currently exist. The theory introduced here lays the foundation for an automated tool that can rapidly generate the freedom spaces of every rigid body within a general flexure system without having to perform traditional computationally expensive finite element analysis. Case studies are provided to demonstrate the utility of the proposed theory.

Mobility Analysis of Interconnected Hybrid Flexure Systems Using Screw Algebra and Graph Theory

2016 ◽  
Author(s):  
Frederick Sun ◽  
Jonathan B. Hopkins
Keyword(s):  
Finite Element Analysis ◽  
Graph Theory ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Mobility Analysis ◽  
Element Analysis ◽  
Computationally Expensive ◽  
Precision Motion ◽  
Automated Tool ◽  
General Method

This paper introduces a general method for determining the mobility analysis of flexure systems of any complexity, including those that can’t be broken into parallel and serial flexure subsystems. Such systems are called interconnected hybrid flexure systems because they possess limbs with intermediate bodies that are connected by flexure systems or elements. The method in this paper utilizes screw algebra and graph theory to enable designers to determine the freedom spaces (i.e., the geometric shapes that represent all the ways a body is permitted to move) for all the bodies joined together by compliant flexure elements within interconnected hybrid flexure systems. Although many flexure-based precision motion stages, compliant mechanisms, and microarchitectured materials possess topologies that are highly interconnected, the theory for performing a mobility analysis of such interconnected flexure systems using traditional screw theory does not currently exist. The theory introduced here lays the foundation for an automated tool that can rapidly generate the freedom spaces of every rigid body within a general flexure system without having to perform traditional computationally expensive finite element analysis. Case studies are provided in the paper to demonstrate the utility of the proposed theory.

Origami Kaleidocycle-Inspired Symmetric Multistable Compliant Mechanisms

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Hongchuan Zhang ◽  
Benliang Zhu ◽  
Xianmin Zhang
Keyword(s):  
Arbitrary Number ◽  
Compliant Mechanisms ◽  
Rotation Angle ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Mobility Analysis ◽  
Stable States ◽  
Deployable Structures ◽  
Basic Dimension ◽  
Metamorphic Robots

Compliant kaleidocycles can be widely used in a variety of applications, including deployable structures, origami structures, and metamorphic robots, due to their unique features of continuous rotatability and multistability. Inspired by origami kaleidocycles, a type of symmetric multistable compliant mechanism with an arbitrary number of units is presented and analyzed in this paper. First, the basic dimension constraints are developed based on mobility analysis using screw theory. Second, the kinematic relationships of the actual rotation angle are obtained. Third, a method to determine the number of stabilities and the position of stable states, including the solution for the parameterized boundaries of stable regions, is developed. Finally, experimental platforms are established, and the validity of the proposed multistable mechanisms is verified.

Kinematics and mobility analysis of carton folds in packing manipulation based on the mechanism equivalent

2002 ◽  
Vol 216 (10) ◽  
pp. 959-970 ◽  
Author(s):  
J S Dai ◽  
J Rees Jones
Keyword(s):  
Graph Theory ◽  
Closed Form ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Mobility Analysis ◽  
Mathematical Basis ◽  
Packaging Process ◽  
Kinematic Geometry ◽  
Position And Orientation

The process of erecting and closing a carton in packing manipulation is seen as a succession of folds in position and orientation from one distinct configuration to another. Permitted manipulations and changes in shape are governed by the geometry of crease lines, dimensions and profiles of the panels. The possibility for panels to fold into successive distinct configurations is determined by the kinematic geometry. This paper presents a mathematical basis which determines the mobility of distinct configurations of a carton to include the degrees of freedom dominating the manipulation and the overconstraint configurations in an erected and closed form, and proposes the kinematic analysis of a carton during packing manipulation. Use is made of the concept of line vectors and screw theory associated with graph theory. The analysis helps to explain some configurations which show how a carton can fold and opens up the way of describing manipulation in the packaging process.

A Passive Brace to Improve Activities of Daily Living Utilizing Compliant Parallel Mechanisms

2016 ◽  
Author(s):  
J. B. Ring ◽  
Charles Kim
Keyword(s):  
Activities Of Daily Living ◽  
Range Of Motion ◽  
Daily Living ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Full Range ◽  
Physical Model Test ◽  
Parallel Mechanisms ◽  
Element Analysis ◽  
System A

Idiopathic scoliosis is a deformity of the spine that affects 2–3% of adolescents. The treatment of scoliosis often requires the use of a rigid brace to align the spine and prevent progression of the deformation. The most common brace, referred to as the Boston brace, has a high success rate in preventing progression of the scoliotic curve. The common root failure is lack of patient compliance in wearing the brace for the prescribed time. This lack in compliance is due to patient discomfort, both physically and emotional, and the patients’ limited ability to perform activities of daily living (ADL) when wearing the brace. The likelihood of needing surgery increases dramatically when bracing is unsuccessful. We seek to improve patients’ comfort by designing a brace that improves range of motion, while remaining stiff in the corrective direction. Primary ranges of motion were acquired using a motion capture system. A kinematic analysis was performed using homogeneous transformations and screw theory to determine primary screw axes of the motions. The required lateral stiffness for the brace was found in literature. Compliant mechanisms are used because they can apply the corrective force, but also allow the patients some range of motion. The mechanism implementation was characterized using finite element analysis and compared to a physical model test. Initial findings confirm that compliant mechanisms are suitable for the application of a scoliosis brace. We have found that the proposed brace can apply the necessary forces at reasonable displacements. The proposed brace will not allow the patient a full range of motion, but we believe that it will achieve an improved range of motion that will increase a patient’s ability to perform activities of daily living.

Mobility Analysis of the Threefold-Symmetric Bricard Linkage and Its Network

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Xiaoke Song ◽  
Hongwei Guo ◽  
Ruiwei Liu ◽  
Fei Meng ◽  
Qiping Chen ◽  
...  
Keyword(s):  
Graph Theory ◽  
Screw Theory ◽  
Analysis Method ◽  
Mobility Analysis ◽  
Topological Constraint ◽  
Constraint Matrix ◽  
Matrix Rank ◽  
Constraint Graph ◽  
The Matrix ◽  
Mechanical Networks

Abstract In this study, the mobility of the threefold-symmetric Bricard linkage and its network are analyzed using screw theory. First, the screw motion equation of the linkage is derived. By applying the modified Grübler–Kutzbach criterion, we deduce that the degree of freedom (DOF) of the linkage is equal to 1. Then, we analyze the mechanical network constructed of threefold-symmetric Bricard linkages and provide its topological constraint graph. Using graph theory and screw theory, the constraint matrix of the mechanical network is obtained. Then, we solve the matrix rank via linear column transformation. Results show that the DOF of the mechanical network is equal to 1. The mobility analysis method of the mechanical network proposed in this study facilitates the solution of the constraint matrix rank and can be used as a reference for other mechanical networks constructed of single-loop linkages.

Structure Synthesis of 3-RRS Type Spatial Compliant Parallel Manipulator

2010 ◽  
Vol 44-47 ◽  
pp. 1375-1379
Author(s):  
Da Chang Zhu ◽  
Li Meng ◽  
Tao Jiang
Keyword(s):  
Parallel Manipulator ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Weight Ratio ◽  
Parallel Manipulators ◽  
Robot System ◽  
New Approach ◽  
Structure Synthesis ◽  
Rigid Joints ◽  
Type 3

Parallel manipulators has been extensively studied by virtues or its high force-to-weight ratio and widely spread applications such as vehicle or flight simulator, a machine tool and the end effector of robot system. However, as each limb includes several rigid joints, assembling error is demanded strictly, especially in precision measurement and micro-electronics. On the other hand, compliant mechanisms take advantage of recoverable deformation to transfer or transform motion, force, or energy and the benefits of compliant mechanisms mainly come from the elimination of traditional rigid joints, but the traditional displacement method reduce the stiffness of spatial compliant parallel manipulators. In this paper, a new approach of structure synthesis of 3-DoF rotational compliant parallel manipulators is proposed. Based on screw theory, the structures of RRS type 3-DoF rotational spatial compliant parallel manipulator are developed. Experiments via ANSYS are conducted to give some validation of the theoretical analysis.

Bistable Compliant Four-Bar Mechanisms With a Single Torsional Spring

2006 ◽  
Author(s):  
Adarsh Mavanthoor ◽  
Ashok Midha
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Mechanism Design ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Stored Energy ◽  
Element Analysis ◽  
Bistable Behavior ◽  
Torsional Spring ◽  
Bistable Mechanism

Significant reduction in cost and time of bistable mechanism design can be achieved by understanding their bistable behavior. This paper presents bistable compliant mechanisms whose pseudo-rigid-body models (PRBM) are four-bar mechanisms with a torsional spring. Stable and unstable equilibrium positions are calculated for such four-bar mechanisms, defining their bistable behavior for all possible permutations of torsional spring locations. Finite Element Analysis (FEA) and simulation is used to illustrate the bistable behavior of a compliant mechanism with a straight compliant member, using stored energy plots. These results, along with the four-bar and the compliant mechanism information, can then be used to design a bistable compliant mechanism to meet specified requirements.

Analysis of Parasitic Motion in Compliant Mechanisms Using Eigenwrenches and Eigentwists

2018 ◽  
Author(s):  
Werner W. P. J. van de Sande ◽  
Just L. Herder
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Degree Of Freedom ◽  
Compliance Matrix ◽  
Parasitic Motion ◽  
Actual Degree ◽  
Motion Metrics ◽  
Mechanism Kinematic ◽  
Kinematic Information

Parasitic motion is undesired in precision mechanisms, it causes unwanted kinematics. These erroneous motions are especially apparent in compliant mechanisms. Usually an analysis of parasitic motion is only valid for one type of mechanism. Kinematic information is imbedded in the compliance matrix of any mechanism; an eigenscrew decomposition expresses this kinematic information as screws. It uses screw theory to identify the lines along which a force yields a parallel translation and a rotation yields a parallel moment. These lines are called eigenwrenches and eigentwists. Any other load on the compliant mechanism will lead to parasitic motion. This article introduces two parasitic motion metrics using eigenscrew decomposition: the parasitic resultant from an applied screw and the deviation of an actual degree of freedom from a desired degree of freedom. These metrics are applicable to all compliant mechanism and allow comparison between two compliant mechanisms. These metrics are applied to some common compliant mechanisms as an example.

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