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.

scholarly journals A Screw Theory Approach for the Type Synthesis of Compliant Mechanisms With Flexures

2009 ◽  
Author(s):  
Hai-Jun Su ◽  
Denis V. Dorozhkin ◽  
Judy M. Vance
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Computational Techniques ◽  
Theory Approach ◽  
Type Synthesis ◽  
Precision Engineering ◽  
Pattern Design ◽  
Design Constraint ◽  
Systematic Formulation

This paper presents a screw theory based approach for the type synthesis of compliant mechanisms with flexures. We provide a systematic formulation of the constraint-based approach which has been mainly developed by precision engineering experts in designing precision machines. The two fundamental concepts in the constraint-based approach, constraint and freedom, can be represented mathematically by a wrench and a twist in screw theory. For example, an ideal wire flexure applies a translational constraint which can be described a wrench of pure force. As a result, the design rules of the constraint-based approach can be systematically formulated in the format of screws and screw systems. Two major problems in compliant mechanism design, constraint pattern analysis and constraint pattern design are discussed with examples in details. This innovative method paves the way for introducing computational techniques into the constraint-based approach for the synthesis and analysis of compliant mechanisms.

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.

Design Synthesis of 2-D Compliant Mechanisms Utilizing Serial Concatenation of Building Blocks

2009 ◽  
Author(s):  
Girish Krishnan ◽  
Charles Kim ◽  
Sridhar Kota
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Building Blocks ◽  
Unique Point ◽  
Compliance Matrix ◽  
Design Synthesis ◽  
Parametric Variation ◽  
Point Of Interest

In this section we implement a characterization based on eigen-twists and eigen-wrenches for the deformation of a compliant mechanism at a given point of interest. For 2-D mechanisms, this involves characterizing the compliance matrix at a unique point called the center of elasticity. At the center of elasticity, the translation and rotational compliances are decoupled. We give an intuitive graphical understanding of compliance at this point by representing the translational compliance as an ellipse and the coupling between the translational and rotational parameters as vectors (Coupling vectors). This representation gives us an intuitive understanding of series and parallel combination of building blocks. We obtain a parametric variation of these quantities for a compliant dyad building block, and show with examples how a mechanism can be synthesized by a combination of building blocks to obtain desired deformation requirements. We also propose a combination of series and parallel concatenation to achieve more than one specification simultaneously. Such a characterization can be extended to synthesize involving multiple ports.

Accuracy and precision: A new viewon kinematic assessment of solid-state hinges and compliant mechanisms

2021 ◽  
pp. 1045389X2110643
Author(s):  
Lucio Flavio Campanile ◽  
Stephanie Kirmse ◽  
Alexander Hasse
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Measurement Theory ◽  
Reference Value ◽  
Strict Sense ◽  
Force System ◽  
Parasitic Motion ◽  
Accuracy And Precision ◽  
Compliant Systems

Compliant mechanisms are alternatives to conventional mechanisms which exploit elastic strain to produce desired deformations instead of using moveable parts. They are designed for a kinematic task (providing desired deformations) but do not possess a kinematics in the strict sense. This leads to difficulties while assessing the quality of a compliant mechanism’s design. The kinematics of a compliant mechanism can be seen as a fuzzy property. There is no unique kinematics, since every deformation need a particular force system to act; however, certain deformations are easier to obtain than others. A parallel can be made with measurement theory: the measured value of a quantity is not unique, but exists as statistic distribution of measures. A representative measure of this distribution can be chosen to evaluate how far the measures divert from a reference value. Based on this analogy, the concept of accuracy and precision of compliant systems are introduced and discussed in this paper. A quantitative determination of these qualities based on the eigenvalue analysis of the hinge’s stiffness is proposed. This new approach is capable of removing most of the ambiguities included in the state-of-the-art assessment criteria (usually based on the concepts of path deviation and parasitic motion).

Compliant Mechanism Reconfiguration Based on Position Space Concept for Reducing Parasitic Motion

2015 ◽  
Author(s):  
Haiyang Li ◽  
Guangbo Hao
Keyword(s):  
Finite Element Analysis ◽  
Parallel Mechanism ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Position Space ◽  
Element Analysis ◽  
Compact Structure ◽  
Parasitic Motion ◽  
Compliant Parallel Mechanism ◽  
Space Concept

This paper introduces a compliant mechanism reconfiguration approach that can be used to minimize the parasitic motions of a compliant mechanism. This reconfiguration approach is based on the position spaces, identified by the screw theory, of independent compliant modules in a compliant mechanism system. The parasitic motions (rotations) of a compliant mechanism are first modelled associated with the variables representing any positions of the compliant modules in the position spaces. The optimal positions of the compliant modules are then obtained where the parasitic motions are reduced to minimal values. A procedure of the compliant mechanism reconfiguration approach is summarized and demonstrated using a decoupled XYZ compliant parallel mechanism as an example. The analytical results show that the parasitic motions of the XYZ compliant parallel mechanism in the example can be dramatically reduced by the position/structure reconfiguration, which is also validated by finite element analysis. The position space of a compliant module contains a number of possible positions, thus a compliant mechanism can also be efficiently reconfigured to a variety of practical patterns such as the configuration with compact structure.

scholarly journals A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
Hai-Jun Su ◽  
Denis V. Dorozhkin ◽  
Judy M. Vance
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Computational Techniques ◽  
Theory Approach ◽  
Flexible Joints ◽  
Precision Engineering ◽  
Design Constraint ◽  
Analysis And Synthesis ◽  
Prismatic Joints

This paper presents a screw theory based approach for the analysis and synthesis of flexible joints using wire and sheet flexures. The focus is on designing flexure systems that have a simple geometry, i.e., a parallel constraint pattern. We provide a systematic formulation of the constraint-based approach, which has been mainly developed by precision engineering experts in designing precision machines. The two fundamental concepts in the constraint-based approach, constraint and freedom, can be represented mathematically by a wrench and a twist in screw theory. For example, an ideal wire flexure applies a translational constraint, which can be described by a wrench of pure force. As a result, the design rules of the constraint-based approach can be systematically formulated in the format of screws and screw systems. Two major problems in compliant mechanism design, constraint pattern analysis, and constraint pattern design are discussed with examples in details. Lastly, a case study is provided to demonstrate the application of this approach to the design of compliant prismatic joints. This innovative method paves the way for introducing computational techniques into the constraint-based approach for the synthesis and analysis of compliant mechanisms.

A Framework and Design Sythesis Tool Used to Generate, Evaluate and Optimize Compliant Mechanism Concepts for Research and Education Activities

2004 ◽  
Author(s):  
Martin L. Culpepper ◽  
Soohyung Kim
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Mems Accelerometer ◽  
Award Winning ◽  
Mechanism Research ◽  
Big Picture ◽  
Research And Education ◽  
New Research ◽  
Student Projects

In 2002, a Microsoft-MIT iCampus effort was initiated to generate methods and tools which accelerate the process by which students and researchers acquire perspective and skill in compliant mechanism design: (1) Experience and skill: A synthesis tool, CoMeT, was developed as a means for researchers and students to gain experience and skill in working with old (education) and new (research) compliant mechanisms. The simulator is based on compliance theory and screw theory. (2) Perspective: A framework, the 5 Fs, was developed to help designers form a holistic perspective on compliant mechanisms. A “big picture” view helps them systematically identify and link the important elements of a compliant mechanism problem. This opens to door for them to properly conceptualize, model and fabricate these mechanisms. In this paper we discuss the work of early compliant mechanism/instrument designers to gain insight into how they thought about, designed and taught others about compliant mechanisms. We explain how their work has influenced the development of our framework and simulator. We then show results obtained by using the framework and simulator at MIT in: (1) Compliant mechanism research: Generation of a compliant mechanism for an R&D 100 award winning, six-axis Nanomanipulator. (2) Compliant mechanism education: Use within student projects to design two devices: A compliant x-y Nanomanipulator with 30×30 μm range and a MEMS accelerometer. Both devices are designed, fabricated and tested in a semester-long class. The paper closes with an appendix which highlights the main steps of a CoMeT study on the screw axis characteristics of a four bar compliant mechanism. The CoMeT simulator and a CoMeT User’s Guide have been made publicly available for academic use at psdam.mit.edu.

scholarly journals Workspace Analysis of a Hybrid Kinematic Machine Tool with High Rotational Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Haiqiang Zhang ◽  
Hairong Fang ◽  
Yuefa Fang ◽  
Bingshan Jiang
Keyword(s):  
Machine Tool ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Main Body ◽  
Parasitic Motion ◽  
Reachable Workspace ◽  
Performance Evaluation Index ◽  
Hybrid Machine ◽  
Five Axis

This paper presents a novel parallel manipulator with one translational and two rotational (1T2R) degrees of freedom that can be employed to form a five-degree-of-freedom hybrid kinematic machine tool for large heterogeneous complex structural component machining in aerospace field. Compared with serial or parallel machine, hybrid machine has the merits of high stiffness, high speed, large workspace, and complicated surface processing ability. To increase stiffness, three-degree-of-freedom redundantly actuated and overconstrained 2PRU-PRPS parallel manipulator (P denotes the active prismatic joint) is proposed, which is utilized as the main body of hybrid machine. By resorting to the screw theory, the degree of freedom of the proposed mechanism is briefly addressed including the initial configuration and general configuration and validated by Grübler-Kutzbach (G-K) equation. Next, kinematic inverse solution and parasitic motion of the parallel manipulator are deduced and the transformational relations between the Euler angle and Tilt-Torsion (T-T) angle are identified. Thirdly, the performance evaluation index of orientation workspace is introduced, and the reachable workspace and joint workspace are formulated. Through specific examples, the reachable workspace, task workspace, and joint workspace of the redundant actuation parallel manipulator are depicted. Compared with overstrained 2PRU-PRS parallel manipulator, corresponding analyses illustrate that the proposed parallel manipulator owns much better orientation capability and is very meaningful to the development of the five-axis hybrid machine tool.

A Method to Evaluate and Calculate the Mobility of a General Compliant Parallel Manipulator

2004 ◽  
Author(s):  
Jingjun Yu ◽  
Shusheng Bi ◽  
Guanghua Zong
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Parallel Manipulators ◽  
Kinematic Characteristic ◽  
Parallel Kinematic Machine ◽  
Compliance Matrix ◽  
Multiple Degrees Of Freedom ◽  
Parallel Kinematic

A compliant parallel manipulator (CPM), is a kind of compliant mechanism characterizes a complicate topological structure and multiple degrees of freedom. As one of the kinematic characteristics of a CPM, the mobility of a CPM become complicate compared to its rigid-counterpart. In order to describe such a complicate kinematic characteristic of a CPM, “primary mobility of a compliant parallel manipulator” concept is proposed. By means of the screw theory, a method of quantifying the primary mobility of the CPM is investigated under the ground that the compliance matrix of the manipulator should be calculated primarily. By using this method, the primary mobility of two typical compliant parallel manipulators, one is a planar 3-RRR CPM and the other a spatial 3-RRPR CPM, is addressed respectively. This proposed method is also instructive for analyzing the instantaneous mobility of a general degenerate-DOF parallel manipulator or a Parallel Kinematic Machine (PKM).

Analytical Representation of Nano-Scale Parasitic Motion in Flexure-Based Selectively Compliant Mechanisms

2007 ◽  
Author(s):  
Chinmaya B. Patil ◽  
S. V. Sreenivasan ◽  
Raul G. Longoria
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Geometric Errors ◽  
Modeling And Analysis ◽  
Parasitic Motion ◽  
Nano Scale ◽  
Flexure Joints ◽  
Improved Design ◽  
Kinetostatic Model ◽  
Spatial Kinematics

Analytical modeling of selectively compliant mechanisms for quantifying the nano-scale parasitic motion is presented. Flexure-based compliant mechanisms are capable of meeting the demanding requirements of the partially constrained ultraprecision motion systems. However, the geometric errors induced by manufacturing tolerances can limit the precision capability. Understanding parasitic motion at the nano-scale necessitates a 3-D model even for mechanisms that are designed to be planar. A spatial kinematics based kinetostatic model is used here. This approach systematically accounts for the geometric errors, and enables estimation of the inherently spatial parasitic motion. Using insights from screw theory, the parasitic motion is classified into intrinsic mechanism errors, and errors that can be minimized by calibration procedures. A metric that quantifies the intrinsic parasitic motion and characterizes the precision capability of the mechanism is identified. Monte Carlo simulation is used to propagate the variance of the geometric errors through the model to determine the statistical moments of the chosen metric. To illustrate the approach, the modeling and analysis is applied to a classical four-bar mechanism with flexure joints. The model is further used to investigate the key system parameters that influence the intrinsic parasitic motion in the mechanism. The simulation results indicate more than 50% improvement in the precision capability of the four-bar mechanism by improved design of flexure joints, without changing the manufacturing tolerance limits.

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