Position-Space-Based Compliant Mechanism Reconfiguration Approach and Its Application in the Reduction of Parasitic Motion

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Haiyang Li ◽  
Guangbo Hao ◽  
Richard C. Kavanagh
Keyword(s):  
Parallel Mechanism ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Geometrical Shape ◽  
Position Space ◽  
Element Analysis ◽  
Parasitic Motion ◽  
Compliant Parallel Mechanism ◽  
Motion Characteristics ◽  
Cross Axis

This paper introduces a position-space-based reconfiguration (PSR) approach to the reconfiguration of compliant mechanisms. The PSR approach can be employed to reconstruct a compliant mechanism into many new compliant mechanisms, without affecting the mobility of the compliant mechanism. Such a compliant mechanism can be decomposed into rigid stages and compliant modules. Each of the compliant modules can be placed at any one permitted position within its position space, which does not change the constraint imposed by the compliant module on the compliant mechanism. Therefore, a compliant mechanism can be reconfigured through selecting different permitted positions of the associated compliant modules from their position spaces. The proposed PSR approach can be used to change the geometrical shape of a compliant mechanism for easy fabrication, or to improve its motion characteristics such as cross-axis coupling, lost motion, and motion range. While this paper focuses on reducing the parasitic motions of a compliant mechanism using this PSR approach, the associated procedure is summarized and demonstrated using a decoupled XYZ compliant parallel mechanism as an example. The parasitic motion of the XYZ compliant parallel mechanism is modeled analytically, with three variables which represent any permitted positions of the associated compliant modules in their position spaces. The optimal positions of the compliant modules in the XYZ compliant parallel mechanism are finally obtained based on the analytical results, where the parasitic motion is reduced by approximately 50%. The reduction of the parasitic motion is verified by finite-element analysis (FEA) results, which differ from the analytically obtained values by less than 7%.

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.

Design of a 3-DOF Compliant Parallel Mechanism for Displacement Amplification

2013 ◽  
Author(s):  
Qiang Zeng ◽  
Kornel F. Ehmann
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Heat Balance ◽  
Parallel Mechanism ◽  
Compliant Mechanism ◽  
Element Analysis ◽  
Resonant Frequencies ◽  
Compact Size ◽  
Compliant Parallel Mechanism ◽  
Monolithic Structure

Prevalent general design methods and applications of compliant displacement amplifiers are focused on 1-DOF units composed into serial structures, which are limited by their output motions, stiffness, heat balance, repeatability and resonant frequencies. To improve the output properties of compliant displacement amplifiers, a monolithic structure is presented in the form of a compliant parallel mechanism. In the proposed moving structure, the compliant mechanism of the displacement amplifier is designed with 3-DOF to generate uniformly magnified output properties in all directions. High first resonant frequencies and amplification ratios are achieved in a compact size compared to existing compliant displacement amplifiers. The related kinematics, amplification ratios and resonant frequencies of the amplifier are analytically modeled, and the results are simulated by finite-element analysis. The proposed design is employable for micro/nano positioning stages operating within a prismatic output workspace.

Design of a Gimbaled Compliant Mechanism Stage for Precision Motion and Dynamic Control in Z, ΘX and ΘY Directions

2004 ◽  
Author(s):  
Spencer E. Szczesny ◽  
Amos G. Winter
Keyword(s):  
Compliant Mechanisms ◽  
Dynamic Testing ◽  
Compliant Mechanism ◽  
Dynamic Control ◽  
Precision Engineering ◽  
Compliance Requirements ◽  
Modes Of Vibration ◽  
Motion Characteristics ◽  
Cross Axis ◽  
Precision Motion

Obtaining precise motion control of a compliant mechanism is often hindered by competing kinematic, mechanic and dynamic requirements. Resonances limit the control bandwidth while compliance requirements limit the mechanism’s directional stiffness. This paper investigates the improvements possible for three-axis Z, θX and θY diaphragm flexure stages through the use of a design (T-Flex) with members complaint in bending and torsion. According to analytical modeling and FEA, the T-Flex is capable of removing problematic resonant modes of vibration without significantly increasing the axial or tilt stiffness. Bench-level experimentation was conducted on various configurations of compliant mechanisms to determine their effects on the motion characteristics for precision engineering applications. The results indicate that by pairing the T-Flex with a radially stiff compliant mechanism, gimbaled motion can be achieved, providing 7.0 nm/μm lateral cross-axis (parasitic) motions. The mechanism exhibits linear axial and tilt stiffness of 0.195 N/μm and 5.37×10−6 N-m/μrad, respectively. Dynamic testing agreed with the FEA prediction of the first natural frequency to within 10%. The T-Flex coupled with the stiff radial flexure has the potential to provide a precise three-axis configuration with a fundamental resonant frequency of 600 Hz.

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.

Design of a Generic Zero Stiffness Compliant Joint

2010 ◽  
Author(s):  
Femke M. Morsch ◽  
Just L. Herder
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Great Promise ◽  
Optimized Design ◽  
Analytic Model ◽  
Total Potential ◽  
Fea Model ◽  
Compliant Joint ◽  
Joint Element ◽  
Cross Axis

The objective of this paper is to design a generic zero stiffness compliant joint. This compliant joint could be used as a generic construction element in a compliant mechanism. To avoid the spring-back behavior of conventional compliant joints, the principle of static balancing is applied, implying that for each position of the joint the total potential energy should be constant. To this end, a conventional balanced mechanism, consisting of two pivoted bodies which are balanced with two zero-free-length springs, is taken as an initial concept. The joint is replaced by a compliant cross-axis flexural pivot and each spring is replaced by a pair of compliant leaf springs. For both parts an analytic model was implemented and a configuration with the lowest energy fluctuation was found through optimization. A FEA model was used to verify the analytic model of the optimized design. A prototype was manufactured and tested. Both the FEA model and the experiment confirm the reduction of the needed moment to rotate the compliant joint. The experiment shows the balanced compliant joint is not completely balanced but the moment required to rotate the joint is reduced by 70%. Thus, a statically balanced compliant generic joint element was designed which bears great promise in designing statically balanced compliant mechanisms and making this accessible to any designer.

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.

Experimental Validation of the Kinematics of a 3PRS Compliant Mechanism for Micromilling

2015 ◽  
Author(s):  
Antonio Ruiz ◽  
Francisco Campa Gomez ◽  
Constantino Roldan-Paraponiaris ◽  
Oscar Altuzarra
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Experimental Validation ◽  
Compliant Mechanism ◽  
Motion Controller ◽  
End Effector ◽  
Compliant Joints ◽  
Hybrid Manipulator ◽  
Compliant Parallel Mechanism ◽  
Actuated Joints

The present work deals with the development of a hybrid manipulator of 5 degrees of freedom for milling moulds for microlenses. The manipulator is based on a XY stage under a 3PRS compliant parallel mechanism. The mechanism takes advantage of the compliant joints to achieve higher repetitiveness, smoother motion and a higher bandwidth, due to the high precision demanded from the process, under 0.1 micrometers. This work is focused on the kinematics of the compliant stage of the hybrid manipulator. First, an analysis of the workspace required for the milling of a single mould has been performed, calculating the displacements required in X, Y, Z axis as well as two relative rotations between the tool and the workpiece from a programmed toolpath. Then, the 3PRS compliant parallel mechanism has been designed using FEM with the objective of being stiff enough to support the cutting forces from the micromilling, but flexible enough in the revolution and spherical compliant joints to provide the displacements needed. Finally, a prototype of the 3PRS compliant mechanism has been built, implementing a motion controller to perform translations in Z direction and two rotations. The resulting displacements in the end effector and the actuated joints have been measured and compared with the FEM calculations and with the rigid body kinematics of the 3PRS.

Application of Rigid-Body-Linkage Static Balancing Techniques to Reduce Actuation Effort in Compliant Mechanisms

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Sangamesh R. Deepak ◽  
Amrith N. Hansoge ◽  
G. K. Ananthasuresh
Keyword(s):  
Rigid Body ◽  
General Framework ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Small Length ◽  
Element Analysis ◽  
Static Balancing ◽  
Free Length ◽  
First Order ◽  
Taylor’S Series

There are analytical methods in the literature where a zero-free-length spring-loaded linkage is perfectly statically balanced by addition of more zero-free-length springs. This paper provides a general framework to extend these methods to flexure-based compliant mechanisms through (i) the well know small-length flexure model and (ii) approximation between torsional springs and zero-free-length springs. We use first-order truncated Taylor's series for the approximation between the torsional springs and zero-free-length springs so that the entire framework remains analytical, albeit approximate. Three examples are presented and the effectiveness of the framework is studied by means of finite-element analysis and a prototype. As much as 70% reduction in actuation effort is demonstrated. We also present another application of static balancing of a rigid-body linkage by treating a compliant mechanism as the spring load to a rigid-body linkage.

Using Rigid-Body Mechanism Topologies to Design Shape-Changing Compliant Mechanisms

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Shape Matching ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Mesh Network ◽  
Adaptive Antenna ◽  
Optimal Size ◽  
Dimensional Synthesis ◽  
Element Analysis

This paper uses rigid-body mechanism topologies to synthesize fully distributed compliant mechanisms that approximate a shape change defined by a set of morphing curves in different positions. For a shape-change problem, a rigid-body mechanism solution is generated first to provide the base topology. This base topology defines a preselected design space for the structural optimization in one of two ways so as to obtain a compliant mechanism solution that is typically superior to the local minimum solutions obtained from searching more expansive design spaces. In the first strategy, the dimensional synthesis directly determines the optimal size and shape of the distributed compliant mechanism having exactly the base topology. In the second strategy, an initial mesh network established from the base topology is used to generate different topologies (in addition to the base), and an improved design domain parameterization scheme ensures that only topologies with well-connected structures are evaluated. The deformation of each generated compliant mechanism is evaluated using geometrically nonlinear finite element analysis (FEA). A two-objective genetic algorithm (GA) is employed to find a group of viable designs that trade off minimizing shape matching error with minimizing maximum stress. The procedure's utility is demonstrated with three practical examples—the first two approximating open-curve profiles of an adaptive antenna and the third approximating closed-curve profiles of a morphing wing.

Non-Dimensional Kinetoelastostatic Maps for Compliant Mechanisms

2013 ◽  
Author(s):  
Santosh D. B. Bhargav ◽  
Harish I. Varma ◽  
G. K. Ananthasuresh
Keyword(s):  
Cross Sections ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Slenderness Ratio ◽  
Element Analysis ◽  
Output Displacement ◽  
Static Responses ◽  
Slender Beams ◽  
Applied Forces ◽  
The Cross

How do we assess the capability of a compliant mechanism of given topology and shape? The kinetoelastostatic maps proposed in this paper help answer this question. These maps are drawn in 2D using two non-dimensional quantities, one capturing the nonlinear static response and the other the geometry, material, and applied forces. Geometrically nonlinear finite element analysis is used to create the maps for compliant mechanisms consisting of slender beams. In addition to the topology and shape, the overall proportions and the proportions of the cross-sections of the beam segments are kept fixed for a map. The finite region of the map is parameterized using a non-dimensional quantity defined as the slenderness ratio. The shape and size of the map and the parameterized curves inside it indicate the complete kinetoelastostatic capability of the corresponding compliant mechanism of given topology, shape, and fixed proportions. Static responses considered in this paper include input/output displacement, geometric amplification, mechanical advantage, maximum stress, etc. The maps can be used to compare mechanisms, to choose a suitable mechanism for an application, or re-design as may be needed. The usefulness of the non-dimensional maps is presented with multiple applications of different variety. Non-dimensional portrayal of snap-through mechanisms is one such example. The effect of the shape of the cross-section of the beam segments and the role of different segments in the mechanism as well as extension to 3D compliant mechanisms, the cases of multiple inputs and outputs, and moment loads are also explained. The effects of disproportionate changes on the maps are also analyzed.

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