Toward a Unified Design Approach for Both Compliant Mechanisms and Rigid-Body Mechanisms: Module Optimization

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Lin Cao ◽  
Allan T. Dolovich ◽  
Arend L. Schwab ◽  
Just L. Herder ◽  
Wenjun (Chris) Zhang
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Optimization Approach ◽  
Structure Model ◽  
Dimensional Synthesis ◽  
Beam Elements ◽  
Compliant Joints ◽  
Design Variables ◽  
Rigid Joints ◽  
Synthesis Approach

Rigid-body mechanisms (RBMs) and compliant mechanisms (CMs) are traditionally treated in significantly different ways. In this paper, we present a synthesis approach that is appropriate for both RBMs and CMs. In this approach, RBMs and CMs are generalized into modularized mechanisms that consist of five basic modules, including compliant links (CLs), rigid links (RLs), pin joints (PJs), compliant joints (CJs), and rigid joints (RJs). The link modules and joint modules are modeled through beam elements and hinge elements, respectively, in a geometrically nonlinear finite-element solver, and subsequently a beam-hinge ground structure model is proposed. Based on this new model, a link and joint determination approach—module optimization—is developed for the type and dimensional synthesis of both RBMs and CMs. In the module optimization approach, the states (both presence or absence and sizes) of joints and links are all design variables, and one may obtain an RBM, a partially CM, or a fully CM for a given mechanical task. Three design examples of path generators are used to demonstrate the effectiveness of the proposed approach to the type and dimensional synthesis of RBMs and CMs.

Topology and Dimensional Synthesis of Compliant Mechanisms Using Discrete Optimization

2005 ◽  
Vol 128 (5) ◽  
pp. 1080-1091 ◽  
Author(s):  
Kerr-Jia Lu ◽  
Sridhar Kota
Keyword(s):  
Discrete Optimization ◽  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Discrete Optimization Problem ◽  
Dimensional Synthesis ◽  
Load Path ◽  
Design Variables ◽  
Gray Areas ◽  
Path Synthesis ◽  
Synthesis Approach

A unified approach to topology and dimensional synthesis of compliant mechanisms is presented in this paper as a discrete optimization problem employing both discrete (topology) and continuous (size) variables. The synthesis scheme features a design parameterization method that treats load paths as discrete design variables to represent various topologies, thereby ensuring structural connectivity among the input, output, and ground supports. The load path synthesis approach overcomes certain design issues, such as “gray areas” and disconnected structures, inherent in previous design schemes. Additionally, multiple gradations of structural resolution and a variety of configurations can be generated without increasing the number of design variables. By treating topology synthesis as a discrete optimization problem, the synthesis approach is incorporated in a genetic algorithm to search for feasible topologies for single-input single-output compliant mechanisms. Two design examples, commonly seen in the compliant mechanisms literature, are included to illustrate the synthesis procedure and to benchmark the performance. The results show that the load path synthesis approach can effectively generate well-connected compliant mechanism designs that are free of gray areas.

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.

The Analysis of a Simplified 2R Pseudo-Rigid-Body Model with Moment Load

2012 ◽  
Vol 224 ◽  
pp. 18-23
Author(s):  
Yun Jiao Zhang ◽  
Guo Wu Wei ◽  
Jian Sheng Dai
Keyword(s):  
Rigid Body ◽  
Objective Function ◽  
Compliant Mechanisms ◽  
Three Dimensional ◽  
Body Model ◽  
Design Variables ◽  
Characteristic Radius ◽  
Rigid Body Model ◽  
Analysis And Synthesis ◽  
Moment Load

Pseudo-rigid-body model (PRBM) method, which simplifies the geometrical nonlinear analysis, has become an important tool for the analysis and synthesis of compliant mechanisms. In this paper, a simplified 2R PRBM with two rigid links and two torsion springs is proposed. The characteristic radius factor and stiffness coefficients are selected as the design variables; in order to be better to simulate the tip point and tip slope, a three-dimensional objective function is formulated to optimize the new pseudo-rigid-body model. It is revealed in this paper that the precision of the tip point simulation can be improved when the coefficient of the tip slope error in the objective function is reduced.

Runner Optimization for In-Mold Assembly of Multi-Material Compliant Mechanisms

2011 ◽  
Author(s):  
Wojciech Bejgerowski ◽  
Satyandra K. Gupta
Keyword(s):  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Polymer Melt ◽  
Injection Molding Process ◽  
Optimization Approach ◽  
Assembly Process ◽  
Molding Process ◽  
Design Variables

The runner system in injection molding process is used to supply the polymer melt from injection nozzle to the gates of final part cavities. Realizing complex multi-material mechanisms by in-mold assembly process requires special runner layout design considerations due to the existence of the first stage components. This paper presents the development of an optimization approach for runner systems in the in-mold assembly of multi-material compliant mechanisms. First, the issues specific to the in-mold assembly process are identified and analyzed. Second, the general optimization problem is formulated by identification of all parameters, design variables, objective functions and constraints. Third, the implementation of the optimization problem in Matlab® environment is described based on a case study of a runner system for an in-mold assembly of a MAV drive mechanism. This multi-material compliant mechanism consists of seven rigid links interconnected by six compliant hinges. Finally, several optimization approaches are analyzed to study their performance in solving the formulated problem. The most appropriate optimization approach is selected. The case study showed the applicability of the developed optimization approach to runner systems for complex in-mold assembled multi-material mechanism designs.

A Review on Compliant Joints and Rigid-Body Constant Velocity Universal Joints Toward the Design of Compliant Homokinetic Couplings

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
D. Farhadi Machekposhti ◽  
N. Tolou ◽  
J. L. Herder
Keyword(s):  
Rigid Body ◽  
Constant Velocity ◽  
Compliant Mechanisms ◽  
Material Selection ◽  
Analytical Data ◽  
Graph Representations ◽  
Common Basis ◽  
Compliant Joints ◽  
Body Joints ◽  
Universal Joints

This paper presents for the first time a literature survey toward the design of compliant homokinetic couplings. The rigid-linkage-based constant velocity universal joints (CV joints) available from literature were studied, classified, their graph representations were presented, and their mechanical efficiencies compared. Similarly, literature is reviewed for different kinds of compliant joints suitable to replace instead of rigid-body joints in rigid-body CV joints. The compliant joints are compared based on analytical data. To provide a common basis for comparison, consistent flexure scales and material selection are used. It was found that existing compliant universal joints are nonconstant in velocity and designed based on rigid-body Hooke's universal joint. It was also discovered that no compliant equivalent exists for cylindrical, planar, spherical fork, and spherical parallelogram quadrilateral joints. We have demonstrated these compliant joints can be designed by combining existing compliant joints. The universal joints found in this survey are rigid-body non-CV joints, rigid-body CV joints, or compliant non-CV joints. A compliant homokinetic coupling is expected to combine the advantages of compliant mechanisms and constant velocity couplings for many applications where maintenance or cleanliness is important, for instance in medical devices and precision instruments.

Using Rigid-Body Mechanism Topologies to Design Path Generating Compliant Mechanisms

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mesh Network ◽  
Optimal Topology ◽  
Optimal Size ◽  
Path Generation ◽  
Dimensional Synthesis ◽  
Straight Line ◽  
Rigid Body Transformation

For a path generation problem, this paper uses the base topology of a single degree-of-freedom (DOF) rigid-body mechanism solution to synthesize fully distributed compliant mechanisms that can trace the same path. Two different strategies are proposed to employ the base topology in the structural optimization so that its design space size can be intelligently reduced from an arbitrary complexity. In the first strategy, dimensional synthesis directly determines the optimal size and shape of the compliant mechanism solution while maintaining the exact base topology. In the second, the base topology establishes an initial mesh network to determine the optimal topology and dimensions simultaneously. To increase the possibility of converging to an optimal design, the objective metrics to evaluate the path generation ability are computed in a novel manner. A section-by-section analysis with a rigid-body transformation is implemented to examine the full path of each candidate mechanism. A two-objective genetic algorithm (GA) is employed to find a group of viable designs that tradeoff minimizing the average Euclidean distance between the desired and actual paths with minimizing the peak distance between corresponding points on those paths. Two synthesis examples generating straight-line and curved paths are presented to demonstrate the procedure's utility.

Design of a parallel gripper based on topology synthesis and evolutionary optimization

2021 ◽  
pp. 1-18
Author(s):  
I-Ting Chi ◽  
Teeranoot Chanthasopeephan ◽  
Dung-An Wang
Keyword(s):  
Genetic Algorithm ◽  
Optimal Design ◽  
Design Process ◽  
Compliant Mechanisms ◽  
Synthesis Process ◽  
Dimensional Synthesis ◽  
Multi Objective Genetic Algorithm ◽  
Constraint Model ◽  
Force Displacement ◽  
Synthesis Approach

Abstract A compliant gripper with nearly parallel gripping motion is developed by a topology synthesis and a dimensional synthesis approach. The topology synthesis process can generate linkage type compliant mechanisms. Suitable boundary conditions of the topology synthesis process are selected to achieve the desired functions of the device. The dimensional synthesis is based on an evolutionary optimal design process. In order to meet various design goals, a nondominated multi-objective genetic algorithm is selected for the optimal design process. A kinetostaic model based on the chained beam constraint model is developed for force-displacement analysis of the designs. Efficiency and accuracy of the design approach are proved by experiments. Appropriate linkage types of compliant mechanisms may be discovered by the topology optimization process before moving on to dimensional synthesis to obtain final designs.

A Graphical, User-Driven Newton-Raphson Technique for Use in the Analysis and Design of Compliant Mechanisms

1988 ◽  
Author(s):  
T. C. Hill ◽  
A. Midha
Keyword(s):  
Compliant Mechanisms ◽  
Easy Access ◽  
Displacement Boundary ◽  
Analysis And Design ◽  
Beam Elements ◽  
Design Variables ◽  
Newton Raphson ◽  
A Chain ◽  
The Stability ◽  
Six Degree Of Freedom

Abstract The analysis and design of compliant mechanisms, undergoing large (geometrically nonlinear) deflections, have been assisted by the Newton-Raphson method to find the loads which satisfy a prescribed set of force and displacement boundary conditions. This paper introduces a graphical, user-driven Newton-Raphson technique that allows easy access to good initial design variable estimates, and subsequently accurate and expeditious solutions. These design variables may include loads as well as material and geometric properties of the beam segments composing the mechanism. A line search step-restriction technique is included to enhance the stability of the method. The method uses six-degree-of-freedom planar beam elements in a chain calculation that cumulatively evaluates the large deflections corresponding to a given load set.

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

2013 ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Adaptive Antenna ◽  
Dimensional Synthesis ◽  
Element Analysis ◽  
Initial Element ◽  
Multi Objective Genetic Algorithm ◽  
Improved Design

This paper uses rigid-body mechanism topologies to synthesize distributed compliant mechanisms that approximate a shape change defined by a set of morphing curves in different positions. A single-actuator compliant mechanism is synthesized from a single degree-of-freedom rigid-body mechanism’s base topology in one of two ways. In one case, the base topology is directly evaluated through dimensional synthesis to determine the compliant mechanism’s optimal dimensions. In the second, the base topology establishes an initial element network for an optimization routine that determines topologies and dimensions simultaneously, and an improved design domain parameterization scheme ensures that only topologies with well-connected structures are evaluated. A multi-objective genetic algorithm is employed to search the design space, and the deformation is evaluated using geometrically nonlinear finite element analysis. The procedure’s utility is demonstrated with two practical examples — one approximating open-curve profiles of an adaptive antenna and the other closed-curve profiles of a morphing wing.

Parameterization Strategy for Optimization of Shape Morphing Compliant Mechanisms Using Load Path Representation

2003 ◽  
Author(s):  
Kerr-Jia Lu ◽  
Sridhar Kota
Keyword(s):  
Compliant Mechanisms ◽  
Element Model ◽  
Structural Deformation ◽  
Load Path ◽  
Aircraft Wings ◽  
Shape Morphing ◽  
Design Variables ◽  
Path Representation ◽  
Flexible Antenna ◽  
Synthesis Approach

The distributed compliance and smooth deformation field of compliant mechanisms provide a viable means to achieve shape morphing in many systems, such as flexible antenna reflectors and morphing aircraft wings. We previously developed a systematic synthesis approach to design shape morphing compliant mechanisms using Genetic Algorithm (GA). However, the design variable definition, in fact, allows the generation of invalid designs (disconnected structures) within the GA. In this research, we developed a load path representation to include the structure connectivity information into the design variables, thus improving the GA efficiency. The number of design variables is also independent of the number of elements in the finite element model that is used to solve for the structural deformation. The shape morphing synthesis approach, incorporating this path representation, is demonstrated through two examples, followed by discussions on further refinements.

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