Optimum Synthesis of Multiloop Planar Mechanisms for the Generation of Paths and Rigid-Body Positions by the Linear Partition of Design Equations

1977 ◽  
Vol 99 (1) ◽  
pp. 116-123 ◽  
Author(s):  
D. H. Bhatia ◽  
C. Bagci
Keyword(s):  
Rigid Body ◽  
Mechanism Design ◽  
Industrial Applications ◽  
Planar Mechanisms ◽  
Loop Closure ◽  
Optimum Synthesis ◽  
Linear Partition ◽  
Closure Equation

The optimum synthesis of multiloop planar mechanisms for the generation of paths and rigid-body positions employing the linear partition of the design equations is presented. Design equations and their applications for the optimum synthesis of the three distinct types of the Stephenson’s six-bar mechanism for the generation of paths and rigid-body positions are presented. The optimum sets of dimensions of a mechanism are determined by minimizing the error in the loop-closure equation of the path dyad and of the loops of the mechanism. Design equations having nine to twelve unknown dimensions are presented. Industrial applications of the design equations are illustrated with design examples.

Optimum Synthesis of Plane Mechanisms for the Generation of Paths and Rigid-Body Positions via the Linear Superposition Technique

1975 ◽  
Vol 97 (1) ◽  
pp. 340-346 ◽  
Author(s):  
C. Bagci ◽  
In-Ping Jack Lee
Keyword(s):  
Rigid Body ◽  
System Design ◽  
Linear Superposition ◽  
Loop Closure ◽  
Numerical Examples ◽  
Optimum Synthesis ◽  
Closure Equation ◽  
Superposition Technique

A method of optimum synthesis of plane mechanisms for the generation of paths and rigid-body positions is presented. The method is developed for the four-bar plane mechanism with six and eight unknown dimensions. Dimensions of the optimum mechanism are determined by minimizing the error in the loop-closure equations for N design points on the path, along with the loop-closure equation of the linkage, where N is not limited by the number of the unknown dimensions of the system. Design equations are linearized by the method of linear superposition. Solution of design equations requires no iterations, and it leads to a series of optimum mechanisms of different efficiency of approximation. Numerical examples are given.

Concurrent Type and Dimensional Synthesis of Planar Mechanisms Using Graph-Theoretic Enumeration, Automatic Loop Closure Equation Generation, and Descent-Based Optimization

2011 ◽  
Author(s):  
Carl A. Nelson
Keyword(s):  
A Priori ◽  
Goal Function ◽  
Dimensional Synthesis ◽  
Planar Mechanisms ◽  
Loop Closure ◽  
Graph Theoretic ◽  
Optimal Mechanism ◽  
Spatial Mechanisms ◽  
Closure Equation

An approach to concurrent type and dimensional synthesis of planar mechanisms is presented. Using graph-theoretic enumeration of mechanisms and determination of loops, automatic loop closure equations are generated. Using constrained optimization routines based on descent methods, and given an appropriate goal function, optimal mechanism designs can be determined. These are not limited to traditional problems such as rigid-body guidance and path generation, but can be more flexibly expressed according to designer needs. This method can be effective at finding mechanism solutions when topology has not been determined a priori and may also be extensible to synthesis of spatial mechanisms. This paper presents the data flow and algorithm outline, simulation results, and examples of nonstandard synthesis problems solvable with this method.

Pseudo-Rigid-Body Model Chain Algorithm: Part 1 — Introduction and Concept Development

2006 ◽  
Author(s):  
Joby Pauly ◽  
Ashok Midha
Keyword(s):  
Boundary Conditions ◽  
Rigid Body ◽  
Mechanism Design ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Loop Closure ◽  
Body Model ◽  
Rigid Body Model ◽  
Model Chain ◽  
Compliant Mechanism Design

Pseudo-rigid-body models help expedite the compliant mechanism design process by aiding the analysis and synthesis of candidate design solutions, using loop-closure techniques for rigid-body mechanisms. Presently, these models are available only for relatively simple compliant beam geometries and loading situations. The chain algorithm is an alternate method for the design and analysis of compliant mechanisms. Though more versatile, insofar as the geometry and loading are concerned, it is not possible to implement this technique in analysis or synthesis problems involving loop-closure equations. This paper proposes the construction of a generalized “pseudo-rigid-body model chain;” it allows the use of pseudo-rigid-body models in conjunction with the chain algorithm to obtain the deformation kinematics of complex compliant members. Such a “pseudo-rigid-body model chain” would possess dual advantages of expediency of modeling through the use of pseudo-rigid-body representations of compliant segments, and the inherent flexibility of the chain algorithm to geometry and load boundary conditions. The proposed technique involves discretization of the planar continuum into initially straight, equal length compliant segments, whose deflections due to the applied load boundary conditions are then determined using appropriate pseudo-rigid-body models. Such a model could potentially be used in the solution of compliant mechanism design and analysis problems when coupled with the use of loop-closure equations.

Identification of Compliant Pseudo-Rigid-Body Four-Link Mechanism Configurations Resulting in Bistable Behavior

2003 ◽  
Vol 125 (4) ◽  
pp. 701-708 ◽  
Author(s):  
Brian D. Jensen ◽  
Larry L. Howell
Keyword(s):  
Energy Storage ◽  
Rigid Body ◽  
Mechanism Design ◽  
Bistable Behavior ◽  
Strongly Coupled ◽  
Present Design ◽  
Stable Equilibria ◽  
Motion Characteristics ◽  
Bistable Mechanism ◽  
Design Challenges

Bistable mechanisms, which have two stable equilibria within their range of motion, are important parts of a wide variety of systems, such as closures, valves, switches, and clasps. Compliant bistable mechanisms present design challenges because the mechanism’s energy storage and motion characteristics are strongly coupled and must be considered simultaneously. This paper studies compliant bistable mechanisms which may be modeled as four-link mechanisms with a torsional spring at one joint. Theory is developed to predict compliant and rigid-body mechanism configurations which guarantee bistable behavior. With this knowledge, designers can largely uncouple the motion and energy storage requirements of a bistable mechanism design problem. Examples demonstrate the power of the theory in bistable mechanism design.

Designing Planar Mechanisms Using a Bi-Invariant Metric in the Image Space of SO (3)

1994 ◽  
Author(s):  
Pierre Larochelle ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Numerical Results ◽  
Image Space ◽  
Dimensional Synthesis ◽  
Invariant Metric ◽  
Planar Mechanisms ◽  
Position And Orientation ◽  
Position Synthesis

Abstract In this paper we present a technique for using a bi-invariant metric in the image space of spherical displacements for designing planar mechanisms for n (> 5) position rigid body guidance. The goal is to perform the dimensional synthesis of the mechanism such that the distance between the position and orientation of the guided body to each of the n goal positions is minimized. Rather than measure these distances in the plane, we introduce an approximating sphere and identify rotations which are equivalent to the planar displacements to a specified tolerance. We then measure distances between the rigid body and the goal positions using a bi-invariant metric on the image space of SO(3). The optimal linkage is obtained by minimizing this distance over all of the n goal positions. The paper proceeds as follows. First, we approximate planar rigid body displacements with spherical displacements and show that the error induced by such an approximation is of order 1/R2, where R is the radius of the approximating sphere. Second, we use a bi-invariant metric in the image space of spherical displacements to synthesize an optimal spherical 4R mechanism. Finally, we identify the planar 4R mechanism associated with the optimal spherical solution. The result is a planar 4R mechanism that has been optimized for n position rigid body guidance using an approximate bi-invariant metric with an error dependent only upon the radius of the approximating sphere. Numerical results for ten position synthesis of a planar 4R mechanism are presented.

Analysis of the single toggle jaw crusher kinematics

2015 ◽  
Vol 13 (2) ◽  
pp. 213-239 ◽  
Author(s):  
Moses Frank Oduori ◽  
Stephen Mwenje Mutuli ◽  
David Masinde Munyasi
Keyword(s):  
Design Methodology ◽  
Loop Closure ◽  
Content Type ◽  
Drive Mechanism ◽  
Jaw Crusher ◽  
Closure Equation

Purpose – This paper aims to obtain equations that can be used to describe the motion of any given point in the swing jaw of a single toggle jaw crusher. Design/methodology/approach – The swing jaw drive mechanism of a single toggle jaw crusher is modelled as a planar crank and rocker mechanism with the swing jaw as the coupler link. Starting with the vector loop closure equation for the mechanism, equations of the position, velocity and acceleration of any given point in the swing jaw are obtained. Findings – Application of the kinematical equations that were obtained is demonstrated using the dimensional data of a practical single toggle jaw crusher. Thus, a description of the kinematics of any given point in the swing jaw of a single toggle jaw crusher is realized. Originality/value – The model of the single toggle jaw crusher mechanism as a planar crank and rocker mechanism is a realistic one. The equations obtained in this paper should be useful in further studies on the mechanics and design of the single toggle jaw crusher.

A Unified Kinetostatic Analysis Framework for Planar Compliant and Rigid Body Mechanisms

2014 ◽  
Author(s):  
Omer Anil Turkkan ◽  
Hai-Jun Su
Keyword(s):  
Mechanism Design ◽  
Static Analysis ◽  
Compliant Mechanisms ◽  
Daily Life ◽  
Analysis Framework ◽  
Planar Mechanisms ◽  
Simulation Tools ◽  
Compliant Joints ◽  
Adams Software ◽  
Simulation Results

Although many dynamic solvers are available for planar mechanisms, there is no readily accessible static solver that can be used in analysis of planar mechanisms with elastic components which achieve motion utilizing deformation of elastic members. New simulation tools are necessary to better understand the compliant mechanisms and to increase their usage in daily life. This framework was developed to fill this gap in planar mechanism design and analysis. The framework was written in MATLAB and is capable of kinematic and static analysis of planar mechanisms with compliant joints or links. Detailed information on implementation of the code is presented and is followed by the capabilities of the framework. Finally, the simulation results were compared with the Adams software to test the validity of the framework.

Optimum Synthesis of Rigid Mechanisms Using a Dynamic Ant-Search Method With Sensitivity Analysis

2019 ◽  
Author(s):  
Nadim Diab ◽  
Omar Itani ◽  
Ahmad Smaili
Keyword(s):  
Sensitivity Analysis ◽  
Optimization Technique ◽  
Design Parameters ◽  
Neighborhood Search ◽  
Intensity Level ◽  
Path Generation ◽  
Exploration And Exploitation ◽  
Planar Mechanisms ◽  
Optimum Synthesis ◽  
Synthesis Of Mechanisms

Abstract Four-bar linkages are commonly used mechanisms in various mechanical systems and components. Several techniques for optimum synthesis of planar mechanisms have been suggested in literature such as the Genetic, Tabu, Simulated Annealing, Swarm-Based and many other algorithms. This paper covers optimization of four-bar mechanisms with path generation tasks using a Dynamic Ant Search (DAS) algorithm. Unlike the Modified Ant Search (MAS) technique where ants unanimously moved between the exploration and exploitation phases, in the proposed algorithm, each ant is free to travel between the two aforementioned phases independent of other ants and as governed by its own pheromone intensity level. Moreover, sensitivity analysis is conducted on the design parameters to determine their corresponding neighborhood search boundaries and thus improve the search while in the exploitation mode. These implemented changes demonstrated a remarkable impact on the optimum synthesis of mechanisms for path generation tasks. A briefing of the MAS based algorithm is first presented after which the proposed modified optimization technique and its implementation on four-bar mechanisms are furnished. Finally, three case studies are conducted to evaluate the efficiency and robustness of the proposed methodology where the performances of the obtained optimum designs are benchmarked with those previously reported in literature.

A New Approach for Exact/Approximate Point Synthesis of Planar Mechanisms

2005 ◽  
Author(s):  
Ahmad Smaili ◽  
Nadim Diab
Keyword(s):  
Synthesis Method ◽  
Dimensional Synthesis ◽  
Gradient Search ◽  
Planar Mechanisms ◽  
Simple Method ◽  
New Approach ◽  
Optimum Synthesis ◽  
Approximate Synthesis ◽  
Optimum Solution ◽  
Synthesis Approach

The aim of this article is to provide a simple method to solve the mixed exact-approximate dimensional synthesis problem of planar mechanism. The method results in a mechanism that can traverse a closed path with the choice of any number of exact points while the rest are approximate points. The algorithm is based on optimum synthesis rather than on precision position methods. Ant-gradient search is applied on an objective function based on log10 of the error between the desired positions and those generated by the optimum solution. The log10 function discriminates on the side of generating miniscule errors (on the order of 10−14) at the exact points while allowing for higher errors at the approximate positions. The algorithm is tested by way of five examples. One of these examples was used to test exact/approximate synthesis method based on precision point synthesis approach.

Optimum Synthesis of Planar Mechanisms for Path Generation Based on a Combined Discrete Fourier Descriptor

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Wen-Yi Lin
Keyword(s):  
Synthesis Method ◽  
Optimization Method ◽  
Path Generation ◽  
Fourier Descriptor ◽  
Planar Mechanisms ◽  
Two Phase ◽  
Phase Synthesis ◽  
Optimum Synthesis ◽  
Centroid Distance ◽  
The One

A two-phase synthesis method is described, which is capable of solving quite challenging path generation problems. A combined discrete Fourier descriptor (FD) is proposed for shape optimization, and a geometric-based approach is used for the scale–rotation–translation synthesis. The combined discrete FD comprises three shape signatures, i.e., complex coordinates (CCs), centroid distance (CD), and triangular centroid area (TCA), which can capture greater similarity of shape. The genetic algorithm–differential evolution (GA–DE) optimization method is used to solve the optimization problem. The proposed two-phase synthesis method, based on the combined discrete FD, successfully solves the challenging path generation problems with a relatively small number of function evaluations. A more accurate path shape can be obtained using the combined FD than the one-phase synthesis method. The obtained coupler curves approximate the desired paths quite well.

Sign in / Sign up

Export Citation Format

Share Document