A General Method of Determining and Eliminating Branching in Planar Multiloop Mechanisms

1988 ◽  
Vol 110 (4) ◽  
pp. 414-422 ◽  
Author(s):  
S. Krishnamurty ◽  
D. A. Turcic
Keyword(s):  
Optimization Process ◽  
Synthesis Process ◽  
General Mechanism ◽  
Mechanism Synthesis ◽  
Jacobian Matrices ◽  
Multiple Modes ◽  
Comprehensive Method ◽  
Design Requirements ◽  
Process Solutions ◽  
General Method

In most mechanism systems, there exists more than one mode of assembly or configuration, of the mechanism for a given set of input conditions. During the synthesis process, branching occurs when the mechanism changes from one configuration to another. Branching in mechanisms renders them unsuitable because they have to be disassembled and reassembled in order for them to correctly perform the design tasks. In this paper, a comprehensive method for the determination and the elimination of branching problems during synthesis in planar multiloop mechanisms with lower kinematic pairs and with multiple modes of assembly is presented. A general method is developed for the identification of all the branching configurations in a given mechanism. Sub-Jacobian matrices are formed for the sets of constraints associated with each potential branching configuration. The signs of the determinant values of the sub-Jacobian matrices are evaluated. By maintaining the signs of the determinant values to be the same, at all times, during the synthesis process, solutions without the effect of branching are achieved for general planar multiloop mechanisms. Implementation of the method in a general mechanism synthesis package is discussed and applications of the method are illustrated by means of examples. This method of determining branching in mechanisms also is ideally suited for implementation in an optimization process to select the appropriate mechanism configuration that best satisfies the design requirements and for maintaining that configuration throughout the entire cycle of operation.

Automated Cam-Mechanism Synthesis and Analysis

1992 ◽  
Author(s):  
Arnold T. Eventoff
Keyword(s):  
Degrees Of Freedom ◽  
Visual Inspection ◽  
Synthesis Process ◽  
Mechanism Synthesis ◽  
Complete Control ◽  
Cam Mechanism ◽  
Cam Follower ◽  
Machine Elements ◽  
Computer Based ◽  
General Method

Abstract An automated computer-based method for deriving the shape of machine elements such as cams is described for complex mechanisms. Traditional cam synthesis concentrates on follower motion; the method described here enables complete control of the required output motion. Output motion is defined for any constant or variable camshaft velocity. The process is not limited by the degrees of freedom, follower shape, follower suspension, or complexity of the mechanism linking followers to output points. The method includes a velocity analysis to predict cam shape, pressure angle, and relative velocity of the follower with respect to the cam. This analysis allows immediate visual inspection and further dynamic and wear analyses. Cam-follower contact stress is readily calculated for an entire cycle of motion during the synthesis process. An example consisting of a five-bar linkage displaced by three cams is synthesized using the methodology. The general method described facilitates development of mechanisms previously not feasible using conventional methods. Servomotor command displacement profiles required for complex systems can also be derived using this method.

A Maximal Loop Approach to Automatic Sketching of Mechanisms

2007 ◽  
Author(s):  
Songhui Nie ◽  
Hongzhao Liu ◽  
Aihong Qiu
Keyword(s):  
Degrees Of Freedom ◽  
Regular Polygon ◽  
Kinematic Chain ◽  
Synthesis Process ◽  
Systematic Design ◽  
Dimensional Synthesis ◽  
Type Synthesis ◽  
Outer Loop ◽  
Comprehensive Method ◽  
Independent Loops

Sketching of mechanisms identified during the type synthesis process constitutes an important link with the subsequent dimensional synthesis process in the systematic design of mechanisms. Based on the independent loops, a simple and comprehensive method for automatically sketching every type of kinematic chain regardless of the number of links and degrees of freedom is proposed. In the method, a maximal feasible outer-loop is derived by the independent loops addition or subtraction such that all the independent loops become its non-crossing inner loops. During automatic sketching of mechanisms process, the joints of kinematic chain are located on vertices of concentric inscribed regular polygon by outer lane to inner lane in terms of the outer loop and the inner loops. The development and application of this algorithm based on the outer loop and the inner loops relationships are demonstrated with the aid of several mechanism examples.

Kinematic Synthesis and Analysis of the Rack and Pinion Multi-Purpose Mechanism

1992 ◽  
Vol 114 (3) ◽  
pp. 428-432 ◽  
Author(s):  
G. K. Ananthasuresh ◽  
S. N. Kramer
Keyword(s):  
General Procedure ◽  
Full Range ◽  
Mechanism Synthesis ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
Monotonic Functions ◽  
Transmission Angle ◽  
Velocity Condition ◽  
Method Of Solution ◽  
Design Requirements

The general procedure for synthesizing the rack and pinion mechanism up to seven precision conditions is developed. To illustrate the method, the mechanism has been synthesized in closed form for three precision conditions of path generation, two positions of function generation, and a velocity condition at one of the precision points. This mechanism has a number of advantages over conventional four bar mechanisms. First, since the rack is always tangent to the pinion, the transmission angle is always 90 deg minus the pressure angle of the rack. Second, with both translation and rotation of the rock occurring, multiple outputs are available. Other advantages include the generation of monotonic functions for a wide variety of motion and nonmonotonic functions for a full range of motion as well as nonlinear amplified motions. In this work the mechanism is made to satisfy a number of amplified motions. In this work the mechanism is made to satisfy a number of practical design requirements such as completely rotatable input crank and others. By including the velocity specification, the designer has considerably more control of the output motion. The method of solution developed in this work uses the complex number method of mechanism synthesis. A numerical example is included.

A Formal Approach to Specifications in Conceptual Design

1992 ◽  
Vol 114 (4) ◽  
pp. 659-666 ◽  
Author(s):  
A. Kusiak ◽  
E. Szczerbicki
Keyword(s):  
Artificial Intelligence ◽  
Key Words ◽  
Conceptual Design ◽  
Design Process ◽  
Formal Method ◽  
Functional Space ◽  
Synthesis Process ◽  
Formal Approach ◽  
Design Specifications ◽  
Design Requirements

In this paper, a methodology for the specification stage in conceptual design is presented. The specification stage provides requirements and transforms them into functions of the designed object. It occurs at the highest level of abstraction and it must provide enough information for the synthesis process where functions are transformed into design components that are further synthesized into the designed object. The proposed approach includes the following issues: specification of requirements, specification of functions, incorporation of logic into functional and requirement trees, representation of requirements-functions interaction, and optimization in the functional space. The methodology presented is illustrated with examples. Key words: design requirements, design specifications, conceptual design, design process, artificial intelligence, formal method

Determining the Number of Distinct Solutions in Planar Mechanism Design

2019 ◽  
Author(s):  
Lawrence Funke ◽  
Jonathan Raney ◽  
Cyler Caldwell
Keyword(s):  
Mechanism Design ◽  
General Mechanism ◽  
Compact Set ◽  
Self Organizing Map ◽  
Mechanism Synthesis ◽  
Modal Assurance Criterion ◽  
Planar Mechanism ◽  
Starting Point ◽  
Distinct Solution ◽  
Som Neural Network

Abstract This work investigates two novel approaches to sorting solutions to planar-mechanism-synthesis problems. The examples contained herein are specific to planar morphing mechanisms, but the procedure is general and can easily be extended to any planar-mechanism-synthesis problem. The results indicate that the two approaches, namely self-organizing map (SOM) neural network and modal assurance criterion (MAC), can be used to sort a set of solution mechanisms into a reduced set of distinct solution groups. Additionally two sorting approaches (inclusive and exclusive) were investigated. This process can be used to take the initial set of solution mechanisms, often numbering in the hundreds, and pare it down to a significantly smaller set of substantially different designs. For the two case studies presented herein, one set was reduced by a factor of ten and the other by a factor of five. This means that a designer has fewer mechanisms to look through and that the differences in these mechanisms are clearer so that considerations such as size and joint locations may more easily be considered. It was found that the MAC method with inclusive sorting is generally a better starting point because it runs quickly and gives a more compact set of distinct solution mechanisms. The paper concludes with some recommendations for best practices for sorting solutions for a general mechanism-design problem.

Application of the Exact Gradient Approach in Optimal Synthesis of Mechanisms

1993 ◽  
Author(s):  
Jawaharlal Mariappan ◽  
Sundar Krishnamurty
Keyword(s):  
Generalized Solution ◽  
Optimization Method ◽  
Solution Procedure ◽  
Optimal Synthesis ◽  
Synthesis Process ◽  
Mechanism Synthesis ◽  
Approximate Methods ◽  
Synthesis Of Mechanisms ◽  
Gradient Based ◽  
Gradient Approach

Abstract This paper presents the application of the unified exact gradient approach to optimal synthesis of mechanisms. The exact gradient approach is a systematic and efficient solution procedure that is applicable for any type of mechanism synthesis problem. In this approach, the exact gradients necessary for optimization are developed using a generalized solution procedure based on matrix methods. Availability of exact gradients in this approach enables the utilization of any gradient-based optimization method in mechanism synthesis process. As a result, this approach will be computationally most efficient, since it will not require direct search methods, or, finite difference approximate methods to find optimal solutions. These salient features of this approach are demonstrated with the aid of several mechanism problems and the results discussed.

Scalable Set-Based Design Optimization and Remanufacturing for Meeting Changing Requirements

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Khalil Al Handawi ◽  
Petter Andersson ◽  
Massimo Panarotto ◽  
Ola Isaksson ◽  
Michael Kokkolaras
Keyword(s):  
Design Optimization ◽  
Working Condition ◽  
Optimal Designs ◽  
Direct Energy Deposition ◽  
Direct Energy ◽  
Design Requirements ◽  
Transition Rules ◽  
Set Based Design ◽  
Manufacturing Technologies ◽  
Process Solutions

Abstract Design requirements are often uncertain in the early stages of product development. Set-based design is a paradigm for exploring, and keeping under consideration, several alternatives so that commitment to a single design can be delayed until requirements are settled. In addition, requirements may change over the lifetime of a component or a system. Novel manufacturing technologies may enable designs to be remanufactured to meet changed requirements. By considering this capability during the set-based design optimization process, solutions can be scaled to meet evolving requirements and customer specifications even after commitment. Such an ability can also support a circular economy paradigm based on the return of used or discarded components and systems to working condition. We propose a set-based design methodology to obtain scalable optimal solutions that can satisfy changing requirements through remanufacturing. We first use design optimization and surrogate modeling to obtain parametric optimal designs. This set of parametric optimal designs is then reduced to scalable optimal designs by observing a set of transition rules for the manufacturing process used (additive or subtractive). The methodology is demonstrated by means of a structural aeroengine component that is remanufactured by direct energy deposition of a stiffener to meet higher loading requirements.

Compliant Mechanism Synthesis Using Degree of Genus and Variable Width Curves

2014 ◽  
Author(s):  
Hong Zhou ◽  
Azher Hussain Naser Mohammed
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Structural Complexity ◽  
Joint Effect ◽  
Synthesis Process ◽  
Mechanism Synthesis ◽  
Shape Morphing ◽  
Optimizing Control ◽  
Material Layout ◽  
Shape And Size

Compliant mechanisms (CMs) utilize elastic deformations for mechanism functions. Their merits primarily come from jointless structures. The structure of a fully CM is a piece of elastic material and is defined by its topology, shape and size. Topology is the overarching material layout of a CM while shape and size are on its structural details, but topology is entangled with shape and size in the synthesis process of a CM because its elastic deformation is from the joint effect of topology, shape and size. Degree of freedom (DOF) and number of links used in rigid mechanism synthesis are not effective to guide the synthesis of CMs since any point of a fully CM can deform and its whole structure forms a single piece. Without effective synthesis guidance, the structural complexity of a synthesized CM can be undesirably high. In this paper, degree of genus (DOG) is introduced for topology guidance of CM synthesis. DOG of a CM is the number of holes and is actively controlled during its synthesis process. With DOG guidance, a synthesized CM will not have overcomplicated topology. Variable width curves (VWCs) are introduced in this paper for shape and size description. Any connection in a CM is defined as a VWC and the entire CM is modeled as a network of VWCs. With VWC description, a synthesized CM will not have unsmooth connection. Under DOG and VWC strategies, CM synthesis is systematized as optimizing control parameters of networks of VWCs. The proposed CM synthesis using DOG and VWC strategies is demonstrated by synthesizing shape morphing compliant mechanisms.

Synthesizing Functional Mechanisms From a Link Soup

2015 ◽  
Author(s):  
Pouya Tavousi ◽  
Kazem Kazerounian ◽  
Horea Ilies
Keyword(s):  
Divide And Conquer ◽  
Synthesis Process ◽  
Synthesis Methods ◽  
Mechanism Synthesis ◽  
New Approach ◽  
Positional Analysis ◽  
Synthesis Procedure ◽  
Functional Mechanisms ◽  
Systematic Synthesis ◽  
Classical Mechanism

The synthesis of functional molecular linkages is constrained by difficulties in fabricating nano-links of arbitrary shapes and sizes. However, the classical mechanism synthesis methods, which assume the ability to manufacture any designed links, do not provide a systematic synthesis process for molecular linkages. We propose a new approach to build functional mechanisms with prescribed mobility by only using elements from a predefined link soup. First, we enumerate an exhaustive set of topologies, while employing divide-and-conquer algorithms to control the generation and elimination of redundant topologies. Then, we construct the linkage arrangements for each valid topology. Finally, we output a set of feasible geometries through a positional analysis step that minimizes the error associated with closure of the loops in the linkage while avoiding geometric interference. The proposed systematic approach outputs the ATLAS of candidate mechanisms, which can be further processed for downstream applications. The resulting synthesis procedure is the first of its kind that is capable of synthesizing functional linkages with prescribed mobility constructed from a soup of primitive entities.

Kinematic Synthesis and Analysis of the Rack-and-Gear Mechanism for Four-Point Path Generation With Prescribed Input Timing

1986 ◽  
Vol 108 (1) ◽  
pp. 10-14 ◽  
Author(s):  
M. Claudio ◽  
S. Kramer
Keyword(s):  
Range Of Motion ◽  
Full Range ◽  
Mechanism Synthesis ◽  
Monotonic Functions ◽  
Transmission Angle ◽  
Wide Range ◽  
Method Of Solution ◽  
Gear Mechanism ◽  
Design Requirements ◽  
Four Bar Linkage

The rack and gear mechanism is synthesized for generating four prescribed path points with input coordination. This mechanism has a number of advantages over the well-known four-bar linkage. First, the transmission angle is always at its optimum value of 90 deg since the rack is always tangent to the gear. Second, with both translation and rotation of the rack occurring, multiple outputs are available. Other advantages include the generation of monotonic functions for a wide range of motion and nonmonotonic functions for the full range of motion as well as nonlinear amplified motions. In this work, the mechanism is made to satisfy a number of practical design requirements such as having a completely rotatable input crank, elimination of the branching defect and others. The method of solution developed in this work employs the Burmester Four-Precision-Point Algorithm with additional relations utilizing the Complex Number Method of Mechanism Synthesis. The solution is programmed on the DEC/PDP 11/70 and is available to interested readers.

Sign in / Sign up

Export Citation Format

Share Document