Configuration and Dimensional Synthesis in Mechanical Design: an Application for Planar Mechanisms

CIRP Annals ◽  
1994 ◽  
Vol 43 (1) ◽  
pp. 145-148 ◽  
Author(s):  
Petri Makkonen ◽  
Jan-Gunnar Persson
Keyword(s):  
Mechanical Design ◽  
Dimensional Synthesis ◽  
Planar Mechanisms

On nonassembly in the optimal dimensional synthesis of planar mechanisms

2001 ◽  
Vol 21 (5) ◽  
pp. 345-354 ◽  
Author(s):  
R.J. Minnaar ◽  
D.A. Tortorelli ◽  
J.A. Snyman
Keyword(s):  
Dimensional Synthesis ◽  
Planar Mechanisms

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.

Optimum dimensional synthesis of planar mechanisms with geometric constraints

Meccanica ◽  
2020 ◽  
Vol 55 (11) ◽  
pp. 2135-2158
Author(s):  
V. García-Marina ◽  
I. Fernández de Bustos ◽  
G. Urkullu ◽  
R. Ansola
Keyword(s):  
Geometric Constraints ◽  
Dimensional Synthesis ◽  
Planar Mechanisms

scholarly journals Two-Swim Operators in the Modified Bacterial Foraging Algorithm for the Optimal Synthesis of Four-Bar Mechanisms

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Betania Hernández-Ocaña ◽  
Ma. Del Pilar Pozos-Parra ◽  
Efrén Mezura-Montes ◽  
Edgar Alfredo Portilla-Flores ◽  
Eduardo Vega-Alvarado ◽  
...  
Keyword(s):  
Differential Evolution ◽  
Mechanical Design ◽  
Differential Evolution Algorithm ◽  
Fine Tuning ◽  
Local Optimum ◽  
Bacterial Foraging Optimization ◽  
Planar Mechanisms ◽  
Bacterial Foraging ◽  
Evolution Algorithm ◽  
Parameter Values

This paper presents two-swim operators to be added to the chemotaxis process of the modified bacterial foraging optimization algorithm to solve three instances of the synthesis of four-bar planar mechanisms. One swim favors exploration while the second one promotes fine movements in the neighborhood of each bacterium. The combined effect of the new operators looks to increase the production of better solutions during the search. As a consequence, the ability of the algorithm to escape from local optimum solutions is enhanced. The algorithm is tested through four experiments and its results are compared against two BFOA-based algorithms and also against a differential evolution algorithm designed for mechanical design problems. The overall results indicate that the proposed algorithm outperforms other BFOA-based approaches and finds highly competitive mechanisms, with a single set of parameter values and with less evaluations in the first synthesis problem, with respect to those mechanisms obtained by the differential evolution algorithm, which needed a parameter fine-tuning process for each optimization problem.

Mechanical Design and Simulation of a Finger Rehabilitation Robot

2013 ◽  
Vol 365-366 ◽  
pp. 805-811
Author(s):  
Jing Jing Yu ◽  
Jin Wu Qian ◽  
Lin Yong Shen ◽  
Ya Nan Zhang
Keyword(s):  
Mechanical Design ◽  
Simulation Method ◽  
Continuous Passive Motion ◽  
Rehabilitation Robot ◽  
Movement Trajectory ◽  
Dimensional Synthesis ◽  
Rehabilitation Training ◽  
Normal Human ◽  
Atlas Method ◽  
Human Finger

Continuous Passive Motion (CPM) has been confirmed as an effective clinical therapy for finger neurological rehabilitation. In this study a finger rehabilitation training robot is designed based on CPM rehabilitation theory. This paper presents the design and simulation of the finger rehabilitation robot. Based on the finger structure and movement trajectory analysis, OPTOTRAK CERTUS motion capture system is used to acquire trajectory parameters of normal human finger movement. Atlas method is employed to accomplish mechanism dimensional synthesis of the finger rehabilitation training robot. The feasibility of the mechanism is verified using a modeling and simulation method with SIMULINK software.

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.

Synthesis of Planar Mechanisms for Pick and Place Tasks With Guiding Locations

2013 ◽  
Author(s):  
Pierre Larochelle
Keyword(s):  
Algebraic Geometry ◽  
Constraint Equation ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Open Chain ◽  
Synthesis Algorithm ◽  
Kinematic Chains ◽  
Synthesis Technique ◽  
Kinematic Inversion

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for planar RR kinematic chains is presented. The methodology uses an analytic representation of the planar RR dyads rigid body constraint equation in combination with an algebraic geometry formulation of the exact synthesis for three prescribed locations to yield designs that exactly reach the prescribed pick & place locations while approximating an arbitrary number of guiding locations. The result is a dimensional synthesis technique for mixed exact and approximate motion generation for planar RR dyads. A solution dyad may be directly implemented as a 2R open chain or two solution dyads may be combined to form a planar 4R closed chain; also known as a planar four-bar mechanism. The synthesis algorithm utilizes only algebraic geometry and does not require the use of a numerical optimization algorithm or a metric on planar displacements. Two implementations of the synthesis algorithm are presented; computational and graphical construction. Moreover, the kinematic inversion of the algorithm is also included. An example that demonstrates the synthesis technique is included.

Formulation of Dimensional Synthesis Procedures for Complex Planar Mechanisms

1987 ◽  
Vol 109 (3) ◽  
pp. 322-328 ◽  
Author(s):  
D. G. Olson ◽  
A. G. Erdman ◽  
D. R. Riley
Keyword(s):  
Graph Theory ◽  
Directed Graph ◽  
Dimensional Synthesis ◽  
Planar Mechanisms

This paper presents an overview of a component-based approach for the dimensional synthesis of planar mechanisms. The components on which the approach is based are called triads, dyads, and free vectors, and can be synthesized for up to five precision positions. A straight-forward method for formulating dimensional synthesis procedures for arbitrarily complex planar mechanisms is developed, and demonstrated by an example using inspection. The method utilizes the concept of the directed graph, which is an enhancement of the usual graph theory representation of mechanisms. Because the method is based on graph theory, it is believed that it could be easily automated.

Curve Cognate Constructions Made Easy

2020 ◽  
Author(s):  
Samantha N. Sherman ◽  
Jonathan D. Hauenstein ◽  
Charles W. Wampler
Keyword(s):  
Mechanical Design ◽  
Planar Mechanisms ◽  
Simple Method ◽  
Planar Curve ◽  
Geometric Drawing

Abstract Cognate linkages are mechanisms that share the same motion, a property that can be useful in mechanical design. This paper treats planar curve cognates, that is, planar mechanisms whose tracing point draws the same curve. While Roberts cognates for planar four-bars are relatively simple to understand from a geometric drawing, the same cannot be said for planar six-bar cognates, especially the intricate diagrams Dijksman presented in cataloging all the known six-bar curve cognates. The purpose of this article is to show how the six-bar cognates can be easily understood using kinematic equations written using complex vectors, giving a simple method for generating these cognates as alternatives in a mechanical design. The simplicity of the approach enables the derivation of cognates for eight-bars and possibly beyond.

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