A Task-Driven Approach to Optimal Synthesis of Planar Four-Bar Linkages for Extended Burmester ProblemSource: Journal of Mechanisms and Robotics:;2017:;volume( 009 ):;issue: 006::page 61005DOI: 10.1115/1.4037801Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: The classic Burmester problem is concerned with computing dimensions of planar four-bar linkages consisting of all revolute joints for five-pose problems. We define extended Burmester problem as the one where all types of planar four-bars consisting of dyads of type RR, PR, RP, or PP (R: revolute, P: prismatic) and their dimensions need to be computed for n-geometric constraints, where a geometric constraint is an algebraically expressed constraint on the pose, pivots, or something equivalent. In addition, we extend it to linear, nonlinear, exact, and approximate constraints. This extension also includes the problems when there is no solution to the classic Burmester problem, but designers would still like to design a four-bar that may come closest to capturing their intent. Machine designers often grapple with such problems while designing linkage systems where the constraints are of different varieties and usually imprecise. In this paper, we present (1) a unified approach for solving the extended Burmester problem by showing that all linear and nonlinear constraints can be handled in a unified way without resorting to special cases, (2) in the event of no or unsatisfactory solutions to the synthesis problem, certain constraints can be relaxed, and (3) such constraints can be approximately satisfied by minimizing the algebraic fitting error using Lagrange multiplier method. We present a new algorithm, which solves new problems including optimal approximate synthesis of Burmester problem with no exact solutions.
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contributor author | Deshpande | |
contributor author | Shrinath;Purwar | |
contributor author | Anurag | |
date accessioned | 2017-12-30T11:43:24Z | |
date available | 2017-12-30T11:43:24Z | |
date copyright | 9/18/2017 12:00:00 AM | |
date issued | 2017 | |
identifier issn | 1942-4302 | |
identifier other | jmr_009_06_061005.pdf | |
identifier uri | http://138.201.223.254:8080/yetl1/handle/yetl/4242799 | |
description abstract | The classic Burmester problem is concerned with computing dimensions of planar four-bar linkages consisting of all revolute joints for five-pose problems. We define extended Burmester problem as the one where all types of planar four-bars consisting of dyads of type RR, PR, RP, or PP (R: revolute, P: prismatic) and their dimensions need to be computed for n-geometric constraints, where a geometric constraint is an algebraically expressed constraint on the pose, pivots, or something equivalent. In addition, we extend it to linear, nonlinear, exact, and approximate constraints. This extension also includes the problems when there is no solution to the classic Burmester problem, but designers would still like to design a four-bar that may come closest to capturing their intent. Machine designers often grapple with such problems while designing linkage systems where the constraints are of different varieties and usually imprecise. In this paper, we present (1) a unified approach for solving the extended Burmester problem by showing that all linear and nonlinear constraints can be handled in a unified way without resorting to special cases, (2) in the event of no or unsatisfactory solutions to the synthesis problem, certain constraints can be relaxed, and (3) such constraints can be approximately satisfied by minimizing the algebraic fitting error using Lagrange multiplier method. We present a new algorithm, which solves new problems including optimal approximate synthesis of Burmester problem with no exact solutions. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | A Task-Driven Approach to Optimal Synthesis of Planar Four-Bar Linkages for Extended Burmester Problem | |
type | Journal Paper | |
journal volume | 9 | |
journal issue | 6 | |
journal title | Journal of Mechanisms and Robotics | |
identifier doi | 10.1115/1.4037801 | |
journal fristpage | 61005 | |
journal lastpage | 061005-9 | |
tree | Journal of Mechanisms and Robotics:;2017:;volume( 009 ):;issue: 006 | |
contenttype | Fulltext |