A Task-Driven Approach to Unified Synthesis of Planar Four-Bar Linkages Using Algebraic Fitting of a Pencil of G-Manifolds

Author:

Ge Q. J.1,Purwar Anurag2,Zhao Ping1,Deshpande Shrinath1

Affiliation:

1. Computational Design Kinematics Laboratory, Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794-2300

2. Computational Design Kinematics Laboratory, Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794-2300 e-mail:

Abstract

This paper studies the problem of planar four-bar motion generation from the viewpoint of extraction of geometric constraints from a given set of planar displacements. Using the image space of planar displacements, we obtain a class of quadrics, called generalized- or G-manifolds, with eight linear and homogeneous coefficients as a unified representation for constraint manifolds of all four types of planar dyads, RR, PR, and PR, and PP. Given a set of image points that represent planar displacements, the problem of synthesizing a planar four-bar linkage is reduced to finding a pencil of G-manifolds that best fit the image points in the least squares sense. This least squares problem is solved using singular value decomposition (SVD). The linear coefficients associated with the smallest singular values are used to define a pencil of quadrics. Additional constraints on the linear coefficients are then imposed to obtain a planar four-bar linkage that best guides the coupler through the given displacements. The result is an efficient and linear algorithm that naturally extracts the geometric constraints of a motion and leads directly to the type and dimensions of a mechanism for motion generation.

Funder

"Division of Civil, Mechanical and Manufacturing Innovation"

Publisher

ASME International

Subject

Industrial and Manufacturing Engineering,Computer Graphics and Computer-Aided Design,Computer Science Applications,Software

Reference38 articles.

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