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Title: Finding straight line generators through the approximate synthesis of symmetric four-bar coupler curves
The approximate path synthesis of four-bar linkages with symmetric coupler curves is presented. This includes the formulation of a polynomial optimization problem, a characterization of the maximum number of critical points, a complete numerical solution by homotopy continuation, and application to the design of straight line generators. Our approach specifies a desired curve and finds several optimal four-bar linkages with a coupler trace that approximates it. The objective posed simultaneously enforces kinematic accuracy, loop closure, and leads to polynomial first order necessary conditions with a structure that remains the same for any desired trace leading to a generalized result. Ground pivot locations are set as chosen parameters, and it is shown that the objective has a maximum of 73 critical points. The theoretical work is applied to the design of straight line paths. Parameter homotopy runs are executed for 1440 different choices of ground pivots for a thorough exploration. These computations found the expected linkages, namely, Watt, Evans, Roberts, Chebyshev, and other previously unreported linkages which are organized into a 2D atlas using the UMAP algorithm.  more » « less
Award ID(s):
2041789
PAR ID:
10483401
Author(s) / Creator(s):
; ;
Publisher / Repository:
Elsevier
Date Published:
Journal Name:
Mechanism and Machine Theory
Volume:
188
Issue:
C
ISSN:
0094-114X
Page Range / eLocation ID:
105310
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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