Title: Multi-modal continuous approximate synthesis of planar four-bar function generators

Authors: Zachary A. Copeland; M. John D. Hayes

Addresses: Department of Mechanical and Aerospace Engineering, Carleton University, Ottawa, ON, Canada ' Department of Mechanical and Aerospace Engineering, Carleton University, Ottawa, ON, Canada

Abstract: This paper introduces a novel multi-modal continuous approximate synthesis algorithm for planar four-bar function generators. The synthesis equation is the sum of the squared input-output (IO) equations integrated over the different prescribed input variable parameter ranges. Every planar four-bar mechanism explicitly generates six distinct functions each uniquely determined by one set of link parameter constants. We will examine the simultaneous continuous approximate synthesis of two related perturbed, but not competing, functions between different pairs of joint variables that, in general, require different link constants to generate. The optimisation involves identifying the best compromise link lengths. Planar 4R and RRRP examples are presented where two different functions, one primary and the other perturbed secondary, are generated over continuous ranges between the specified input variable parameter and the associated output variable parameter. The area between the prescribed and generated continuous IO curves is both a measure of the design and structural errors.

Keywords: planar four-bar mechanisms; algebraic input-output; IO equations; continuous approximate synthesis; multi-modal continuous approximate synthesis.

DOI: 10.1504/IJMRS.2023.129451

International Journal of Mechanisms and Robotic Systems, 2023 Vol.5 No.3, pp.246 - 269

Received: 15 Jun 2022
Accepted: 29 Sep 2022
Published online: 09 Mar 2023 *

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