Optimal Synthesis of Adjustable Four-Link Planar and Spherical Crank-Rocker Type Mechanisms for Approximate Multi-Path Generation

Abstract

The well known synthesis problem of obtaining dimensions of a four-link mechanism such that a point on the coupler link traces a desired path has been extensively studied. There are two types of path generation–path specified by a finite number of precision points where the prescribed points must be exactly traced, and continuous path generation where the path is approximately traced by the coupler point. In various application, more than one or multiple paths are required to be traced by the coupler point and in such cases, adjustable four-link mechanisms where one of the dimension or parameters of the mechanism can be changed is a possible solution. This thesis deals with the synthesis of planar and spherical adjustable four-link crank-rocker type mechanisms for multiple continuous path generation. Approximate multiple path generation is typically solved as an optimization problem where the dimensions and parameters of the four-link mechanism are obtained such that the objective functions, typically in terms of an error between the desired and obtained path, is minimized. In this thesis, we present a two-stage optimization to obtain four-link mechanism dimensions such that the adjustable four-link mechanism can approximately trace multiple desired paths. In the first stage, the parameters in the driving side of the four-link mechanism is obtained and in the second stage, the parameters of the driven side are obtained. In case of adjustable planar four-link mechanism, a novel optimization objective function based on circle-fitting is used and for spherical adjustable mechanisms a novel plane-fitting based objective function is used. The use of these objective functions results in a lesser number of variables to be searched and thus the method presented in this work is more efficient than existing optimization based algorithms available in literature. Several examples are presented for synthesis of adjustable planar and spherical four-link mechanism for tracing multiple paths. In particular, a spherical mechanism which can generate an oval and an‘ 8’shaped path by one single adjustment is synthesized. This mechanism has been made using 3D printing and it is shown that the mechanism indeed traces the desired oval and ‘8’ shaped paths. This mechanism is being planned for use in a flapping wing micro air vehicle where the oval shaped path is known to make the vehicle to move forward while the ‘8’ shaped path results in a hovering motion.