Coordination of Coupler-Point Positions and Crank Rotations in Connection With Roberts’ Configuration

Abstract

In this paper a geometrical solution is given to the problem of finding four-bar linkages having 5 given coupler-point positions coordinated with 4 given crank angles. It may also be possible to find solutions if one given coupler-point position together with a given crank angle, corresponding to this position, is replaced by two given link lengths. It has been found thus far that four-bar linkages, satisfying the stated conditions, are easy to obtain if the problem is related to Roberts’ law. To get a view of the possibilities, the degenerations of cognate circle-point curves and cognate center-point curves, linked to each other by the configuration (CR ) of Roberts, are investigated. As an example at the end of the paper a straight-line mechanism has been designed so that the coupler point moves along this line with an approximately uniform velocity.