Kinematic analysis and synthesis of an adjustable six-bar linkage

This paper investigates the kinematics of an adjustable six-bar linkage where the rotation of the input crank is converted into the oscillation of the output link. This single-degree-of freedom planar linkage will be used as a variable-speed transmission mechanism where the input crank rotates at a constant speed and the output link consists of an overrunning clutch mounted on the output shaft. The analysis uses a novel technique in which kinematic coefficients are obtained with respect to an independent variable. Then kinematic inversion is used to express the kinematic coefficients with respect to the input variable of the linkage. This technique decouples the position equations and provides additional insight into the geometry of the adjustable linkage. The angle through which the output link oscillates, for each revolution of the input crank, can be adjusted by a control arm. This arm allows a fixed pivot to be temporarily released and moved along a circular arc about a permanent ground pivot. The paper shows how to determine the angle of oscillation of the output link for a specified position of the fixed pivot and investigates the extreme positions of the output link corresponding to the extreme positions of a point on the coupler link. For this reason, the paper includes a study of the geometry of the path traced by a coupler point and determines the location of the ground pivot of the control arm which will cause the output link to remain stationary during a complete rotation of the input crank. Finally, the paper shows how the kinematic analysis results can be used, in a straightforward manner, to redesign the control arm.