Angular Velocity and Acceleration Extrema: Implications for Force Analysis in Planar 4R Mechanisms

The algebraic input-output (IO) equation expresses one joint angle tangent half-angle parameter in terms of another as an implicit function scaled by the link lengths. There are six distinct IO equations for any given four-bar linkage. Using one of them, we propose algorithms leading to the mechanism configurations corresponding to extreme angular velocities and accelerations which, in turn, directly implies the values for the magnitudes of the extreme shaking forces and moments in the non-moving ground-fixed link. A detailed example is presented where the mechanism configurations for extreme shaking force and moment magnitudes are compared to the configurations corresponding to extreme values of angular velocity and acceleration.