Four-bar motion generation with elasticity constraints and optimization

In conventional planar four-bar motion generation, all mechanism links are assumed rigid or non-deforming. Although the assumption of link rigidity in kinematic synthesis may be generally appropriate and often practiced, a statically loaded planar four-bar mechanism will undergo a degree of elastic deflection, particularly the crank and follower links. In this work, a non-linear optimization problem is formulated for planar four-bar motion generation that considers an applied coupler force and corresponding crank static torque, crank transverse deflection, and follower buckling. The output from the non-linear optimization problem - mechanism fixed and moving pivot loci - are input for a search algorithm that down selects a mechanism solution that satisfies transmission angle conditions, Grashof conditions, and a mechanism compactness condition. The final output of the presented method is planar four-bar motion generator that approximates prescribed coupler poses with satisfactory crank deflection and without follower buckling and also satisfies conditions for link rotatability, transmission angle and compactness.