Dynamics of a Flexible Rod in a Quick Return Mechanism

The equations of motion in matrix form are formulated for a flexible rod in a quick return mechanism using Hamilton’s principle and the assumed mode method. The rod is considered as an Euler beam. The crank is assumed to be rigid and rotating at a constant angular speed. The translating-rotating joint connecting the crank to the flexible rod is assumed to be a frictionless moving point support for the flexible rod. This support is regarded as a very stiff spring acting on the rotating flexible rod. Results of numerical simulations are presented for various prescribed crank positions, crank lengths, and crank speeds.