Kinematic and Dynamic Analyses of a Crank-Shaper Quick Return Mechanism

Abstract

This paper presents the kinematic and dynamic analyses of a quick return mechanism. The links are assumed to be rigid. The crank is driven by an external torque. Geometric constraints between different components in the system are formulated by using a set of nonlinear algebraic constraint equation. The Hamilton’s principle and Lagrange multiplier method are applied to formulate the dynamic equation of the mechanism. Reducing the differential-algebraic equations and employing the Runge-Kutta numerical method, the exact and approximate motions of the slider are obtained and compared. The one-to-one relationships of slider position, angles of links with respect to crank angle hold for the system with one degree of freedom. The numerical results of the case with constant input angular velocity and that of constant input forque are obtained and discussed.